On the asymptotic efficiency of tests and estimates

Bahadur, R. R. (1960) On the asymptotic efficiency of tests and estimates Sankhya, 22 (3-4). pp. 229-252. ISSN 0972-7671

Full text not available from this repository.

Official URL: http://sankhya.isical.ac.in/search/2234/2234013.ht...

Abstract

Let x1, x2, ... be a sequence of independent and identically distributed observations with distributions determined by a real valued parameter θ. For each n=1, 2, ..., let Tn = Tn (x1, x2... xn) be a statistic such that the sequence Tn is a consistent estimate of θ. It is shown, under weak regularity conditions on the sample space of a single observation, that the asymptotic effective standard deviation of Tn cannot be less than [nI(θ)]{½}. The asymptotic effective standard deviation of Tn is defined, roughly speaking, as the solution τ of the equation P(|Tn-θ|≥ ε|θ)=P(|N|≥ ε/τ) when n is large and ε is a small positive number, where N denotes a standard normal variable. It is also shown, under stronger regularity conditions, that the asymptotic effective standard deviation of the maximum likelihood estimate of θ is [nI(θ)]-{½}. These conclusions concerning estimates are derived from certain conclusions concerning the relative efficiency of alternative statistical tests based on large samples.

Item Type:Article
Source:Copyright of this article belongs to Indian Statistical Institute.
ID Code:27033
Deposited On:08 Dec 2010 12:49
Last Modified:11 May 2011 04:42

Repository Staff Only: item control page