On the performance of kernel estimators for high-dimensional, sparse binary data

Birgit Grund, Peter Hall

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

We develop mathematical models for high-dimensional binary distributions, and apply them to the study of smoothing methods for sparse binary data. Specifically, we treat the kernel-type estimator developed by Aitchison and Aitken (Biometrika63 (1976), 413-420). Our analysis is of an asymptotic nature. It permits a concise account of the way in which data dimension, data sparseness, and distribution smoothness interact to determine the over-all performance of smoothing methods. Previous work on this problem has been hampered by the requirement that the data dimension be fixed. Our approach allows dimension to increase with sample size, so that the theoretical model may accurately reflect the situations encountered in practice; e.g., approximately 20 dimensions and 40 data points. We compare the performance of kernel estimators with that of the cell frequency estimator, and describe the effectiveness of cross-validation.

Original languageEnglish (US)
Pages (from-to)321-344
Number of pages24
JournalJournal of Multivariate Analysis
Volume44
Issue number2
DOIs
StatePublished - Feb 1993

Keywords

  • Binary data
  • Cell frequency estimator
  • Cross-validation
  • Kernel estimator
  • Kullback-Leibler loss
  • Mean squared error
  • Smoothing
  • Sparseness
  • Squared error
  • Use of dimensionality

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