Browsing by Author "Welsh, AH"

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Distribution-function-based bivariate quantiles
(2002-10-01)
Chen, LA
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Welsh, AH
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交大名義發表
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National Chiao Tung University
We introduce bivariate quantiles which are defined through the bivariate distribution function. This approach ensures that, unlike most multivariate medians or the multivariate M-quartiles, the bivariate quantiles satisfy an analogous property to that of the univariate quantiles in that they partition R-2 into sets with a specified probability content. The definition of bivariate quantiles leads naturally to the definition of quantities such as the bivariate median, bivariate extremes, the bivariate quantile curve, and the bivariate trimmed mean. We also develop asymptotic representations for the bivariate quantiles. (C) 2002 Elsevier Science (USA).
Estimators for the linear regression model based on Winsorized observations
(2001-01-01)
Chen, LA
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Welsh, AH
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Chan, W
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統計學研究所
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Institute of Statistics
We develop an asymptotic, robust version of the Gauss-Markov theorem for estimating the regression parameter vector beta and a parametric function c'beta in the linear regression model. In a class of estimators for estimating beta that are linear in a Winsorized observation vector introduced by Welsh (1987), we show that Welsh's trimmed mean has smallest asymptotic covariance matrix. Also, for estimating a parametric function c'beta, the inner product of c and the trimmed mean has the smallest asymptotic variance among a class of estimators linear in the Winsorized observation vector. A generalization of the linear Winsorized mean to the multivariate context is also given. Examples analyzing American lobster data and the mineral content of bones are used to compare the robustness of some trimmed mean methods.