Asymptotic properties of a solution to the likelihood equation with life-testing applications

Basu, A. P. ; Ghosh, J. K. (1980) Asymptotic properties of a solution to the likelihood equation with life-testing applications Journal of the American Statistical Association, 75 (370). pp. 410-414. ISSN 0162-1459

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Official URL: http://www.jstor.org/pss/2287468

Abstract

The asymptotic properties of a solution of the maximum likelihood equation for the case of independent and nonidentically distributed random variables are considered. A set of sufficient conditions for its consistency and asymptotic normality is given. As an application, suppose Yi(i = 1, 2, ...., n) has exponential density fθ(y) = θ εy, θ > 0, y > 0, and is censored if Yi > ci. Let Xi = min (Yi, ci) be the censored observation. A sufficient condition for the asymptotic normality of a solution of the likelihood equation is obtained as a special case of the general theorem. Justification for the Edgeworth expansion for this estimate is provided for a special case. We also consider the problem of estimating θ when instead of Xi one can observe only whether Yi has exceeded ci.

Item Type:Article
Source:Copyright of this article belongs to American Statistical Association.
ID Code:22650
Deposited On:24 Nov 2010 08:05
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