Weighted kernel estimators in nonparametric binomial regression

Abstract

This paper is concerned with nonparametric binomial regression. Two kernel-based binomial regression estimators and their bias-adjusted versions are proposed, whose kernels are weighted by the inverses of variance estimators of the observed proportion at each covariate. Asymptotic theories for deriving asymptotic mean squared errors (AMSEs) of proposed estimators are developed. Comparisons with other estimators discussed by several authors are implemented through the AMSEs. From these considerations, together with the simulation results, the advantages of our weighting scheme are reported.

A Note on Local Likelihood Regression for Binary Response Data

“…As an alternative estimator, a type of weighted local estimator, which is constructed taking into consideration variance heteroscedasticity, discussed in Okumura and Naito (2004), might be recommended. Here, the estimator will require such a modification that n −2 is added to the denominator of the estimator (e.g., Fan, 1993).…”

Non-parametric kernel regression for multinomial data

“…However, the local likelihood approach does not always yield an estimator since the optimization steps sometimes cannot find a solution. This difficulty in the local likelihood approach was also pointed out in Okumura and Naito [11] in a binomial setting. Therefore, in this paper we propose the use of a more efficient estimator that is a variant of Nadaraya-Watson estimators of p j (x) (j = 1, .…”

Bandwidth selection for kernel binomial regression

“…Note that linear-type estimators are not necessarily contained in this class because they may take values outside [0, 1]. Okumura and Naito [3] have proposed the weighted kernel estimator and its efficient bias-adjusted version, which is motivated by the kernel-based estimator such as the Nadaraya-Watson estimator [4,5] discussed by Staniswalis and Cooper [1] in a binomial setting. The aim of this article is to propose an efficient bandwidth selection method for the bias-adjusted kernel estimator based on a plug-in (PI) method in the binomial setting.…”

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In nonparametric binomial regression, the weighted kernel estimator of the regression function and its efficient bias-adjusted version have been proposed by Okumura and Naito (2004) with consideration to differences of variances of observed response proportions at covariates. The aim of this article is to propose an effective data-based method for bandwidth selection of the bias-adjusted estimator.

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