Robust estimation for ordinal regression

被引：12

作者：

Croux, C. ^{[1
]}

Haesbroeck, G. ^{[2
]}

Ruwet, C. ^{[2
]}

机构：

[1] Katholieke Univ Leuven, Fac Business & Econ, Louvain, Belgium

[2] Univ Liege, Dept Math, Liege, Belgium

来源：

JOURNAL OF STATISTICAL PLANNING AND INFERENCE | 2013年 / 143卷 / 09期

关键词：

Breakdown point; Diagnostic plot; Influence function; Ordinal regression; Weighted maximum likelihood; Robust distances; GENERALIZED LINEAR-MODELS; LATENT VARIABLE MODELS; LOGISTIC-REGRESSION; BINARY REGRESSION; BOUNDED-INFLUENCE; BREAKDOWN;

D O I：

10.1016/j.jspi.2013.04.008

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：

Ordinal regression is used for modelling an ordinal response variable as a function of some explanatory variables. The classical technique for estimating the unknown parameters of this model is Maximum Likelihood (ML). The lack of robustness of this estimator is formally shown by deriving its breakdown point and its influence function. To robustify the procedure, a weighting step is added to the Maximum Likelihood estimator, yielding an estimator with bounded influence function. We also show that the loss in efficiency due to the weighting step remains limited. A diagnostic plot based on the Weighted Maximum Likelihood estimator allows to detect outliers of different types in a single plot. (C) 2013 Elsevier B.V. All rights reserved.

引用

页码：1486 / 1499

页数：14

共 24 条

[1]

[Anonymous], 1986, WILEY SERIES PROBABI

[2]

[Anonymous], 2001, Quantitative Models in Marketing Research

[3]

[Anonymous], 1980, J R STAT SOC B

[4] A characteristic function approach to the biased sampling model, with application to robust logistic regression [J].

Bondell, Howard D. .

JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 2008, 138 (03) :742-755

[5] Robust inference for generalized linear models [J].

Cantoni, E ;

Ronchetti, E .

JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 2001, 96 (455) :1022-1030

[6]

CARROLL RJ, 1993, J ROY STAT SOC B MET, V55, P693

[7] A BOUNDED INFLUENCE, HIGH BREAKDOWN, EFFICIENT REGRESSION ESTIMATOR [J].

COAKLEY, CW ;

HETTMANSPERGER, TP .

JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 1993, 88 (423) :872-880

[8]

COPAS JB, 1988, J R STAT SOC B, V50, P225

[9] Implementing the Bianco and Yohai estimator for logistic regression [J].

Croux, C ;

Haesbroeck, G .

COMPUTATIONAL STATISTICS & DATA ANALYSIS, 2003, 44 (1-2) :273-295

[10] The breakdown behavior of the maximum likelihood estimator in the logistic regression model [J].

Croux, C ;

Flandre, C ;

Haesbroeck, G .

STATISTICS & PROBABILITY LETTERS, 2002, 60 (04) :377-386

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