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2017 Robust inference for ordinal response models
Maria Iannario, Anna Clara Monti, Domenico Piccolo, Elvezio Ronchetti
Electron. J. Statist. 11(2): 3407-3445 (2017). DOI: 10.1214/17-EJS1314


The present paper deals with the robustness of estimators and tests for ordinal response models. In this context, gross-errors in the response variable, specific deviations due to some respondents’ behavior, and outlying covariates can strongly affect the reliability of the maximum likelihood estimators and that of the related test procedures.

The paper highlights that the choice of the link function can affect the robustness of inferential methods, and presents a comparison among the most frequently used links. Subsequently robust $M$-estimators are proposed as an alternative to maximum likelihood estimators. Their asymptotic properties are derived analytically, while their performance in finite samples is investigated through extensive numerical experiments either at the model or when data contaminations occur. Wald and $t$-tests for comparing nested models, derived from $M$-estimators, are also proposed. $M$ based inference is shown to outperform maximum likelihood inference, producing more reliable results when robustness is a concern.


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Maria Iannario. Anna Clara Monti. Domenico Piccolo. Elvezio Ronchetti. "Robust inference for ordinal response models." Electron. J. Statist. 11 (2) 3407 - 3445, 2017.


Received: 1 March 2017; Published: 2017
First available in Project Euclid: 6 October 2017

zbMATH: 06790064
MathSciNet: MR3709859
Digital Object Identifier: 10.1214/17-EJS1314

Keywords: link functions , M-estimation , Ordinal response models , robust estimators , Robust tests , robust weights , shelter effects


Vol.11 • No. 2 • 2017
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