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• W2092185780 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., $E(varepsilon^2_i) = sigma^2_i notequiv operatorname{const.}$ 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." @default.
• W2092185780 created "2016-06-24" @default.
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• W2092185780 date "1987-06-01" @default.
• W2092185780 modified "2023-10-16" @default.
• W2092185780 title "Estimation of Heteroscedasticity in Regression Analysis" @default.
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• W2092185780 doi "https://doi.org/10.1214/aos/1176350364" @default.
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