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SUBSAMPLE AND HALF-SAMPLE METHODS

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GUTTI JOGESH BABU

*Department of Statistics, 319 Classroom Building, The Pennsylvania State University,*

University Park, PA 16802, U.S.A.
(Received October 31, 1990; revised November 18, 1991)

**Abstract.**
Hartigan's subsample and half-sample methods are both
shown to
be inefficient methods of estimating the sampling distributions. In the
sample mean
case the bootstrap is known to correct for skewness. But irrespective of the
population, the estimates based on the subsample method, have skewness
factor zero.
This problem persists even if we take only samples of size less than or
equal to half
of the original sample. For linear statistics it is possible to correct this by
considering estimates based on subsamples of size *lambda* *n*, when the
sample size
is *n*. In the sample mean case *lambda* can be taken as
0.5(1-1/\sqrt5). In
spite of these negative results, the half-sample method is useful in
estimating the
variance of sample quantiles. It is shown that this method gives as good an
estimate
as that given by the bootstrap method. A major advantage of the half-sample
method is
that it is shown to be robust in estimating the mean square error of
estimators of
parameters of a linear regression model when the errors are heterogeneous.
Bootstrap
is known to give inconsistent results in this case; although, it is more
efficient
in the case of homogeneous errors.

*Key words and phrases*:
Half-sample method, bootstrap, variance
estimation, linear models, asymptotic relative efficiency, Bahadur's
representation,
quantiles.

**Source**
( TeX ,
DVI ,
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