Browsing by Author "Chen, LA"

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A multivariate parallelogram and its application to multivariate trimmed means
(2003-09-01)
Shiau, JJH
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Chen, LA
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統計學研究所
;
Institute of Statistics
This paper introduces a multivariate parallelogram that can play the role of the univariate quantile in the location model, and uses it to define a multivariate trimmed mean. It assesses the asymptotic efficiency of the proposed multivariate trimmed mean by its asymptotic variance and by Monte Carlo simulation.
An efficient class of weighted trimmed means for linear regression models
(1997-07-01)
Chen, LA
;
統計學研究所
;
Institute of Statistics
We propose and study a class of weighted trimmed means based on the symmetric quantile functions for the location and linear regression models. A robustness comparison with the underlying distribution of a symmetric-type heavy tail is given. The weighted trimmed mean in optimal trimming under symmetric distributions is shown to have an asymptotic variance very close to the Cramer-Rao lower bound. For fixed weight setting, the weighted trimmed mean is still relatively more efficient in terms of asymptotic variance than the trimmed mean based on regression quantiles. From the parametric point of view, the computationally easy weighted trimmed mean is shown to be an efficient alternative to maximum likelihood estimation which is usually computationally difficult for most underlying distributions except the ideal case of normal ones. From the nonparametric point of view, this weighted trimmed mean is shown to be an efficient alternative robust estimator. A methodology for confidence ellipsoids and hypothesis testing based on the weighted trimmed mean is also introduced.
Bivariate regression splines
(1996-04-01)
Chen, LA
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統計學研究所
;
Institute of Statistics
Towards the construction of multivariate spline functions, we introduce a way to set linear restrictions in the generation of bivariate regression splines. The hyperplanes in R(2) are used in the role of ''knot'' to slice the domain of explanatory variables; hence, we have the flexibility in domain partition which includes rectangle, parallelogram, trapezoid and trapezium.
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
;
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.
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
;
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.
Multivariate polynomial spline spaces
(1999-09-01)
Chen, LA
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Hsu, YJ
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Chiang, YC
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應用數學系
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統計學研究所
In this paper we construct bases of certain spaces of multivariate polynomial splines defined on rectangular partitions. These bases are presented by polynomials, truncated power functions and products of these functions. This setting provides a natural generalization of the two-dimensional polynomial spline, proposed by Chui and Wang [3], to p variables.
Multivariate regression splines
(1997-11-06)
Chen, LA
;
統計學研究所
;
Institute of Statistics
Multivariate regression splines of arbitrary order assuming known knots using the additional function are developed. Model description and possible parameter tests for obtaining regression splines are also stated in detail for the triplicate case. A simulation study of drawn data from the Lubricant nonlinear regression model, where ''Lubricant'' is referred to lubricant data that we use in application, to compare the mean squares errors for the multivariate regression spline models and the multivariate polynomial models show the need of employing the multivariate regression splines in the approximation of the nonlinear regression models. (C) 1997 Elsevier Science B.V.
Multivariate regression splines
(1997-11-06)
Chen, LA
;
統計學研究所
;
Institute of Statistics
Multivariate regression splines of arbitrary order assuming known knots using the additional function are developed. Model description and possible parameter tests for obtaining regression splines are also stated in detail for the triplicate case. A simulation study of drawn data from the Lubricant nonlinear regression model, where ''Lubricant'' is referred to lubricant data that we use in application, to compare the mean squares errors for the multivariate regression spline models and the multivariate polynomial models show the need of employing the multivariate regression splines in the approximation of the nonlinear regression models. (C) 1997 Elsevier Science B.V.
Robust type Gauss-Markov theorem and Rao's first order efficiency for the symmetric trimmed mean
(2002-09-01)
Thompson, P
;
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.
Symmetric regression quantile and its application to robust estimation for the nonlinear regression model
(2004-12-01)
Chen, LA
;
Tran, LT
;
Lin, LC
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統計學研究所
;
Institute of Statistics
Populational conditional quantiles in terms of percentage alpha are useful as indices for identifying outliers. We propose a class of symmetric quantiles for estimating unknown nonlinear regression conditional quantiles. In large samples, symmetric quantiles are more efficient than regression quantiles considered by Koenker and Bassett (Econometrica 46 (1978) 33) for small or large values of alpha, when the underlying distribution is symmetric, in the sense that they have smaller asymptotic variances. Symmetric quantiles play a useful role in identifying outliers. In estimating nonlinear regression parameters by symmetric trimmed means constructed by symmetric quantiles, we show that their asymptotic variances can be very close to (or can even attain) the Cramer-Rao lower bound under symmetric heavy-tailed error distributions, whereas the usual robust and nonrobust estimators cannot. (C) 2003 Elsevier B.V. All rights reserved.
Tensor product polynomial splines
(1997-01-01)
Chen, LA
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Chan, WY
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Lee, TS
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統計學研究所
;
Institute of Statistics
This paper presents a unified study of smoothing tensor product piecewise polynomials as tensor product polynomial splines. This study generalizes the theory of univariate polynomial splines of Poirier (1973) and Smith (1979) to the multivariate setting, and the method proposed herein provides various spline bases that gives great flexibility for selecting models. An example analyzing an Australia wine industry data shows simple tensor product spline can capture the trend in the data appropriately to law of economics whereas multiple lineal model fails in capturing the trend (see Maddala (1988)).
Tensor product polynomial splines
(1997-01-01)
Chen, LA
;
Chan, WY
;
Lee, TS
;
統計學研究所
;
Institute of Statistics
This paper presents a unified study of smoothing tensor product piecewise polynomials as tensor product polynomial splines. This study generalizes the theory of univariate polynomial splines of Poirier (1973) and Smith (1979) to the multivariate setting, and the method proposed herein provides various spline bases that gives great flexibility for selecting models. An example analyzing an Australia wine industry data shows simple tensor product spline can capture the trend in the data appropriately to law of economics whereas multiple lineal model fails in capturing the trend (see Maddala (1988)).
The symmetric type two-stage trimmed least squares estimator for the simultaneous equations model
(2000-10-01)
Chen, LA
;
Thompson, P
;
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.
Two-stage regression quantiles and two-stage trimmed least squares estimators for structural equation models
(1996)
Chen, LA
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Portnoy, S
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統計學研究所
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Institute of Statistics
We propose a two-stage trimmed least squares estimator for the parameters of structural equation model and provide the corresponding asymptotic distribution theory. The estimator is based on two-stage regression quantiles, which generalize the standard Linear model regression quantiles introduced by Koenker and Bassett (1978). The asymptotic theory is developed by means of ''Barhadur'' representations for the two-stage regression quantiles and the two-stage trimmed least squares estimator. The representations approximate these estimators as sums of independent random variables plus an additive term involving the first stage estimator. Asymptotic normal distributions are derived from these representations, and a simulation comparing some two-stage estimators is presented.
Two-stage Welsh's trimmed mean for the simultaneous equations model
(2001-12-01)
Chen, LA
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Liang, KY
;
Liu, CC
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統計學研究所
;
Institute of Statistics
This paper discusses the large sample theory of the two-stage Welsh's trimmed mean for the limited information simultaneous equations model. Besides having asymptotic normality, this trimmed mean, as the two-stage least squares estimator, is a generalized least squares estimator. It also acts as a robust Aitken estimator for the simultaneous equations model. Examples illustrate real data analysis and large sample inferences based on this trimmed mean.