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MINIMUM MSE ESTIMATION BY LINEAR COMBINATIONS OF ORDER STATISTICS 1
Author(s) -
Samanta M.
Publication year - 1985
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1985.tb00561.x
Subject(s) - mathematics , estimator , statistics , mean squared error , censoring (clinical trials) , minimum variance unbiased estimator , combinatorics , bias of an estimator , order statistic , minimum mean square error , sample size determination , exponential function , sample mean and sample covariance , mathematical analysis
Summary In this paper we assume that in a random sample of size n drawn from a population having the pdf f(x; θ) the smallest r 1 observations and the largest r 2 observations are censored (r 1 ≥0, r 2 ≥0). We consider the problem of estimating θ on the basis of the middle n ‐ r 1 ‐ r 2 observations when either f(x;θ)=θ ‐1 f(x/θ) or f(x;θ) = (aθ) 1 f(x‐θ)/aθ) where f(·) is a known pdf, a (<0) is known and θ (>0) is unknown. The minimum mean square error (MSE) linear estimator of θ proposed in this paper is a “shrinkage” of the minimum variance linear unbiased estimator of θ. We obtain explicit expressions of these estimators and their mean square errors when (i) f(·) is the uniform pdf defined on an interval of length one and (ii) f(·) is the standard exponential pdf, i.e., f(x) = exp(–x), x≥0. Various special cases of censoring from the left (right) and no censoring are considered.