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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/216

Title: Local polynomial estimation of contingency table cell probabilities
Authors: AERTS, Marc
Augustyns, Ilse
JANSSEN, Paul
Keywords: Mathematical Statistics
Non and semiparametric methods
Issue Date: 1997
Publisher: GORDON BREACH SCI PUBL LTD
Citation: Statistics, 30(2). p. 127-148
Abstract: For sparse tables unsmoothed cell proportions are known to be inappropriate estimators of the cell probabilities. Using information from neighboring cells, several smooth estimators of cell probabilities have been investigated (e.g. penalized likelihood, kernel and geometric combination estimators). Here we propose local polynomial smoothers to estimate the cell probabilities of a d-dimensional ordinal contingency table. Under minimal smoothness conditions, we obtain the convergence to zero of the mean sum of squared errors at the optimal rate. This result is valid since, in contrast to other existing nonparametric estimators, local polynomial smoothers have the same behaviour at boundary and interior cells. Smooth estimation of cell probabilities of a d-dimensional table requires the choice of a bandwidth matrix. So far only diagonal bandwidth matrices received attention. We consider a general d x d matrix that permits smoothing in orientations different from the main directions. Some simulated examples illustrate that local polynomial smoothers with a general bandwidth matrix provide a very appealing alternative to already existing estimators.
URI: http://hdl.handle.net/1942/216
ISI #: 000071287100003
Type: Journal Contribution
Validation: ecoom, 1999
Appears in Collections: Research publications

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