Topics in nonparametric regression : mean functional estimation and bootstrap confidence intervals for local estimating equations /
Nonparametric regression is discussed as it arises in the settings of mean estimation and confidence interval construction for local estimating equations. The first situation concerns a generalization of a missing data problem, considered by Cheng (1990, 1994), in which data comes in two forms - on...
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| Format: | Thesis Book |
| Language: | English |
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[Place of publication not identified] :
[publisher not identified] ;
1998.
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| Online Access: | http://proxy.library.tamu.edu/login?url=http://proquest.umi.com/pqdweb?did=737708641&sid=1&Fmt=2&clientId=2945&RQT=309&VName=PQD |
| Summary: | Nonparametric regression is discussed as it arises in the settings of mean estimation and confidence interval construction for local estimating equations. The first situation concerns a generalization of a missing data problem, considered by Cheng (1990, 1994), in which data comes in two forms - one in which a covariate X is observed, and the other in which both X and a response Y are observed. If the missing data probabilities are independent of X, then the distribution of X is the same in the two populations. The goal is to estimate the marginal distribution of Y, and more specifically its mean. Cheng based his estimates on the regression of Y on X in the first population, using parametric and nonparametric regression, and showed that the two methods were roughly comparable in asymptotic efficiency. Motivated by a currently ongoing study. we consider a different problem, namely, one in which the two populations are physically distinct in such a way that the distribution of X differs between the populations. We show that, under many circumstances, the nonparametric modification of Cheng's method appropriate to this situation has zero asymptotic efficiency relative to the parametric approach. Secondly, we formulate a method for the construction of bootstrap confidence intervals for nonparametrically estimated functions in the context of four powerful generalizations of the usual local polynomial regression methodology: local polynomial methods in generalized linear models; varying coefficient generalized linear models. where the possibly multivariate coefficients in a generalized linear model are estimated nonparametrically; local likelihood methods; and local estimating equations, which generalize nonparametric regression to the estimating equation context. The technique is a simple combination of the wild-bootstrap idea of Hardle & Marron (1991) along with the estimating function bootstrap of Kauermann & Tutz (1998). |
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| Item Description: | Vita. "Major Subject: Statistics". |
| Physical Description: | xi, 82 leaves : illustrations ; 28 cm. Issued also on microfiche from University Microfilms Inc. |
| Bibliography: | Includes bibliographical references: pages 69-70. |