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UPA Perpustakaan Universitas Jember

Robustness issues for CUB models

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The present paper deals with a parametric class of models implemented for
ordered categorical data, denoted as cub model, which is defined as a discrete mixture
of a shifted binomial and a uniform random variable. For these models, robustness
issues are considered. In particular, the influence function is introduced and subse-
quently used to define the robustness measures for categorical data. By exploiting the
peculiar parametrization of the cub models, diagnostic plots are proposed which allow
to display the effect of a contamination in the data, simultaneously for all categories.
The breakdown point is also considered and a computational procedure is suggested to
determine an upper bound. The paper provides evidence that, despite the limited range
of the support, contaminations in the data can heavily affect the inferential procedures
and hence robustness topics are indeed relevant for ordinal data.

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