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Asymptotic inference in discrete response models

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Abstract

Regression models for discrete responses have found numerous applications. We consider logit, probit and cumulative logit models for qualitative data, and the loglinear and linear Poisson model for counted data. Statistical analysis of these models relies heavily on asymptotic likelihood theory, i.e. asymptotic properties of the maximum likelihood estimator and the likelihood ratio as well as related test statistics. In practical situations, previously published conditions assuring these properties may be too strong, or it is difficult to see whether they apply. This paper contributes to a clarification of this point and characterizes to some extent situations where asymptotic theory is applicable and where it is not. In particular, sharp upper bounds on the admissible growth of regressors are given.

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Authors and Affiliations

  1. Universität Regensburg, Postfach, D-8400, Regensburg

    Ludwig Fahrmeir & Heinz Kaufmann

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  1. Ludwig Fahrmeir
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  2. Heinz Kaufmann
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Fahrmeir, L., Kaufmann, H. Asymptotic inference in discrete response models. Statistische Hefte 27, 179–205 (1986). https://doi.org/10.1007/BF02932567

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  • DOI: https://doi.org/10.1007/BF02932567

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