Pitman's closeness criterion and shrinkage estimates of the variance and the S.D.
Date Issued
2011
Author(s)
Abstract
Pitman’s closeness criterion (PCC) became a controversial topic since some
statisticians expressed their wish to exclude it from the evaluation criteria of
estimates. Herein, PCC is studied for an estimate t and its shrinkage ct,
when the unknown parameter of interest is positive; 0 < c < 1. PCC is
transitive for shrinkage estimates with decreasing shrinkage coefficients and
only t’s distribution is needed to compute its value. When is the variance 2
or the standard deviation , exact calculations and simulations confirm that
ct, which improves t’s mean square error, may not improve often t’s distance
from and PCC takes large values. Consequently, some statisticians, their
clients and some statistics’ users will not use shrinkage estimates of 2 and
of . For this group, PCC is a useful information tool to be used along with
other evaluation criteria, as suggested by Rao (1993).
statisticians expressed their wish to exclude it from the evaluation criteria of
estimates. Herein, PCC is studied for an estimate t and its shrinkage ct,
when the unknown parameter of interest is positive; 0 < c < 1. PCC is
transitive for shrinkage estimates with decreasing shrinkage coefficients and
only t’s distribution is needed to compute its value. When is the variance 2
or the standard deviation , exact calculations and simulations confirm that
ct, which improves t’s mean square error, may not improve often t’s distance
from and PCC takes large values. Consequently, some statisticians, their
clients and some statistics’ users will not use shrinkage estimates of 2 and
of . For this group, PCC is a useful information tool to be used along with
other evaluation criteria, as suggested by Rao (1993).
File(s)![Thumbnail Image]()
Name
Pitmans.pdf
Size
86.81 KB
Format
Adobe PDF
Checksum (MD5)
2cfbd854854f0584fe7f015f4b656c13