Statistical Modelling 4 (2004), 91–112

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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