Robust and Efficient Adaptive Estimation of Binary-Choice Regression Models

Research output: Working paperDiscussion paperOther research output

239 Downloads (Pure)

Abstract

The binary-choice regression models such as probit and logit are used to describe the effect of explanatory variables on a binary response vari- able. Typically estimated by the maximum likelihood method, estimates are very sensitive to deviations from a model, such as heteroscedastic- ity and data contamination. At the same time, the traditional robust (high-breakdown point) methods such as the maximum trimmed like- lihood are not applicable since, by trimming observations, they induce the separation of data and non-identification of parameter estimates. To provide a robust estimation method for binary-choice regression, we con- sider a maximum symmetrically-trimmed likelihood estimator (MSTLE) and design a parameter-free adaptive procedure for choosing the amount of trimming. The proposed adaptive MSTLE preserves the robust prop- erties of the original MSTLE, significantly improves the infinite-sample behavior of MSTLE, and additionally, ensures asymptotic efficiency of the estimator under no contamination. The results concerning the trim- ming identification, robust properties, and asymptotic distribution of the proposed method are accompanied by simulation experiments and an application documenting the infinite-sample behavior of some existing and the proposed methods.
Original languageEnglish
Place of PublicationTilburg
PublisherEconometrics
Number of pages30
Volume2007-12
Publication statusPublished - 2007

Publication series

NameCentER Discussion Paper
Volume2007-12

Fingerprint

Trimming
Maximum likelihood
Contamination
Experiments

Keywords

  • asymptotic efficiency
  • binary-choice regression
  • breakdown point
  • maximum likelihood estimation
  • robust estimation
  • trimming

Cite this

Cizek, P. (2007). Robust and Efficient Adaptive Estimation of Binary-Choice Regression Models. (CentER Discussion Paper; Vol. 2007-12). Tilburg: Econometrics.
Cizek, P. / Robust and Efficient Adaptive Estimation of Binary-Choice Regression Models. Tilburg : Econometrics, 2007. (CentER Discussion Paper).
@techreport{09af7c4a65bd4684855be527d5a7d169,
title = "Robust and Efficient Adaptive Estimation of Binary-Choice Regression Models",
abstract = "The binary-choice regression models such as probit and logit are used to describe the effect of explanatory variables on a binary response vari- able. Typically estimated by the maximum likelihood method, estimates are very sensitive to deviations from a model, such as heteroscedastic- ity and data contamination. At the same time, the traditional robust (high-breakdown point) methods such as the maximum trimmed like- lihood are not applicable since, by trimming observations, they induce the separation of data and non-identification of parameter estimates. To provide a robust estimation method for binary-choice regression, we con- sider a maximum symmetrically-trimmed likelihood estimator (MSTLE) and design a parameter-free adaptive procedure for choosing the amount of trimming. The proposed adaptive MSTLE preserves the robust prop- erties of the original MSTLE, significantly improves the infinite-sample behavior of MSTLE, and additionally, ensures asymptotic efficiency of the estimator under no contamination. The results concerning the trim- ming identification, robust properties, and asymptotic distribution of the proposed method are accompanied by simulation experiments and an application documenting the infinite-sample behavior of some existing and the proposed methods.",
keywords = "asymptotic efficiency, binary-choice regression, breakdown point, maximum likelihood estimation, robust estimation, trimming",
author = "P. Cizek",
note = "Subsequently published in Journal of the American Statistical Association, 2008 Pagination: 30",
year = "2007",
language = "English",
volume = "2007-12",
series = "CentER Discussion Paper",
publisher = "Econometrics",
type = "WorkingPaper",
institution = "Econometrics",

}

Cizek, P 2007 'Robust and Efficient Adaptive Estimation of Binary-Choice Regression Models' CentER Discussion Paper, vol. 2007-12, Econometrics, Tilburg.

Robust and Efficient Adaptive Estimation of Binary-Choice Regression Models. / Cizek, P.

Tilburg : Econometrics, 2007. (CentER Discussion Paper; Vol. 2007-12).

Research output: Working paperDiscussion paperOther research output

TY - UNPB

T1 - Robust and Efficient Adaptive Estimation of Binary-Choice Regression Models

AU - Cizek, P.

N1 - Subsequently published in Journal of the American Statistical Association, 2008 Pagination: 30

PY - 2007

Y1 - 2007

N2 - The binary-choice regression models such as probit and logit are used to describe the effect of explanatory variables on a binary response vari- able. Typically estimated by the maximum likelihood method, estimates are very sensitive to deviations from a model, such as heteroscedastic- ity and data contamination. At the same time, the traditional robust (high-breakdown point) methods such as the maximum trimmed like- lihood are not applicable since, by trimming observations, they induce the separation of data and non-identification of parameter estimates. To provide a robust estimation method for binary-choice regression, we con- sider a maximum symmetrically-trimmed likelihood estimator (MSTLE) and design a parameter-free adaptive procedure for choosing the amount of trimming. The proposed adaptive MSTLE preserves the robust prop- erties of the original MSTLE, significantly improves the infinite-sample behavior of MSTLE, and additionally, ensures asymptotic efficiency of the estimator under no contamination. The results concerning the trim- ming identification, robust properties, and asymptotic distribution of the proposed method are accompanied by simulation experiments and an application documenting the infinite-sample behavior of some existing and the proposed methods.

AB - The binary-choice regression models such as probit and logit are used to describe the effect of explanatory variables on a binary response vari- able. Typically estimated by the maximum likelihood method, estimates are very sensitive to deviations from a model, such as heteroscedastic- ity and data contamination. At the same time, the traditional robust (high-breakdown point) methods such as the maximum trimmed like- lihood are not applicable since, by trimming observations, they induce the separation of data and non-identification of parameter estimates. To provide a robust estimation method for binary-choice regression, we con- sider a maximum symmetrically-trimmed likelihood estimator (MSTLE) and design a parameter-free adaptive procedure for choosing the amount of trimming. The proposed adaptive MSTLE preserves the robust prop- erties of the original MSTLE, significantly improves the infinite-sample behavior of MSTLE, and additionally, ensures asymptotic efficiency of the estimator under no contamination. The results concerning the trim- ming identification, robust properties, and asymptotic distribution of the proposed method are accompanied by simulation experiments and an application documenting the infinite-sample behavior of some existing and the proposed methods.

KW - asymptotic efficiency

KW - binary-choice regression

KW - breakdown point

KW - maximum likelihood estimation

KW - robust estimation

KW - trimming

M3 - Discussion paper

VL - 2007-12

T3 - CentER Discussion Paper

BT - Robust and Efficient Adaptive Estimation of Binary-Choice Regression Models

PB - Econometrics

CY - Tilburg

ER -

Cizek P. Robust and Efficient Adaptive Estimation of Binary-Choice Regression Models. Tilburg: Econometrics. 2007. (CentER Discussion Paper).