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Likelihood-based local linear estimation of the conditional variance function. (English) Zbl 1089.62507
Summary: We consider estimation of mean and variance functions with kernel-weighted local polynomial fitting in a heteroscedastic nonparametric regression model. Our preferred estimators are based on a localized normal likelihood, using a standard local linear form for estimating the mean and a local log-linear form for estimating the variance. It is important to allow two bandwidths in this problem, separate ones for mean and variance estimation. We provide data-based methods for choosing the bandwidths. We also consider asymptotic results, and study and use them. The methodology is compared with a popular competitor and is seen to perform better for small and moderate sample sizes in simulations. A brief example is provided.

62G08 Nonparametric regression and quantile regression
62G20 Asymptotic properties of nonparametric inference
62G07 Density estimation
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