# Revisiting consistency of a recursive estimator of mixing distributions

@inproceedings{Dixit2021RevisitingCO, title={Revisiting consistency of a recursive estimator of mixing distributions}, author={Vaidehi Dixit and Ryan Martin}, year={2021} }

Estimation of the mixing distribution under a general mixture model is a very difficult problem, especially when the mixing distribution is assumed to have a density. Predictive recursion (PR) is a fast, recursive algorithm for nonparametric estimation of a mixing distribution/density in general mixture models. However, the existing PR consistency results make rather strong assumptions, some of which fail for a class of mixture models relevant for monotone density estimation, namely, scale…

## One Citation

### A PRticle filter algorithm for nonparametric estimation of multivariate mixing distributions

- Computer Science
- 2022

A new strategy is proposed, which is referred to as PRticle ﬁlter , wherein the basic PR algorithm is augmented with a adaptively reweights an initial set of particles along the updating sequence which are used to obtain Monte Carlo approximations of the normalizing constants.

## References

SHOWING 1-10 OF 47 REFERENCES

### CONSISTENCY OF A RECURSIVE ESTIMATE OF MIXING DISTRIBUTIONS

- Mathematics
- 2009

Mixture models have received considerable attention recently and Newton [Sankhyā Ser. A 64 (2002) 306-322] proposed a fast recursive algorithm for estimating a mixing distribution. We prove almost…

### Estimating a Mixing Distribution on the Sphere Using Predictive Recursion

- MathematicsSankhya B
- 2022

Mixture models are commonly used when data show signs of heterogeneity and, often, it is important to estimate the distribution of the latent variable responsible for that heterogeneity. This is a…

### Concentration rate and consistency of the posterior distribution for selected priors under monotonicity constraints

- Mathematics, Computer Science
- 2014

It is proved that the posterior distribution based on both priors concentrates at the rate (n/log(n))−1/3, which is the minimax rate of estimation up to a log(n) factor.

### Semiparametric inference in mixture models with predictive recursion marginal likelihood

- Mathematics
- 2011

Predictive recursion is an accurate and computationally efficient algorithm for nonparametric estimation of mixing densities in mixture models. In semiparametric mixture models, however, the…

### Stochastic Approximation and Newton’s Estimate of a Mixing Distribution

- Mathematics
- 2008

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…

### On empirical estimation of mode based on weakly dependent samples

- MathematicsComput. Stat. Data Anal.
- 2020

### EM Estimation for Finite Mixture Models with Known Mixture Component Size

- MathematicsCommun. Stat. Simul. Comput.
- 2015

This work considers the use of an EM algorithm for fitting finite mixture models when mixture component size is known and shows robustness to the choice of starting values and exhibits numerically stable convergence properties.

### Empirical Priors and Posterior Concentration Rates for a Monotone Density

- MathematicsSankhya A
- 2018

In a Bayesian context, prior specification for inference on monotone densities is conceptually straightforward, but proving posterior convergence theorems is complicated by the fact that desirable…

### Maximum Smoothed Likelihood Density Estimation for Inverse Problems

- Mathematics
- 1995

We consider the problem of estimating a pdf f from samples X 1 , X 2 ,..., X n of a random variable with pdf Kf, where K is a compact integral operator. We employ a maximum smoothed likelihood…

### A nonparametric empirical Bayes framework for large-scale multiple testing.

- MathematicsBiostatistics
- 2012

Simulations and real data examples demonstrate that the proposed PRtest's careful handling of the nonnull density can give a much better fit in the tails of the mixture distribution which, in turn, can lead to more realistic conclusions.