A Bayesian Knots Selection Method for Regression Spline Estimation

• Main Authors: Yang, Bo-Wei, 楊博崴
• Other Authors: 黃子銘
• Format: Others
• Language: zh-TW
• Published: 2018
• Online Access: http://ndltd.ncl.edu.tw/handle/5253wr

碩士 === 國立政治大學 === 統計學系 === 106 === In nonparametric regression, it is common to approximate the regression fun-ction using a spline function, and then obtain the regression function estimate using least squares. When approximating the regression function using a spline, it is imp-ortant to choose the number of knots and knot locations. In this thesis, we use three variable selection methods to select knots. The first and second methods are forward and backward selection. We replace the usual residual-based variance estimator in the test statistics by a more robust estimator. The third method is the Bayesian variable selection method. Given the appropriate parameters of the prior distribution, variables are selected based on the posterior probabilities of latent variables. In the process of computing the posterior probabilities, the componentwise Gibbs sampler is used to reduce the computational burden. Simulation experiments are carried out in this study to compare the three me-thods in a nonparametric regression setting. ISE (integrated squared error) is used to evaluate knot selection results. In those experiments, regression functions with dif-ferrent degrees of smoothness, and data of different sample sizes and error variance levels, are considered. It is found that when the function is relatively smooth, both the forward and backward selection methods are superior to the Bayesian variable select-ion method regardless of the sizes of the sample and the levels of error variance, and the Bayesian method has the problem of selecting unnecessary knots. The Bayesian method outperforms the other two methods when the regression function has a steep pattern and the error variance is large.