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• W3100213981 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." @default.
• W3100213981 created "2020-11-23" @default.
• W3100213981 creator A5007070769 @default.
• W3100213981 creator A5081850677 @default.
• W3100213981 date "2008-08-01" @default.
• W3100213981 modified "2023-10-03" @default.
• W3100213981 title "Stochastic Approximation and Newton’s Estimate of a Mixing Distribution" @default.
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• W3100213981 doi "https://doi.org/10.1214/08-sts265" @default.
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