Research On Bayesian Estimation Methods Of The Nonparametric Regressive Model And Its Application

Nonparametric regressive model has gained much attention recently, primarily due to the fact that they can describe some nonlinear features exhibited by many datas itself in applications. At the same time, nonparametric methods are certainly flexible in reducing modeling biases so that they become the most important methods of studying nonparametric model. The focuses of this thesis are the selections of bandwidth h in the local linear estimator and smoothing parametricλin the smoothing spline regression based on the Bayesian method. The text establishes the nonparametric autoregressive forecast model on our country's population growth rates from 1949 to 2007. The contents of the thesis are as follows:(1) The nonparametric regression model y= f(x)+εis considered, where f(x) is a smooth function. The Bayesian local linear estimator of nonparametric function f(x) is constructed by the average of samples from posterior distribution, with the condition that the prior distribution of bandwidth h is Gamma distribution.And then posterior distribution of parameters and a sampling method are also given.(2) The smoothing spline estimator of trend function of time series with AR (p) errors is constructed by the Bayesian method of the smoothing spline regression. The smoothing parameter A is regarded as a random variable in the smoothing spline estimation of trend function and gives the posterior distribution of A is given. Then, the Markov chain sample is obtained from the posterior distribution of A by the Gibbs sampling algorithm and the Bayesian estimator ofλis constructed by the posterior mean value.(3) This paper simply establishes the linear autoregressive 2-D model, nonparametric autoregressive 1-D model based on Bayesian local linear estimation and Smoothing spline estimation on our country population growth rates from 1949 to 2007 after the first order difference of data,while fits and forecasts with models. Then, our country population growth rates are fitted and forecasted by the inverse of formula for the stationary processing of data. The results of fitting and forecast indicate that nonparametric regression 1-D model is more advantageous than the linear autoregressive 2-D model.