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2002•Communication in Statistics- Theory and MethodsRequires access

SEMIPARAMETRIC REGRESSION WITH MULTIPLICATIVE ADJUSTMENT

Kanta Naito

Open publisher page 9 citations

Abstract

This paper is concerned with regression using both of parametric model and nonparametric smoothing. The parametric model is seen as a crude guess of the true regression function and it is adjusted by nonparametric factor. The nonparametric adjustment factor is determined by a criterion called local L 2-fitting. A class of regression estimators with multiplicative adjustment is constructed. Estimators in the class are connected by one parameter α and it is shown that the bias function of an estimator in the class is linear in α, while the variance is free for α. This makes possible to discover the best estimator in the class. Relations to the local polynomial smoothers are also discussed.

About this research paper

What this paper is about

This paper is concerned with regression using both of parametric model and nonparametric smoothing. The parametric model is seen as a crude guess of the true regression function and it is adjusted by nonparametric factor. The nonparametric adjustment factor is determined by a criterion called local L 2-fitting. A class of regression estimators with multiplicative adjustment is constructed. Estimators in the class are connected by one parameter α and it is shown that the bias function of an estimator in the class is linear in α, while the variance is free for α. This makes possible to discover the best estimator in the class. Relations to the local polynomial smoothers are also discussed.

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OpenAlex reports 9 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

This paper is concerned with regression using both of parametric model and nonparametric smoothing. The parametric model is seen as a crude guess of the true regression function and it is adjusted by nonparametric factor. The nonparametric adjustment factor is determined by a criterion called local L 2-fitting. A class of regression estimators with multiplicative adjustment is constructed. Estimators in the class are connected by one parameter α and it is shown that the bias function of an estimator in the class is linear in α, while the variance is free for α. This makes possible to discover the best estimator in the class. Relations to the local polynomial smoothers are also discussed.

Key concepts: Semiparametric regression, Nonparametric regression, Estimator, Nonparametric statistics, Mathematics, Multiplicative function, Polynomial regression, Additive model

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