Research On Nonparametric Model Specification Test With Continuous And Discrete Variables

The test of model specification is a very important step in statistical modeling and also one of the important problems in statistical application research.When conducting empirical research,a basic premise is to set up the correct model form.However,when the results are inconsistent with the actual economic operation,there may be a model specification error phenomenon,then the test of the model specification is particularly important.The paper mainly studies one kind of nonparametric test methods: parametric model to nonparametric model specification test.As people have entered the era of high-density,multi-type and multilevel data in recent years,it is of great practical significance to complicate the form of data and carry out theoretical research and empirical analysis on the basis of continuous variables and discrete variables.Firstly,the basic theory of modeling is reviewed and sorted,especially the nonparametric kernel estimation under continuous and discrete variables is summarized.Secondly,the paper discusses the general test procedure under the linear regression model,and summarizes the existing test statistics,and on this basis,adds the classification variables,and constructs the statistics used to test the correctness of parametric regression model under the continuous and discrete variables.Then,the asymptotic distribution of the improved test statistics is deduced,and the Monte Carlo simulation method is used to compare the test statistics before and after improvement.In addition,the paper empirically studies the financial index,stock price change and industry characteristics of listed companies.Firstly,parametric and nonparametric methods are used to analyze the influence of financial indicators on stock price changes of listed companies.And on this basis to join the categorical variable of industry characteristics,then the new test statistics are used to test whether the parameter model under continuous and discrete variables is a model that reflects data laws.The main conclusions are as follows: First,This paper improves the statistics used by Fan,Li and Zheng’s tests.The weight function of the existing statistic is replaced by the weight function of Hardle and Mammen’s test,and the asymptote distribution of the new test statistic is deduced.Then,the Monte Carlo simulation method is used to compare the old and new test statistics,and it is concluded that the improved statistics is more advantageous for the test,and the improved statistics is more suitable for the statistical test of the nonparametric model.Second,the paper combines the new model with empirical research on the relationship between stock price and financial indicators under industry classification.The improved test statistics are used to analyze the test problem of parametric model specification,and the conclusion is that the non-parametric model is better than the parametric model in measuring data,which provides some new research ideas for the nonparametric problem.