Sankhya: The Indian Journal of Statistics

2002, Volume 64, Series A, Pt. 2, 306--322

ON A NONPARAMETRIC RECURSIVE ESTIMATOR OF THE MIXING DISTRIBUTION

By

MICHAEL A. NEWTON, University of Wisconsin-Madison, USA

SUMMARY. Routinely in statistical applications hierarchical models arise in which unobserved random effects contribute to heterogeneity amongst sampling units. An easily computable, smooth nonparametric estimate of the underlying mixing distribution can be derived as an approximate nonparametric Bayes estimate under a Dirichlet process prior. I discuss the recursive estimation algorithm, its consistency properties, and its application in several examples, including its use as a model diagnostic in the analysis of DNA microarray gene expression data.

*AMS (1991) subject classification}. *Primary 65C60; secondary 62G07.

*Key words and phrases: *Random effects distribution, hierarchical modeling, stochastic approximation algorithm, Dirichlet process.