%0 Journal Article
%T Asymptotic Results for Goodness-of-Fit Tests Using a Class of Generalized Spacing Methods with Estimated Parameters
%A Andrew Luong
%J Open Journal of Statistics
%P 731-746
%@ 2161-7198
%D 2018
%I Scientific Research Publishing
%R 10.4236/ojs.2018.84048
%X A class of pseudo</span></span><span><span><span style=\"font-family:&quot;\"> </span></span></span><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\">distances is used to derive test statistics using transformed data or
spacings for testing goodness-of-fit for parametric models. These statistics
can be considered as density based statistics and expressible as simple
functions of spacings. It is known that when the null hypothesis is simple,</span></span></span><span><span><span style=\"font-family:&quot;\"> </span></span></span><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\">the
statistics follow asymptotic normal distributions without unknown parameters.
In this paper we emphasize results for the null composite hypothesis</span></span></span><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\">:</span></span></span><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\"> the
parameters can be estimated by a generalized spacing method (GSP) first which
is equivalent to minimize a pseudo</span></span></span><span><span><span style=\"font-family:&quot;\"> </span></span></span><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\">distance
from the class which is considered; subsequently the estimated parameters are
used to replace the parameters in the pseudo</span></span></span><span><span><span style=\"font-family:&quot;\"> </span></span></span><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\">distance
used for estimation</span></span></span><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\">;</span></span></span><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\"> goodness-of-fit statistics for the composite hypothesis can be
constructed and shown to have again an asymptotic normal distribution without
unknown parameters.</span></span></span><span><span><span style=\"font-family:&quot;\"> </span></span></span><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\">Since these statistics are related to a discrepancy measure, these tests
can be shown to be consistent in general. Furthermore, due to the simplicity of
these statistics and
%K Density Based Tests
%K EDF Tests
%K Anderson-Darling Statistic
%K Hellinger Distance Statistic
%K Pseudo-Distance
%K Maximum Spacing Method
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=86874