On The Structure Of Several Statistical Models And Data Analysis

Most statistical models are constructed 1)ased on data aiid used to find the pattern of the real world reflected by the data. There are closed relationship 1)etween data and related models. On o~e hand, the information contained in the data. can be used to 1)Uild. to verify and to modify the model, and on the other hand, a few influeiitial points or outliers in the dat a could make serious misleading in model btii lcling. Therefore iclent ifying influential points and improving models?efficiency according to the characteristics presented by data are ver important in practice. In this dissertation, we studied how to diagnose the outliers of two kinds of models and how to improve efficiency data of two kinds of models.Diagnostics?Diagnostics on outliers of partial least scjua.re (PLS) regression model: The second order local influence approach suggested by Wu & Luo (1993a. b) is used to identify the outliers of PLS model. After obtaining the close formulas of the estimated parameters and derivatives related to relevant eigenvectors after perturbatioii we provide the formulation for identifying the multiutliers of PLS model. Simulation study illustrates the effeteness of the new method.?Diagnostics on outliers of least absolute deviation (LAD) estimations of AR(p) model:the influence function tha.t provided by Hample (1974) is used to find the outliers of LAD estimations of AR(p) model. The asymptotic distribution of the LAD estimations prodecl by Jiang (2000) is used to deduce the diagnostic forimilation.Modification of Algorithm and Model?PLS modification method: The traditiona.l PLS method is very ineffective in certain situations. An algorithm is suggested to overcome these problems. Examples demonstrated the effectiveness of the new method.?Bandwidth selection for convolution kernel estimation of survival function: To provide a criterion for datariven 1)andwidth. we deduced the Bahaclurvpe representatlolI of the estimator and asymptotic exl)ression for its mean square(l errors. Simulat ion study shows tha.t for common surviva.l functions such a.s \Xeil)iull, the kernel estimation with locally selected bandwidth is superior than traditional kaplan-I\Ieier estimation.