Estimation And Application Of Binary PROBIT Model

The Probit model originated from the statistical processing of biological experiments.With the development of the model,the Probit model has become one of the most widely used statistical models due to its good statistical properties.For further application and research,expand the applicable field of the model.Based on the research of the parameter binary Probit model,this paper develops the nonparametric binary Probit model and the varying-coefficient binary Probit model,and conducts an exploratory study on the theoretical issues,while using the binary Probit model.The actual problem was empirically analyzed.The content of this article is divided into six chapters.The first chapter is the introduction,which explains the research background and research significance of this paper.The related literatures of Probit model at home and abroad are reviewed,and the research methods and innovations of this paper are proposed.The second chapter reviews the estimation method,large sample property and model checking process of the parameter binary Probit model,and verifies the small sample properties of the model through numerical simulation program.The third chapter develops the nonparametric binary Probit model,proposes an estimation method suitable for the model,and conducts an exploratory study on the statistical inference properties of the model.The fourth chapter innovatively proposes the varying-coefficient binary Probit model,and makes an exploratory study on the estimation method of the model;The fifth chapter uses the binary Probit model to study the related factors that affect residents' subjective well-being;The sixth chapter summarizes the research content of the full text,and forecasts the future research direction.This paper focuses on method research and does the following work in theoretical research: the binary Probit model is taken as the research object,and the nonparametric binary Probit model and the varying-coefficient binary Probit model with unknown observation data are constructed.Scenarios use the local weighted kernel likelihood function estimation method and the improved one-step local weighted kernel likelihood method to estimate the proposed model.Compared with the local weighted kernel likelihood function estimation method,one-step local weighted kernel likelihood estimation The method can reduce the number of iterative calculations,the algorithm is simpler and clearer,and the convergence speed of its estimator is also faster.The research results prove that both types of estimation methods have good statistical properties.In the model estimation method,the estimator of the model is derived by selecting the appropriate kernel function and bandwidth,and the estimator is statistically tested.Finally,the numerical simulation results show that the small sample of the estimator has good performance.The empirical part mainly analyzes individuals,using the China Comprehensive Social Survey(CGSS)data from 2015,establish a binary Probit model to analyze the relationship between personal education level,social security,personal income,age and other related factors and subjective well-being.