A recursive algorithm for nonparametric analysis with missing data.

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A recursive algorithm for nonparametric analysis with missing data.
(Formerly, ``A partial predictive recursion'')

Michael A. Newton ,
and Yunlei Zhang

* Biometrika *, ** 86 **, 15-26, 1999.

Formerly Technical Report 965, Department of Statistics,
University of Wisconsin, Madison. First issued, August 1996.

### Abstract:

Nonparametric Bayesian analysis has proved to be computationally
demanding when data are arbitrarily censored, truncated, or otherwise
degraded prior to observation. The mixture of Dirichlet processes
posterior that arises in such problems has been analyzed most effectively
using Markov chain Monte Carlo. As a computationally simple alternative,
we introduce a recursive approximation
based on one-step posterior predictive distributions.
Asymptotic calculations provide theoretical support for
this approximation, and we investigate its actual behavior
in several numerical examples.
The method overcomes a diffuse prior defect inherent in the
exact Bayes estimate from interval censored data.
From a non-Bayesian perspective, this new recursion
may be used to obtain solutions of the self-consistency
equation.

*Key words:* Dirichlet process,
interval censoring, nonparametric mixtures, nonparametric maximum
likelihood, Polya urn, prior feedback, random effects, self-consistency, truncation.

Data sets analysed