Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.3/45320

Title

Parameter estimation in semi-linear models using a maximal invariant likelihood function

Author(s)

Bhowmik, Jahar L.;  King, Maxwell L.

Abstract

In this paper, we consider the problem of estimation of semi-linear regression models. Using invariance arguments, Bhowmik and King [2007. Maximal invariant likelihood based testing of semi-linear models. Statist. Papers 48, 357-383] derived the probability density function of the maximal invariant statistic for the non-linear component of these models. Using this density function as a likelihood function allows us to estimate these models in a two-step process. First the non-linear component parameters are estimated by maximising the maximal invariant likelihood function. Then the non-linear component, with the parameter values replaced by estimates, is treated as a regressor and ordinary least squares is used to estimate the remaining parameters. We report the results of a simulation study conducted to compare the accuracy of this approach with full maximum likelihood and maximum profile-marginal likelihood estimation. We find maximising the maximal invariant likelihood function typically results in less biased and lower variance estimates than those from full maximum likelihood.

Publication type

Journal article

Research centre

Swinburne University of Technology. Faculty of Life and Social Sciences

Source

Journal of Statistical Planning and Inference, Vol. 139, no. 4 (Apr 2009), pp. 1276-1285

Publication year

2009

Keyword(s)

Maximum likelihood estimation;  Non-linear modelling;  Simulation experiment;  Two-step estimation

Publisher

Elsevier B.V.

ISSN

0378-3758

Publisher URL

http://dx.doi.org/10.1016/j.jspi.2008.07.011

Copyright

Copyright © 2008 Elsevier B.V. All rights reserved.

Peer reviewed