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Nonparametric and Semiparametric Regression for Independent Data

In: The Work of Raymond J. Carroll

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  • Hua Liang

    (The George Washington University)

Abstract

Consider the linear model y i = x i T β + σ i 𝜀 i , i = 1 , ⋯ , n , $$\displaystyle{y_{i} = \mathbf{x}_{i}^{T}\beta +\sigma _{ i}\varepsilon _{i},i = 1,\cdots \,,n,}$$ where β is an unknown parameter vector and the { 𝜀 i } $$\{\varepsilon _{i}\}$$ 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.

Suggested Citation

  • Hua Liang, 2014. "Nonparametric and Semiparametric Regression for Independent Data," Springer Books, in: Marie Davidian & Xihong Lin & Jeffrey S. Morris & Leonard A. Stefanski (ed.), The Work of Raymond J. Carroll, edition 127, chapter 0, pages 293-370, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-05801-6_4
    DOI: 10.1007/978-3-319-05801-6_4
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