COLLOQUIUM
A Shift Parameter Estimation Based
on Smoothed Kolmogorov-Smirnov
Professor Feridun Tasdan
Western Illinois University
Abstract: A new procedure of shift parameter estimation in
the two-sample location problem is investigated and
compared with existing estimators. The proposed procedure
smooths the empirical distribution functions of each random
sample and replaces empirical distribution functions in the
two-sample Kolmogorov-Smirnov method. The smoothed
Kolmogorov-Smirnov is minimized with respect to an
arbitrary shift variable in order to find an estimate of the shift
parameter. The proposed procedure can be considered the
smoothed version of a very little known method of shift
parameter estimation from RSL (Rao, Schuster, Littell). Their
estimator will be discussed and compared with the proposed
estimator. An example and simulation studies have been
performed to compare the proposed procedure with existing
shift parameter estimators such as Hodges-Lehmann and
least squares in addition to RSL's estimator. The results show
that the proposed estimator has lower Mean Square Error
(MSE) as well as higher relative efficiency against RSL's
estimator under normal or contaminated normal model
assumptions. Moreover, the proposed estimator performs
competitively against Hodges-Lehmann and least squares
shift estimators. Smoother function and bandwidth selections
are also discussed and several alternatives are proposed in
the study.
Department of
Mathematics
Thursday,
November 7,
2013
3:45 p.m.
204 Morgan Hall
Refreshments will be
served at 3:30 p.m.