TITLE:
Asymptotic Results for Goodness-of-Fit Tests Using a Class of Generalized Spacing Methods with Estimated Parameters
AUTHORS:
Andrew Luong
KEYWORDS:
Density Based Tests, EDF Tests, Anderson-Darling Statistic, Hellinger Distance Statistic, Pseudo-Distance, Maximum Spacing Method
JOURNAL NAME:
Open Journal of Statistics,
Vol.8 No.4,
August
27,
2018
ABSTRACT: A class of pseudo 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, the
statistics follow asymptotic normal distributions without unknown parameters.
In this paper we emphasize results for the null composite hypothesis: the
parameters can be estimated by a generalized spacing method (GSP) first which
is equivalent to minimize a pseudo distance
from the class which is considered; subsequently the estimated parameters are
used to replace the parameters in the pseudo distance
used for estimation; goodness-of-fit statistics for the composite hypothesis can be
constructed and shown to have again an asymptotic normal distribution without
unknown parameters. 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 they come a no
extra cost after fitting the model, they can be considered as alternative
statistics to chi-square statistics which require a choice of intervals and
statistics based on empirical distribution (EDF) using the original data with a
complicated null distribution which might depend on the parametric family being
considered and also might depend on the vector of true parameters but EDF tests
might be more powerful against some specific models which are specified by the
alternative hypothesis.