Estimation and Testing of Mean Curves in Nonparametric Regression

• Main Authors: Shen, Wan-Chen, 沈琬貞
• Other Authors: Shiau Horng, Jyh-Jen
• Format: Others
• Language: en_US
• Published: 1996
• Online Access: http://ndltd.ncl.edu.tw/handle/86683575878670215996

碩士 === 國立交通大學 === 統計學研究所 === 84 === Assume that we observe repeated measurements data from populations with unknown mean curves and covariance structures. In this article, we discuss how to estimate the unknown mean curves and covariance structures using nonparametric regression. Another interest is to test whether the mean curves of two populations are different. First, we use cubic smoothing splines to estimate mean curves. Then; we use the eigenvectors and eigenvalues of the sample covariance matrix to estimate the covariance structure. From these, we can get a statistic; Tn; to test the hypothesis of equal mean curves. For the cases that data are serially correlated and data come from a Gaussian process, we use Monte Carlo method to find the empirical distribution of Tn and then decide the critical region. When the difference between two mean curves is a constant, we compare the power of Tn with the traditional Hotelling T2 statistic at 0.95 significance level. We also propose a bootstrap method when analyzing the real data. Finally, we will deal with two real examples using the method developed in this paper.