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August 2008 Stochastic Approximation and Newton’s Estimate of a Mixing Distribution
Ryan Martin, Jayanta K. Ghosh
Statist. Sci. 23(3): 365-382 (August 2008). DOI: 10.1214/08-STS265


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 [Sankhyā 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. "Stochastic Approximation and Newton’s Estimate of a Mixing Distribution." Statist. Sci. 23 (3) 365 - 382, August 2008.


Published: August 2008
First available in Project Euclid: 28 January 2009

zbMATH: 1329.62361
MathSciNet: MR2483909
Digital Object Identifier: 10.1214/08-STS265

Rights: Copyright © 2008 Institute of Mathematical Statistics


Vol.23 • No. 3 • August 2008
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