# Stochastic Approximation Algorithm for Estimating Mixing Distribution for Dependent Observations

Estimating 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.

## Authors

• 3 publications
• 3 publications
• ### On nonparametric estimation of a mixing density via the predictive recursion algorithm

Nonparametric estimation of a mixing density based on observations from ...
12/05/2018 ∙ by Ryan Martin, et al. ∙ 0

• ### Estimating β-mixing coefficients

The literature on statistical learning for time series assumes the asymp...
03/04/2011 ∙ by Daniel J. McDonald, et al. ∙ 0

• ### Nonparametric estimation of the conditional density function with right-censored and dependent data

In this paper, we study the local constant and the local linear estimato...
07/10/2019 ∙ by Xianzhu Xiong, et al. ∙ 0

• ### Bayesian estimation of a decreasing density

Suppose X_1,..., X_n is a random sample from a bounded and decreasing de...
01/08/2018 ∙ by Geurt Jongbloed, et al. ∙ 0

• ### Estimating a mixing distribution on the sphere using predictive recursion

Mixture models are commonly used when data show signs of heterogeneity a...
10/20/2020 ∙ by Vaidehi Dixit, et al. ∙ 0

• ### GradientDICE: Rethinking Generalized Offline Estimation of Stationary Values

We present GradientDICE for estimating the density ratio between the sta...
01/29/2020 ∙ by Shangtong Zhang, et al. ∙ 51