Statistical Modelling 4 (2004), 91112
Joint modelling of
location and scale parameters of the t distribution
Julian Taylor and Arunas Verbyla
BiometricsSA, The University of Adelaide and South Australian Research and
Development Institute,
PMB 1, Glen Osmond, South Australia 5064,
Australia.
eMail: julian.taylor@adelaide.edu.au
Abstract:
Joint modelling of location and scale parameters has generally been
confined to exponential families. In this paper the location and scale
parameters of the t distribution are allowed to depend on
covariates. The closed form of the likelihood allows inference to
proceed in a similar fashion to the Gaussian location and scale model
and provides a framework for a simple scoring algorithm to estimate
the parameters. The algorithm includes a procedure to estimate the
degrees of freedom parameter of the t distribution. Homogeneity
and asymptotic tests are discussed and a methodology is derived to detect
heteroscedasticity when the response is t
distributed. Simulations reveal considerable bias in the estimates
of the degrees of freedom parameter and only minor bias in the
estimated fixed effects associated with the
scale parameter. In comparison, the estimated location effects are
well behaved. To illustrate the joint modelling of location and
scale parameters of the t distribution the methodology is
applied to two data sets.
Keywords:
heteroscedastic regression; location and scale models; maximum
likelihood; random effects; t distribution
Downloads:
Data and
R-package Hett 0.1 in zipped archive
See http://www.r-project.org
for information on the R Project for Statistical Computing.
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