Browsing by Author "Thompson, P"

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Generalized and pseudo-generalized trimmed means for the linear regression with AR(l) error model
(2004-04-15)
Lai, YH
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Thompson, P
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Chen, LA
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統計學研究所
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Institute of Statistics
We propose a generalized and pseudo-generalized trimmed means for the linear regression with AR(1) errors model. These will play the role of robust-type generalized and pseudo-generalized estimators for this regression model. Their asymptotic distributions are developed. (C) 2003 Elsevier B.V. All rights reserved.
Robust type Gauss-Markov theorem and Rao's first order efficiency for the symmetric trimmed mean
(2002-09-01)
Thompson, P
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Yang, EK
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Chen, LA
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統計學研究所
;
Institute of Statistics
In Chen and Chiang [2] and Chen, Thompson and Hung [3], the symmetric trimmed mean has been shown, for various linear models, to have the efficiency of having asymptotic covariance matrices close to the CramerRao lower bounds for some heavy tail error distributions. In this paper, we investigate some further theoretical results for this symmetric trimmed mean for the linear regression model. From the nonparametric point of view, we develop a robust version of the Gauss-Markov theorem for the problem of estimating regression parameter vector beta and parametric vector function Cbeta where the best estimators are this trimmed mean and C multiplied by it, respectively. In addition, we show that these best estimators are the best Mallows-type bounded influence linear symmetric trimmed means. Finally, from the parametric aspect, we show that the symmetric trimmed mean is Rao's first order efficient for a heavy tail error distribution.
The symmetric type two-stage trimmed least squares estimator for the simultaneous equations model
(2000-10-01)
Chen, LA
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Thompson, P
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Hung, HN
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統計學研究所
;
Institute of Statistics
A two-stage symmetric regression quantile is considered as an alternative for estimating the population quantile for the simultaneous equations model. We introduce a two-stage symmetric trimmed least squares estimator (LSE) based on this quantile. It is shown that, under mixed multivariate normal errors, this trimmed LSE has asymptotic variance much closer to the Cramer-Rao lower bound than some usual robust estimators. It can even achieve the Cramer-Rao lower bound when the contaminated variance goes to infinity. This suggests that the symmetric-type quantile function is as efficient in other statistical applications, such as outlier detection. A Monte Carlo study under asymmetric error distribution and a real data analysis are also presented.
Trimmed least squares estimator as best trimmed linear conditional estimator for linear regression model
(1998)
Chen, LA
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Thompson, P
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統計學研究所
;
Institute of Statistics
A class of trimmed linear conditional estimators based on regression quantiles for the linear regression model is introduced. This class serves as a robust analogue of non-robust linear unbiased estimators. Asymptotic analysis then shows that the trimmed least squares estimator based on regression quantiles (Koenker and Bassett (1978)) is the best in this estimator class in terms of asymptotic covariance matrices. The class of trimmed linear conditional estimators contains the Mallows-type bounded influence trimmed means (see De Jongh et al (1988)) and trimmed instrumental variables estimators. A large sample methodology based on trimmed instrumental variables estimator for confidence ellipsoids and hypothesis testing is also provided.