Semiparametric functional data analysis for longitudinal/clustered data: theory and application

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Title: Semiparametric functional data analysis for longitudinal/clustered data: theory and application
Author: Hu, Zonghui
Abstract: Semiparametric models play important roles in the & #64257 ;eld of biological statistics . In this dissertation , two types of semiparametic models are to be studied . One is the partially linear model , where the parametric part is a linear function . We are to investigate the two common estimation methods for the partially linear models when the data is correlated ? ? longitudinal or clustered . The other is a semiparametric model where a latent covariate is incorporated in a mixed effects model . We will propose a semiparametric approach for estimation of this model and apply it to the study on colon carcinogenesis . First , we study the pro & #64257 ;lekernel and back & #64257 ;tting methods in partially linear models for clustered /longitudinal data . For independent data , despite the potential rootn inconsistency of the back & #64257 ;tting estimator noted by Rice (1986 ) , the two estimators have the same asymptotic variance matrix as shown by Opsomer and Ruppert (1999 ) . In this work , theoretical comparisons of the two estimators for multivariate responses are investigated . We show that , for correlated data , back & #64257 ;tting often produces a larger asymptotic variance than the pro & #64257 ;lekernel method ; that is , in addition to its bias problem , the back & #64257 ;tting estimator does not have the same asymptotic ef & #64257 ;ciency as the pro & #64257 ;lekernel estimator when data is correlated . Consequently , the common practice of using the back & #64257 ;tting method to compute pro & #64257 ;lekernel estimates is no longer advised . We illustrate this in detail by following Zeger and Diggle (1994 ) , Lin and Carroll (2001 ) with a working independence covariance structure for nonparametric estimation and a correlated covariance structure for parametric estimation . Numerical performance of the two estimators is investigated through a simulation study . Their application to an ophthalmology dataset is also described . Next , we study a mixed effects model where the main response and covariate variables are linked through the positions where they are measured . But for technical reasons , they are not measured at the same positions . We propose a semiparametric approach for this misaligned measurements problem and derive the asymptotic properties of the semiparametric estimators under reasonable conditions . An application of the semiparametric method to a colon carcinogenesis study is provided . We & #64257 ;nd that , as compared with the corn oil supplemented diet , & #64257 ;sh oil supplemented diet tends to inhibit the increment of bcl2 (oncogene ) gene expression in rats when the amount of DNA damage increases , and thus promotes apoptosis .
URI: http : / /hdl .handle .net /1969 .1 /3088
Date: 2006-04-12

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Semiparametric functional data analysis for longitudinal/clustered data: theory and application. Available electronically from http : / /hdl .handle .net /1969 .1 /3088 .

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