Jayanta K. Ghosh
Stochastic Approximation and Newton's Estimate of a Mixing Distribution.
Fri, 02/18/2011 - 16:01 — SomNambulAuthors: Ryan Martin, Jayanta K. Ghosh
Subjects: Methodology
AbstractMany 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.The Bayes oracle and asymptotic optimality of multiple testing procedures under sparsity.
Fri, 02/19/2010 - 16:01 — SomNambulAuthors: Jayanta K. Ghosh, Malgorzata Bogdan, Arijit Chakrabarti, Florian Frommlet
Subjects: Statistics
AbstractWe investigate the asymptotic optimality of a large class of multiple testing
rules using the framework of Bayesian Decision Theory. We consider a parametric
setup, in which observations come from a normal scale mixture model and assume
that the total loss is the sum of losses for individual tests. Our model can be
used for testing point null hypotheses of no signals (zero effects), as well as
to distinguish large signals from a multitude of very small effects.Consistency of a recursive estimate of mixing distributions.
Tue, 08/25/2009 - 22:41 — SomNambulAuthors: Surya T. Tokdar, Ryan Martin, Jayanta K. Ghosh
Subjects: gr. Statistics
AbstractMixture models have received considerable attention recently and Newton
[Sankhy\={a} Ser. A 64 (2002) 306--322] proposed a fast recursive algorithm for
estimating a mixing distribution. We prove almost sure consistency of this
recursive estimate in the weak topology under mild conditions on the family of
densities being mixed. This recursive estimate depends on the data ordering and
a permutation-invariant modification is proposed, which is an average of the
original over permutations of the data sequence.
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