Families of densities with non-constant carriers which have finite dimensional sufficient statistics

Ghosh, J. K. ; Roy, K. K. (1972) Families of densities with non-constant carriers which have finite dimensional sufficient statistics Sankhya Series A, 34 . pp. 205-226. ISSN 0581-572X

Full text not available from this repository.

Official URL: http://sankhya.isical.ac.in/search/34a3/34a3026.ht...

Abstract

Let X1,X2,....,Xn be independently and identically distributed random variables with common density function fθ(x). Let the carrier Xθ = {x: fθ(x) > 0} of the density fθ (x) be an open interval (a(θ), b(θ)). If a(θ), b(θ) are continuous and monotonic in opposite sense and if there is a continuous real-valued statistic which is sufficient for the given family of densities for a sample of size n ≥ 2, then we prove fθ(x) has the following form fθ(x) = g(θ).h(x). In our second theorem we have the same conclusion where a(θ), b(θ) are constinuous and monotonic in the same sense and there is a continuous statistic taking values in R2, which is sufficient for a sample of size n ≥ 3. In the last section we investigate cases when a(θ), b(θ) are monotonic and the sufficient statistic is k-dimensional, k ≥ 2.

Item Type:Article
Source:Copyright of this article belongs to Indian Statistical Institute.
ID Code:22663
Deposited On:24 Nov 2010 08:03
Last Modified:02 Jun 2011 07:27

Repository Staff Only: item control page