Stochastic Approximation Algorithm for Estimating Mixing Distribution for Dependent Observations

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dc.contributor.authorGuha, Nilabja
dc.contributor.authorRoy, Anindya
dc.date.accessioned2021-01-25T18:33:20Z
dc.date.available2021-01-25T18:33:20Z
dc.description.abstractEstimating the mixing density of a mixture distribution remains an interesting problem in statistics literature. Using a stochastic approximation method, Newton and Zhang (1999) introduced a fast recursive algorithm for estimating the mixing density of a mixture. Under suitably chosen weights the stochastic approximation estimator converges to the true solution. In Tokdar et. al. (2009) the consistency of this recursive estimation method was established. However, the proof of consistency of the resulting estimator used independence among observations as an assumption. Here, we extend the investigation of performance of Newton's algorithm to several dependent scenarios. We first prove that the original algorithm under certain conditions remains consistent when the observations are arising form a weakly dependent process with fixed marginal with the target mixture as the marginal density. For some of the common dependent structures where the original algorithm is no longer consistent, we provide a modification of the algorithm that generates a consistent estimator.en_US
dc.description.urihttps://arxiv.org/abs/2006.14734en_US
dc.format.extent42 pagesen_US
dc.genrejournal articles preprintsen_US
dc.identifierdoi:10.13016/m2omds-kok1
dc.identifier.citationNilabja Guha and Anindya Roy, Stochastic Approximation Algorithm for Estimating Mixing Distribution for Dependent Observations, https://arxiv.org/abs/2006.14734en_US
dc.identifier.urihttp://hdl.handle.net/11603/20604
dc.language.isoen_USen_US
dc.relation.isAvailableAtThe University of Maryland, Baltimore County (UMBC)
dc.relation.ispartofUMBC Mathematics Department Collection
dc.relation.ispartofUMBC Faculty Collection
dc.rightsThis item is likely protected under Title 17 of the U.S. Copyright Law. Unless on a Creative Commons license, for uses protected by Copyright Law, contact the copyright holder or the author.
dc.subjectdensityen_US
dc.subjectstochastic approximationen_US
dc.subjectmachine learningen_US
dc.subjectalgorithmen_US
dc.titleStochastic Approximation Algorithm for Estimating Mixing Distribution for Dependent Observationsen_US
dc.typeTexten_US

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