Research On The Methods For Estimation Of The Partial Nonlinear Models

When integration of the parametric model and non-parametric model into semiparametric model,the extended model would exhibit the properties of easily interpretability featured by parametric model and flexibility of non-parametric model.If the structure of model is further extended from partially linear extends into partially nonlinear structure,the extended model would not only still enjoy the property of non-parametric model,but also overcome the limitation of linear function in the partially linear model.Further,this integrated model is more easily to be applied to the complex data structure in reality as it enables to uncover the flexible structural relationship between dependent variable and independent variable.Therefore,there are important practical and theoretical implications to study the parameter estimation on partially nonlinear model and applies it practically.To this end,this paper will systematically explore the issues of parameter estimation on partially nonlinear model from the two perspectives of Frequentist Statistics and Bayesian Statistics.The partially model focused in this study consist of the following three parts:the linear or linear term in the mean value of dependent variable,the unknown functional form in the mean value of dependent variable and the last one is error term that usually takes the form of normal distribution.In generally,a two-stage estimation method that combines with the least square technique and non-parametric estimation is commonly used in the estimation of partially model.However,this estimation method highly depends on an assumption on the distribution of observed sample.This paper proposes an empirical likelihood method without the assumption on the distribution of sample to estimate the parameters of model.Practically,there are also some prior information available for the unknown functional form in the model.Therefore,from the perspective of Bayesian Statistics,this paper further provides a parametric Bayesian estimation using b-spline estimation and Gaussian process as priori information.Finally,this paper examines the performance of different estimations using simulation method,and applies our methods to the data of stock market from USA and Japan.Specifically,using 240 observations in 2018,this paper establishes partially non-linear model for the relationship between Nikkei index,Dow Jones industries average index and the exchange rate between US dollar(USD)and Japanese Yen(JPY)to explore the relationship between Japanese stock market and American stock market.The empirical result confirms that the validity and practicability of parametric estimation on partially non-linear model.