Nonparametric and Semiparametric Regression for Independent Data

Hua Liang
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Hua Liang: The George Washington University

Chapter Chapter 4 in The Work of Raymond J. Carroll, 2014, pp 293-370 from Springer

Abstract: 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.

Keywords: Semiparametric Regression; Independent Data; Usual Confidence Interval; Unknown Parameter Vector; Least Squares (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-05801-6_4

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DOI: 10.1007/978-3-319-05801-6_4

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