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June, 1987 Estimation of Heteroscedasticity in Regression Analysis
Hans-Georg Muller, Ulrich Stadtmuller
Ann. Statist. 15(2): 610-625 (June, 1987). DOI: 10.1214/aos/1176350364

Abstract

Consider the regression model $Y_i = g(t_i) + \varepsilon_i, 1 \leq i \leq n$, with nonrandom design variables $(t_i)$ and measurements $(Y_i)$ for the unknown regression function $g(\cdot)$. We assume that the data are heteroscedastic, i.e., $E(\varepsilon^2_i) = \sigma^2_i \not\equiv \operatorname{const.}$ and investigate how to estimate $\sigma^2_i$. If $\sigma^2_i = \sigma^2(t_i)$ with a smooth function $\sigma^2(\cdot)$, initial estimators $\tilde{\sigma}^2_i$ can be improved by kernel smoothers and the resulting class of estimators is shown to be uniformly consistent. These estimates can be used to improve the estimation of the regression function $g$ itself in parametric and nonparametric models. Further applications are suggested.

Citation

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Hans-Georg Muller. Ulrich Stadtmuller. "Estimation of Heteroscedasticity in Regression Analysis." Ann. Statist. 15 (2) 610 - 625, June, 1987. https://doi.org/10.1214/aos/1176350364

Information

Published: June, 1987
First available in Project Euclid: 12 April 2007

zbMATH: 0632.62040
MathSciNet: MR888429
Digital Object Identifier: 10.1214/aos/1176350364

Subjects:
Primary: 62G05
Secondary: 62J02

Rights: Copyright © 1987 Institute of Mathematical Statistics

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Vol.15 • No. 2 • June, 1987
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