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

被引:1
作者
Bhowmik, Jahar L. [2 ,3 ]
King, Maxwell L. [1 ]
机构
[1] Monash Univ, Dept Econometr & Business Stat, Clayton, Vic 3800, Australia
[2] Swinburne Univ Technol, Fac Life & Social Sci, Hawthorn, Vic 3122, Australia
[3] Monash Univ, Dept Econometr, Clayton, Vic 3800, Australia
基金
澳大利亚研究理事会;
关键词
Maximum likelihood estimation; Non-linear modelling; Simulation experiment; Two-step estimation; STRONG UNIVERSAL CONSISTENCY; NONPARAMETRIC REGRESSION; CONVERGENCE; RATES; EXPECTATIONS;
D O I
10.1016/j.jspi.2008.07.011
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
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. (C) 2008 Elsevier B.V. All rights reserved.
引用
收藏
页码:1276 / 1296
页数:21
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