Book chapter
Nonparametric and Semiparametric Regression for Independent Data
The Work of Raymond J. Carroll, pp 293-370
13 May 2014
Abstract
Consider the linear model yi=xiTβ+σi𝜀i,i=1,⋯,n,\documentclass[12pt]{minimal}
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$$\displaystyle{y_{i} = \mathbf{x}_{i}^{T}\beta +\sigma _{ i}\varepsilon _{i},i = 1,\cdots \,,n,}$$
\end{document} where β is an unknown parameter vector and the {𝜀i}\documentclass[12pt]{minimal}
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$$\{\varepsilon _{i}\}$$
\end{document} are i.i.d. errors. It is well known that ordinary least squares (LS) estimators are unbiased and consistent, but are not efficient when errors are heteroscedastic, and the usual standard error estimators of LS estimators are biased. Hence the usual confidence intervals and test statistics are biased and may lead to incorrect conclusions.
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Details
- Title
- Nonparametric and Semiparametric Regression for Independent Data
- Creators
- Hua Liang - George Washington University
- Publication Details
- The Work of Raymond J. Carroll, pp 293-370
- Publisher
- Springer International Publishing; Cham
- Resource Type
- Book chapter
- Language
- English
- Academic Unit
- School of Biomedical Engineering, Science, and Health Systems
- Scopus ID
- 2-s2.0-84930839609
- Other Identifier
- 991019320513504721