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arXiv · 1102.3592

Stochastic Approximation and Newton's Estimate of a Mixing Distribution

Ryan Martin·Jayanta K. Ghosh
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Abstract

Many statistical problems involve mixture models and the need for computationally efficient methods to estimate the mixing distribution has increased dramatically in recent years. Newton [Sankhya Ser. A 64 (2002) 306--322] proposed a fast recursive algorithm for estimating the mixing distribution, which we study as a special case of stochastic approximation (SA). We begin with a review of SA, some recent statistical applications, and the theory necessary for analysis of a SA algorithm, which includes Lyapunov functions and ODE stability theory. Then standard SA results are used to prove consistency of Newton's estimate in the case of a finite mixture. We also propose a modification of Newton's algorithm that allows for estimation of an additional unknown parameter in the model, and prove its consistency.

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Ryan Martin, Jayanta K. Ghosh. 2011-02-17. Stochastic Approximation and Newton's Estimate of a Mixing Distribution. https://doi.org/10.1214/08-sts265

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