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In real life, we frequently come across data sets that involve someindependent explanatory variable(s) generating a set of ordinal responses.These ordinal responses may correspond to an underlying continuous latentvariable, which is linearly related to the covariate(s), and takes a particular(ordinal) label depending on whether this latent variable takes value in somesuitable interval specified by a pair of (unknown) cut-offs. The most efficientway of estimating the unknown parameters (i.e., the regression coefficients andthe cut-offs) is the method of maximum likelihood (ML). However, contaminationin the data set either in the form of misspecification of ordinal responses, orthe unboundedness of the covariate(s), might destabilize the likelihoodfunction to a great extent where the ML based methodology might lead tocompletely unreliable inferences. In this paper, we explore a minimum distanceestimation procedure based on the popular density power divergence (DPD) toyield robust parameter estimates for the ordinal response model. This paperhighlights how the resulting estimator, namely the minimum DPD estimator(MDPDE), can be used as a practical robust alternative to the classicalprocedures based on the ML. We rigorously develop several theoreticalproperties of this estimator, and provide extensive simulations to substantiatethe theory developed.

Robust and Efficient Estimation in Ordinal Response Models using the Density Power Divergence