Non-parametric kernel regression for multinomial data

• Published in: Journal of multivariate analysis Vol. 97; no. 9; pp. 2009 - 2022
• Main Authors: Okumura, Hidenori, Naito, Kanta
• Format: Journal Article
• Language: English
• Published: San Diego, CA Elsevier Inc 01.10.2006; Elsevier; Taylor & Francis LLC
• Series: Journal of Multivariate Analysis
• Subjects: Algorithms; Data smoothing; Exact sciences and technology; Kernel smoothing; Mathematics; Multinomial data; Multivariate analysis; Non-parametric regression; Non-parametric regression Multinomial data Kernel smoothing Power-divergence measure; Nonparametric inference; Parameter estimation; Power-divergence measure; Probability and statistics; Regression analysis; Sciences and techniques of general use; Simulation; Statistics; Studies; Multinomial data; Power-divergence measure; 62G08; 62G20; Non-parametric regression; 62H12; Kernel smoothing; 62G08; 62G20; 62H12; Smoothing methods; Bandwith selection; Nonparametric regression; Multivariate analysis; Kernel method; Statistical method; Smoothing parameter; Regression function; Multinomial distribution; Asymptotic approximation; Non-parametric regression; Multinomial data; Kernel smoothing; Power-divergence measure; Biased estimation
• ISSN: 0047-259X; 1095-7243
• DOI: 10.1016/j.jmva.2005.12.008

This paper presents a kernel smoothing method for multinomial regression. A class of estimators of the regression functions is constructed by minimizing a localized power-divergence measure. These estimators include the bandwidth and a single parameter originating in the power-divergence measure as smoothing parameters. An asymptotic theory for the estimators is developed and the bias-adjusted estimators are obtained. A data-based algorithm for selecting the smoothing parameters is also proposed. Simulation results reveal that the proposed algorithm works efficiently.