Advances and Applications in Statistics
Volume 2, Issue 2, Pages 101 - 117
(August 2002)
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LEAST-SQUARES ESTIMATION OF PARETO PARAMETERS BY JUDGMENT ORDERED RANKED-SET SAMPLES
Elies Kouider (UAE)
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Abstract: The use
of ranked-set sampling procedure when estimating the
population mean, location and scale parameters and
its advantage over the use of a simple random
sampling is well established in the literature. It
is usually recommended when measuring sample units
is expensive or difficult, while ranking could be
achieved cheaply and easily. However, even if
ranking is difficult, but there exists an easily
ranked concomitant variable, then it is used to
judgment order the variable of interest. In this
article, the ranked-set sampling concept is reviewed
in the estimation with particular consideration of
imperfect ordering using the least-squares theory.
The best linear unbiased and best linear invariant
estimators of the mean, location and scale
parameters of the Pareto II distribution are
derived. Variances and mean square errors of the
mentioned estimators are calculated. The best linear
invariant estimator is found to be uniformly more
efficient than the best linear unbiased estimator,
which in turn is more efficient than the ranked-set
sample mean, in both the perfect as well as the
imperfect cases. Furthermore, in the case of
imperfect ordering, the amount of increase in the
precision of the reviewed estimators heavily depends
upon the amount of correlation that exists between
the variable of interest and the concomitant
variable. |
Keywords and phrases: best linear unbiased estimator, best linear invariant estimator, ranked-set sample, relative efficiency, location and scale parameters, imperfect ranking, concomitant variable, Pareto II distribution. |
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