Bandwidth selection for local polynomial smoothing of multinomial data
type: Item
instance of: scholarly article
title: Bandwidth selection for local polynomial smoothing of multinomial data
zbMATH Open document ID: 0922.62020
published in: Computational Statistics
publication date: 1999-09-14T00:00:00Z
review text: The paper deals with the development of methodology for selecting local and global bandwidths for local polynomial smoothing of multinomial data. Let \(P=(P_{1}, \ldots,P_{k})^{T}\) denote the probabilities of a \(k\)-cell multinomial distribution and let \(\bar P=(\bar P_{1},\ldots,\bar P_{k})^{T}\) be cell proportions. The performance of the estimator \(\hat P^{A}(h)\) for estimating \(P^{A}=I_{A}P\) is measured by \[ MSSE_{A}(h,P)=\sum_{i\in A} E[\hat P_{i}(h)-P_{i}]^{2}, \] where \(A\) is a subset of the set of indexes \(\{1,\ldots,k\}\), \(h>0\) is the bandwidth. The optimal bandwidth is \(h_{M}^{A}= {\text{arg min}}_{h>0}(MSSE_{A}(h,P))\). A double smoothing bandwidth selection strategy involves replacing the unknown \(P\) in \(MSSE_{A}(h,P)\) by an estimate \(S_{g^{A} \bar P}\), where \(g^{A}\) is another bandwidth, \(S_{h}\) is a smoother matrix. The authors propose an algorithm for searching the optimal bandwidth. An application of the obtained bandwidth selection strategy to mine data is presented.
Mathematics Subject Classification ID: 62G07
Mathematics Subject Classification ID: 62H12
Mathematics Subject Classification ID: 62H17
zbMATH DE Number: 1336637
zbMATH Keywords: categorical data
zbMATH Keywords: contingency tables
zbMATH Keywords: double smoothing
zbMATH Keywords: kernel estimators
author: Ilse Augustyns
author: M. P. Wand
reviewed by: Aleksandr D. Borisenko
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1336637