Bernoulli

  • Bernoulli
  • Volume 6, Number 6 (2000), 1121-1134.

Minimal sufficient statistics in location-scale parameter models

Lutz Mattner

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Abstract

Let f be a probability density on the real line, let n be any positive integer, and assume the condition (R) that logf is locally integrable with respect to Lebesgue measure. Then either logf is almost everywhere equal to a polynomial of degree less than n, or the order statistic of n independent and identically distributed observations from the location-scale parameter model generated by f is minimal sufficient. It follows, subject to (R) and n≥3, that a complete sufficient statistic exists in the normal case only. Also, for f with (R) infinitely divisible but not normal, the order statistic is always minimal sufficient for the corresponding location-scale parameter model. The proof of the main result uses a theorem on the harmonic analysis of translation- and dilation-invariant function spaces, attributable to Leland (1968) and Schwartz (1947).

Article information

Source
Bernoulli, Volume 6, Number 6 (2000), 1121-1134.

Dates
First available in Project Euclid: 5 April 2004

Permanent link to this document
https://projecteuclid.org/euclid.bj/1081194163

Mathematical Reviews number (MathSciNet)
MR1809738

Zentralblatt MATH identifier
1067.62503

Keywords
characterization complete sufficient statistics equivariance exponential family, independence infinitely divisible distribution mean periodic functions normal distribution order statistics transformation model

Citation

Mattner, Lutz. Minimal sufficient statistics in location-scale parameter models. Bernoulli 6 (2000), no. 6, 1121--1134. https://projecteuclid.org/euclid.bj/1081194163


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