Density approximation by summary statistics: An information-theoretic approach

Zvi Gilula, Shelby J. Haberman

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

In the case of exponential families, it is a straightforward matter to approximate a density function by use of summary statistics; however, an appropriate approach to such approximation is far less clear when an exponential family is not assumed. In this paper, a maximin argument based on information theory is used to derive a new approach to density approximation from summary statistics which is not restricted by the assumption of validity of an underlying exponential family. Information-theoretic criteria are developed to assess loss of predictive power of summary statistics under such minimal knowledge. Under these criteria, optimal density approximations in the maximin sense are obtained and shown to be related to exponential families. Conditions for existence of optimal density approximations are developed. Applications of the proposed approach are illustrated, and methods for estimation of densities are provided in the case of simple random sampling. Large-sample theory for estimates is developed.

Original languageEnglish
Pages (from-to)521-534
Number of pages14
JournalScandinavian Journal of Statistics
Volume27
Issue number3
DOIs
StatePublished - 2000

Keywords

  • Exponential families
  • Optimal predictive densities
  • Probability prediction

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