Topics on Nonparametric Methods for Longitudinal Data Analysis and Jumps Detection PDF Download

Author: Shengji Jia
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Languages : en
Pages : 0

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Book Description
In this thesis we investigate the nonparametric methods applied for longitudinal data analysis and jumps detection. The first part is about efficient semi-parametric regression for longitudinal data with nonparametric covariance estimation. Improving estimation efficiency for regression coefficients is an important issue in the analysis of longitudinal data, which involves estimating the covariance matrix of errors. But challenges arise in estimating the covariance matrix of longitudinal data collected at irregular or unbalanced time points. We develop a regularization method for estimating the covariance function and a stepwise procedure for estimating the parametric components efficiently in the varying-coefficient partially linear model. This procedure is also applicable to the varying-coefficient temporal mixed effects model. Our method utilizes the structure of the covariance function and thus has faster rates of convergence in estimating the covariance functions and outperforms the existing approaches. The second part is about adaptive jumps detection via nonparametric screening and multiple testing procedure. In many applications, it may appear that a regression function is smooth except at several points where jump discontinuities occur. But challenges arise when the number of jumps is quite large and unknown. We develop a jumps detection procedure via nonparametric screening and multiple testing. The candidates of jumps are first detected through screening and then a multiple testing procedure is applied to rule out the noises. Our proposed method is quite robust in jumps detection and doesn't depend on the choice of tuning parameter and threshold in the screening procedure. All the two procedures are easy to implement and their numerical performance are investigated using both simulated and real data.