2020/06/25 by Nilabja Guha, Anindya Roy, Guha, Nilabja +1
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Bayesian Modeling and Causal Inference #FOS: Mathematics #Statistical Methods and Bayesian Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2006.14734
openalex publication_date 2020/06/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Estimating the mixing density of a mixture distribution remains an\ninteresting problem in statistics literature. Using a stochastic approximation\nmethod, Newton and Zhang (1999) introduced a fast recursive algorithm for\nestimating the mixing density of a mixture. Under suitably chosen weights the\nstochastic approximation estimator converges to the true solution. In Tokdar\net. al. (2009) the consistency of this recursive estimation method was\nestablished. However, the proof of consistency of the resulting estimator used\nindependence among observations as an assumption. Here, we extend the\ninvestigation of performance of Newton's algorithm to several dependent\nscenarios. We prove that the original algorithm under certain conditions\nremains consistent even when the observations are arising from a weakly\ndependent stationary process with the target mixture as the marginal density.\nWe show consistency under a decay condition on the dependence among\nobservations when the dependence is characterized by a quantity similar to\nmutual information between the observations.\n