Selection model is an important part of the modeling analysis, economics in looking for the true model, in the design of multiple models assume that are separate from the actual setting, then according to this problem is the separation of absolute choice model, it has the identity and the separation of assumption in mathematical statistics, thus can take advantage of each other during solve processing model is analyzed. The available methods are mainly divided into two types: on the one hand, it refers to the improved LR test; on the other hand, it refers to the embedding coefficient λ to transform the problem into a conventional parameter for testing. This paper mainly discusses the connection and characteristics of the two in the application period, and shows the special function of alternative hypothesis H1 in these test methods, as well as its specific relationship with prior information. At this point, we should clearly recognize the relationship between mathematical tools, economic theoretical knowledge, statistics and other contents as shown in the figure 1 below^{[1]:}

In the study, Pesaran et al. conducted Cox tests on the linear econometric model and could propose two separate PDF forms. The actual single econometric model formula is shown as follows:

In the above formula, Y represents the endogenous variable and X represents the exogenous variable, which does not meet the following conditions:

Thus

Assume that

The n the results can be verified. Under the condition of H0, the following formula can be obtained:

In the formula, _{r}_{ij}, which meets the following conditions:

Considering T1 as a statistic, a COX test can be constructed to select the model. As another way to solve the problem, embedded verification has two choices in practical application. When the econometric model is in PDF form, the model formula can be obtained as follows:

The actual assumptions are:

At this time, the result verification found that under the condition of H0, the formula of the actual statistic was:

There is a gradual normal distribution trend of zero mean during the overall operation, and the specific results are shown as follows:

In the above formula, E1 represents the expectation of _{i}_{i}_{i}_{i}_{i}_{i}

When the econometric model uses the equation model for calculation and analysis, the following formula can be obtained:

Based on this, the embedded analysis can obtain the following model:

The actual assumptions are:

As the above model formula is nonlinear under the condition of _{v}θ_{y}

In the above formula, the condition of
_{i}^{T}

In order to construct the test using

Therefore, in the above formula, except for the substitution of

Under weak conditions,

And meet the following conditions:

It follows that the actual asymptotic is equal to the square of the standardized Score test statistic. By using
^{[2,3]:}

According to the model obtained from the above research, the relationship of embedded test is analyzed. The actual equation model is as follows:

And can be incorporated into the following models:

Among them,

The actual regression equation model is as follows:

It can be seen from this that the above formula can be transformed into the econometric model equation proposed in previous studies under the condition that _{i}_{j}_{0} is met. In other words, in the Gaussian model, if the condition _{i}_{j}_{i}_{j}

Common mathematical statistics problems require that both the original hypothesis (H0) and the alternative hypothesis (H1) in hypothesis testing have all the possibilities of the problem. Therefore, if the original hypothesis is rejected, the alternative hypothesis must be accepted, and vice versa. In other words, the alternative hypothesis has a certain degree of substitution, after the original hypothesis has been rejected, the alternative hypothesis will take over and become true.

It should be noted that when testing the selection model based on the hypothesis, the substitutability of the alternative hypothesis will be affected, because there are many models that can be selected, so the alternative hypothesis will have a new change. According to the structure analysis of the single econometric model constructed in this study, under the condition that it belongs to the Kuopmen-Darmois family function, the test statistics will be presented intuitively, and the specific form is as follows:^{[4,5]}

From the perspective of practice, there are two main functions of alternative hypothesis during model selection: on the one hand, if the prior information makes people not fully believe that it is true, the alternative hypothesis only plays an indicative role; If the prior information proves that it is likely to be true, the alternative hypothesis not only has an indicative function, but also considers the possibility of using FJ to replace FI after the original hypothesis is rejected.

Accurate understanding of assumptions plays a positive role in the empirical analysis of economic absolute income hypothesis. As a social discipline, economics needs to effectively integrate statistical data, mathematical statistics, qualitative and quantitative analysis and other contents in practical research. Among them, regression analysis method, as the main form of econometric analysis, will put forward assumptions about unknown functions and various forms of statistical distribution. If you do not want to carry out hypothetical analysis, you can directly use semi-parametric and non-parametric methods to conduct research. The effective integration of regression analysis method and factor analysis can be called path analysis. Econometric model includes discrete selection model, quantile regression, multiple linear regression, linear regression model and so on. After the EM algorithm was put forward in the 1970s, the mathematical statistics method was put forward by researchers in the integration innovation and development of computer technology. Although variance analysis and regression analysis in the traditional sense are still widely used, the practical application effect is far inferior to that of mathematical statistics.^{[6,7]}

The absolute income hypothesis proposed by Keynes effectively integrates consumption expenditure and income level, and puts forward that the absolute income level affects the actual consumption level in practice verification. In essence, absolute income hypothesis mainly involves the following contents: First, actual consumption expenditure is a stable function with real income as the core; Second, the income level represents the absolute actual income level at the present stage; Third, the marginal propensity to consume is positive, but lower than 1. Fourth, marginal consumption will change with the change of real income level, and the two are inversely proportional; Fifth, marginal consumption shows a propensity level lower than average consumption. To transform real problems into economic models is to study the mathematical and physical processes of the economic absolute income hypothesis by combining mathematical statistics, and the detailed explanation is as follows:

This paper mainly analyzes the relationship between residents' income and consumption level in the early 21st century, and constructs the unitary regression model as follows:

In the above formula, GDPP refers to China's per capita GDP and CONSP refers to China's residents' consumption level, which is a constant term. According to the theoretical analysis of absolute income hypothesis, this value is greater than 0 and less than 1.

In order to further verify the validity of this hypothesis, relevant data information should be collected first and data pretreatment should be done well. Secondly, the scatter diagram should be used to compare and analyze the change relationship of the two indicators, Combined with the above analysis, it is found that there is a linear relationship between the income level and consumption of urban residents in China. Therefore, measurement software can be selected to represent the above analysis model in practical analysis and calculation. At the same time, regression analysis should be carried out in combination with the software. The specific results are shown in the following table. The actual regression equation is:

Data results obtained by the least square method

Source | SS | DF | MS | Number Of Obs=23 |
||

Model | 3164162.45 | 1 | 3164162.45 | |||

Residual | 23237.0765 | 21 | 1106.52745 | |||

Total | 3187399.52 | 22 | 144881.796 | |||

Consp | Coef | Std Err | T | P>|t| | [95%Conf Interval] | |

Gdpp | .3861803 | .0072217 | 53.47 | 0.000 | .3711619 | .4011987 |

_Cons | 201.1189 | 14.88402 | 13.51 | 0.000 | 170.1659 | 232.0719 |

Durbin-Watson D-Statistic(2,23)=.5506366 |

Combined with the above results, it is found that the actual marginal propensity to consume is 0.3862, and the value is 53.47. In the significance test analysis, it is found that in the early 21st century, for every yuan of income increase of urban residents in China, there will be 0.39 yuan for consumption, which is in line with the absolute income hypothesis. As the DW value reaches 0.55, there may be error series, which requires researchers to conduct in-depth exploration of relevant values and models.

Combined with the analysis of the economic absolute income hypothesis studied above, it can be seen that the income proposed by Keynes is the absolute real income at this stage, and the actual calculation formula is as follows:

In the above formula, C refers to consumption and β refers to marginal propensity to consume. The corresponding calculation formula is as follows:

In the above formula, Y represents income, and α refers to the indispensable part of spontaneous consumption. In other words, if income is zero, basic living consumption must be achieved, and the product between the two refers to the consumption generated by income. It can be seen that the calculation formula of absolute real income has certain economic meaning.

This paper makes an empirical analysis of absolute income hypothesis from the perspective of mathematical statistics, and specifically studies the income level and consumption expenditure of residents in China, the United States, The United Kingdom and India. The data obtained are from statistical databases of various countries and international statistical yearbooks. Based on the original data collected, to determine the level of national income per capita, a calculation based on the GDP deflator is required. This paper studies the year 2010 as the benchmark and makes a general statistical analysis on the basis of grasping relevant exchange rates, thus obtaining the per capita consumption expenditure level of the four countries. Combined with the above analysis, it can be found that the gap between China and India is not large, while the US and UK are also very close, so it can be seen that China and India are more backward than the UK and US.

According to the analysis of the per capita consumption level of the above research, after obtaining relevant data, the panel data analysis method is used to construct the research model as shown below, and the software Eviews5.1 is used for simulation analysis, and the results can be obtained as shown in the following table 2[8,9]:

Model research results

Public intercept | The coefficient of | Intercept | ||||||
---|---|---|---|---|---|---|---|---|

The United States | China | India | Britain | The United States | China | India | Britain | |

−788.5 | 0.746268 | 0.338316 | 0.465463 | 0.723108 | −1149.727 | 904.4732 | 869.8939 | −624.6401 |

−0.94514 | 9.903561 | 0.432146 | 0.205649 | 9.877384 | ||||

0.3486 | 0 | 0.6673 | 0.8378 | 0 |

In the table analysis above, the penultimate row refers to the value of t, and the last row refers to the value of P. Through comparative analysis, it is found that in terms of independent consumption level and marginal consumption tendency, the gap between China and India and the UK and the US is very significant, while the overall level between the UK and the US is more similar, which further verifies the colorful expected results proposed in the analysis of this paper. The actual indicators are as follows:

Index analysis

R-Squared | Adjusted R-Squared | S.E.Of Regression | Sum-Squared-Resid | Log-Likelibood | Durbin-Watson Stat | F-Statistic |
---|---|---|---|---|---|---|

0.992482 | 0.991542 | 909.5101 | 46323679 | −522.565 | 1.27245 | 0 |

Combined with the above table 4 analysis, it is found that the model has a strong fitting effect and can intuitively present the income differences between China and India and between the UK and the US. At this time, to accurately study the changes of residents' income and consumption in China, we can analyze the data of each country separately. Since Both China and India are developing countries, the actual intercept does not change, and the slope coefficient will change with individual changes. The corresponding function form is shown as follows:

Actual design is shown in the following table:

Intercept design of China and India

intercept | The coefficient of | |
---|---|---|

China | India | |

107.3149 | 0.347539 | 0.417531 |

5.892645 | 16.63877 | 11.56917 |

0 | 0 | 0 |

In the table above, the penultimate row refers to the value of t, and the last row refers to the value of P. Based on this analysis, it is found that the overall development level and resident income of China and India are similar, no matter the propensity level of marginal consumption or the level of independent consumption, which further verifies the apriori expected results of absolute income hypothesis.

In addition, the development of China and India should be compared with other information shown in the table below. The final result shows that China's spontaneous consumption level is higher than India's, while India's marginal propensity to consume is higher than China's. According to the comparison results of China and India, the model shown below is also used to analyze Britain and America. The actual intercept design is shown in the following table 5:

Other information

R-Squared | Adjusted R-Squared | S.E.Of Regression | Sum-Squared-Resid | Log-Likelibood | Durbin-Watson Stat | P(F-Statistic) |
---|---|---|---|---|---|---|

0.916297 | 0.907328 | 27.69846 | 21481.73 | −149.554 | 1.154365 | 0 |

Intercept design of UK and US

Intercept | System | |
---|---|---|

The United States | Britain | |

−1597.671 | 0.735813 | 0.730557 |

−0.793540 | 0.735813 | 11.75955 |

0.4339 | 0 | 0 |

The final results show that there is a great difference in the level of discretionary consumption expenditure between the two countries, while the actual marginal propensity to consume is consistent. A comparative analysis of the two models shows that the intercepts of China and India are positive, while those of the UK and the US are negative. Because the intercept refers to the content of autonomous consumption expenditure, which is expressed as individual payment in developing countries, and refers to the welfare expenditure of individuals by the government in developing countries, it is clear that there are great differences in welfare treatment between the UK and the US. In terms of actual marginal propensity to consume, China and India are lower than the United States and The United Kingdom, which is the most striking difference between developed and developing countries.

To sum up, absolute income hypothesis, as the most unique theoretical knowledge in the employment theory system proposed by Keynes, plays a positive role in the research of economics. Therefore, the empirical analysis of relevant hypotheses based on mathematical statistics should not only master the application methods, but also select a model based on practical research experience, and accumulate more valuable information, so as to provide effective basis for empirical analysis.

#### Intercept design of UK and US

Intercept | System | |
---|---|---|

The United States | Britain | |

−1597.671 | 0.735813 | 0.730557 |

−0.793540 | 0.735813 | 11.75955 |

0.4339 | 0 | 0 |

#### Intercept design of China and India

intercept | The coefficient of | |
---|---|---|

China | India | |

107.3149 | 0.347539 | 0.417531 |

5.892645 | 16.63877 | 11.56917 |

0 | 0 | 0 |

#### Other information

R-Squared | Adjusted R-Squared | S.E.Of Regression | Sum-Squared-Resid | Log-Likelibood | Durbin-Watson Stat | P(F-Statistic) |
---|---|---|---|---|---|---|

0.916297 | 0.907328 | 27.69846 | 21481.73 | −149.554 | 1.154365 | 0 |

#### Data results obtained by the least square method

Source | SS | DF | MS | Number Of Obs=23 |
||

Model | 3164162.45 | 1 | 3164162.45 | |||

Residual | 23237.0765 | 21 | 1106.52745 | |||

Total | 3187399.52 | 22 | 144881.796 | |||

Consp | Coef | Std Err | T | P>|t| | [95%Conf Interval] | |

Gdpp | .3861803 | .0072217 | 53.47 | 0.000 | .3711619 | .4011987 |

_Cons | 201.1189 | 14.88402 | 13.51 | 0.000 | 170.1659 | 232.0719 |

Durbin-Watson D-Statistic(2,23)=.5506366 |

#### Model research results

Public intercept | The coefficient of | Intercept | ||||||
---|---|---|---|---|---|---|---|---|

The United States | China | India | Britain | The United States | China | India | Britain | |

−788.5 | 0.746268 | 0.338316 | 0.465463 | 0.723108 | −1149.727 | 904.4732 | 869.8939 | −624.6401 |

−0.94514 | 9.903561 | 0.432146 | 0.205649 | 9.877384 | ||||

0.3486 | 0 | 0.6673 | 0.8378 | 0 |

#### Index analysis

R-Squared | Adjusted R-Squared | S.E.Of Regression | Sum-Squared-Resid | Log-Likelibood | Durbin-Watson Stat | F-Statistic |
---|---|---|---|---|---|---|

0.992482 | 0.991542 | 909.5101 | 46323679 | −522.565 | 1.27245 | 0 |

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Index Evaluation Based on Logistic Distribution Fitting Transition Probability Function Children's Educational Curriculum Evaluation Management System in Mathematical Equation Model Query Translation Optimization and Mathematical Modeling for English-Chinese Cross-Language Information Retrieval The Effect of Children’s Innovative Education Courses Based on Fractional Differential Equations Fractional Differential Equations in the Standard Construction Model of the Educational Application of the Internet of Things Optimization research on prefabricated concrete frame buildings based on the dynamic equation of eccentric structure and horizontal-torsional coupling Optimization in Mathematics Modeling and Processing of New Type Silicate Glass Ceramics Green building considering image processing technology combined with CFD numerical simulation MCM of Student’s Physical Health Based on Mathematical Cone Sports health quantification method and system implementation based on multiple thermal physiology simulation Research on visual optimization design of machine–machine interface for mechanical industrial equipment based on nonlinear partial equations Research on identifying psychological health problems of college students by logistic regression model based on data mining Abnormal Behavior of Fractional Differential Equations in Processing Computer Big Data Mathematical Modeling Thoughts and Methods Based on Fractional Differential Equations in Teaching A mathematical model of PCNN for image fusion with non-sampled contourlet transform Nonlinear Differential Equations in Computer-Aided Modeling of Big Data Technology The Uniqueness of Solutions of Fractional Differential Equations in University Mathematics Teaching Based on the Principle of Compression Mapping Financial customer classification by combined model Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Recognition of Electrical Control System of Flexible Manipulator Based on Transfer Function Estimation Method Automatic Knowledge Integration Method of English Translation Corpus Based on Kmeans Algorithm Real Estate Economic Development Based on Logarithmic Growth Function Model Design of Tennis Mobile Teaching Assistant System Based on Ordinary Differential Equations Financial Crisis Early Warning Model of Listed Companies Based on Fisher Linear Discriminant Analysis High Simulation Reconstruction of Crowd Animation Based on Optical Flow Constraint Equation Construction of Intelligent Search Engine for Big Data Multimedia Resource Subjects Based on Partial Least Squares Structural Equation 3D Animation Simulation of Computer Fractal and Fractal Technology Combined with Diamond-Square Algorithm Analysis of the Teaching Quality of Physical Education Class by Using the Method of Gradient Difference The Summation of Series Based on the Laplace Transformation Method in Mathematics Teaching Optimal Solution of the Fractional Differential Equation to Solve the Bending Performance Test of Corroded Reinforced Concrete Beams under Prestressed Fatigue Load Animation VR scene mosaic modeling based on generalized Laplacian equation Radial Basis Function Neural Network in Vibration Control of Civil Engineering Structure Optimal Model Combination of Cross-border E-commerce Platform Operation Based on Fractional Differential Equations The influence of accounting computer information processing technology on enterprise internal control under panel data simultaneous equation Research on Stability of Time-delay Force Feedback Teleoperation System Based on Scattering Matrix BIM Building HVAC Energy Saving Technology Based on Fractional Differential Equation Construction of comprehensive evaluation index system of water-saving irrigation project integrating penman Montei the quation Human Resource Management Model of Large Companies Based on Mathematical Statistics Equations Data Forecasting of Air-Conditioning Load in Large Shopping Malls Based on Multiple Nonlinear Regression Analysis of technical statistical indexes of college tennis players under the win-lose regression function equation Automatic extraction and discrimination of vocal main melody based on quadratic wave equation Analysis of wireless English multimedia communication based on spatial state model equation Optimization of Linear Algebra Core Function Framework on Multicore Processors Optimisation of Modelling of Finite Element Differential Equations with Modern Art Design Theory Mathematical function data model analysis and synthesis system based on short-term human movement Human gait modelling and tracking based on motion functionalisation The Control Relationship Between the Enterprise's Electrical Equipment and Mechanical Equipment Based on Graph Theory Financial Accounting Measurement Model Based on Numerical Analysis of Rigid Normal Differential Equation and Rigid Functional Equation Mathematical Modeling and Forecasting of Economic Variables Based on Linear Regression Statistics Nonlinear Differential Equations in Cross-border E-commerce Controlling Return Rate Differential equation model of financial market stability based on Internet big data 3D Mathematical Modeling Technology in Visualized Aerobics Dance Rehearsal System Children’s cognitive function and mental health based on finite element nonlinear mathematical model Fractional Differential Equations in Electronic Information Models BIM Engineering Management Oriented to Curve Equation Model Leakage control of urban water supply network and mathematical analysis and location of leakage points based on machine learning Analysis of higher education management strategy based on entropy and dissipative structure theory Prediction of corporate financial distress based on digital signal processing and multiple regression analysis Mathematical Method to Construct the Linear Programming of Football Training Multimedia sensor image detection based on constrained underdetermined equation The Size of Children's Strollers of Different Ages Based on Ergonomic Mathematics Design Application of Numerical Computation of Partial Differential Equations in Interactive Design of Virtual Reality Media Stiffness Calculation of Gear Hydraulic System Based on the Modeling of Nonlinear Dynamics Differential Equations in the Progressive Method Knowledge Analysis of Charged Particle Motion in Uniform Electromagnetic Field Based on Maxwell Equation Relationship Between Enterprise Talent Management and Performance Based on the Structural Equation Model Method Term structure of economic management rate based on parameter analysis of estimation model of ordinary differential equation Influence analysis of piano music immersion virtual reality cooperation based on mapping equation Chinese painting and calligraphy image recognition technology based on pseudo linear directional diffusion equation Label big data compression in Internet of things based on piecewise linear regression Animation character recognition and character intelligence analysis based on semantic ontology and Poisson equation Design of language assisted learning model and online learning system under the background of artificial intelligence Application of machine learning in stock selection Comparative analysis of CR of ideological and political education in different regions based on improved fuzzy clustering Action of Aut( G ) on the set of maximal subgroups ofp -groupsThe internal mechanism of corporate social responsibility fulfillment affecting debt risk in China: analysis of intermediary transmission effect based on degree of debt concentration and product market competitive advantage Study on transmission characteristics in three kinds of deformed finlines based on edge-based finite element method Asymptotic stability problem of predator–prey system with linear diffusion Research on loyalty prediction of e-commerce customer based on data mining Algebraic Equations in Educational Model of College Physical Education Course Education Professional English Translation Corpus Under the Binomial Theorem Coefficient Geometric Tolerance Control Method for Precision Machinery Based on Image Modeling and Novel Saturation Function Retrieval and Characteristic Analysis of Multimedia Tester Based on Bragg Equation Semiparametric Spatial Econometric Analysis of Household Consumption Based on Ordinary Linear Regression Model Video adaptive watermark embedding and detection algorithm based on phase function equation English Learning Motivation of College Students Based on probability Distribution Scientific Model of Vocational Education Teaching Method in Differential Nonlinearity Research on mobile Awareness service and data privacy Protection based on Linear Equations computing protocol Vocal Music Teaching Model Based on Finite Element Differential Mathematical Equations Research on threat assessment problems of island air defence system based on the leader-follower model Studying a matching method combining distance proximity and buffer constraints The trend and influence of media information Propagation based on nonlinear Differential equation Research on the construction of early warning model of customer churn on e-commerce platform Study on inefficient land use determination method for cities and towns from a city examination perspective A sentiment analysis method based on bidirectional long short-term memory networks Evaluation of ecosystem health in Futian mangrove wetland based on the PSR-AHP model A study of local smoothness-informed convolutional neural network models for image inpainting Towards more efficient control of the ironmaking blast furnace: modelling gaseous reduction of iron ores in H _{2}-N_{2}atmosphereAlgorithm of overfitting avoidance in CNN based on maximum pooled and weight decay Mathematical Calculus Modeling in Improving the Teaching Performance of Shot Put Application of Nonlinear Differential Equation in Electric Automation Control System Higher Mathematics Teaching Curriculum Model Based on Lagrangian Mathematical Model Decisions of competing supply chain with altruistic retailer under risk aversion Optimization of Color Matching Technology in Cultural Industry by Fractional Differential Equations The Marketing of Cross-border E-commerce Enterprises in Foreign Trade Based on the Statistics of Mathematical Probability Theory Application of Linear Partial Differential Equation Theory in Guiding Football Scientific Training The Evolution Model of Regional Tourism Economic Development Difference Based on Spatial Variation Function System Model of Shipping Enterprise Safety Culture Based on Dynamic Calculation Matrix Model The Inner Relationship between Students' Psychological Factors and Physical Exercise Based on Structural Equation Model (SEM) Analysis and Research on Influencing Factors of Ideological and Political Education Teaching Effectiveness Based on Linear Equation Fractional Differential Equations in Sports Training in Universities Examination and Countermeasures of Network Education in Colleges and Universities Based on Ordinary Differential Equation Model Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model Chinese-English Contrastive Translation System Based on Lagrangian Search Mathematical Algorithm Model