A Penalty Function Approach to Smoothing Large Sparse Contingency Tables

The Annals of Statistics · 1983 · Volume 11 · Issue 1

Abstract

Probabilities in a large sparse contingency table are estimated by maximizing the likelihood modified by a roughness penalty. It is shown that if certain smoothness criteria on the underlying probability vector are met, the estimator proposed is consistent in a one-dimensional table under a sparse asymptotic framework. Suggestions are made for techniques to apply the estimator in practice, and generalization to higher dimensional tables is considered.

Keywords

62E20, 62G05, Large sparse contingency tables, maximum penalized likelihood, smoothing of probability estimates, sparse asymptotics

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