# Generalized likelihood ratio test for normal mixtures

@article{Jiang2016GeneralizedLR, title={Generalized likelihood ratio test for normal mixtures}, author={Wenhua Jiang and Cun-Hui Zhang}, journal={Statistica Sinica}, year={2016} }

Let X1, . . . , Xn be independent observations with Xi ∼ N(θi, 1), where (θ1, . . . , θn) is an unknown vector of normal means. Let fn(x) = ∑n i=1(d/dx)Pn{Xi ≤ x}/n be the average marginal density of observations. We consider the problem of testing H0 : fn ∈ F0, where F0 is a family of mixture densities. This includes detecting nonzero normal means with F0 = {fδ0} and testing homogeneity in mixture models with F0 = {fδμ}. We study a generalized likelihood ratio test (GLRT) based on the…

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## References

SHOWING 1-10 OF 27 REFERENCES

Probability inequalities for likelihood ratios and convergence rates of sieve MLEs

- Mathematics
- 1995

Let Y 1 ,...,Y n be independent identically distributed with density p 0 and let F be a space of densities. We show that the supremum of the likelihood ratios Π i=1 n p(Y i )/p 0 (Y i ), where the…

General maximum likelihood empirical Bayes estimation of normal means

- Mathematics, Computer Science
- 2009

Simulation experiments demonstrate that the GMLEB outperforms the James―Stein and several state-of-the-art threshold estimators in a wide range of settings without much down side.

Entropies and rates of convergence for maximum likelihood and Bayes estimation for mixtures of normal densities

- Mathematics
- 2001

We study the rates of convergence of the maximum likelihood estimator (MLE) and posterior distribution in density estimation problems, where the densities are location or location-scale mixtures of…

GENERALIZED MAXIMUM LIKELIHOOD ESTIMATION OF NORMAL MIXTURE DENSITIES

- Mathematics
- 2009

We study the generalized maximum likelihood estimator of location and location-scale mixtures of normal densities. A large deviation inequality is ob- tained which provides the convergence rate n…

TESTING FOR HOMOGENEITY IN MIXTURE MODELS

- MathematicsEconometric Theory
- 2017

Statistical models of unobserved heterogeneity are typically formalized as mixtures of simple parametric models and interest naturally focuses on testing for homogeneity versus general mixture…

Higher criticism for detecting sparse heterogeneous mixtures

- Mathematics
- 2004

Higher criticism, or second-level significance testing, is a multiplecomparisons concept mentioned in passing by Tukey. It concerns a situation where there are many independent tests of significance…

The average likelihood ratio for large-scale multiple testing and detecting sparse mixtures

- Mathematics
- 2013

Large-scale multiple testing problems require the simultaneous assessment of many p-values. This paper compares several methods to assess the evidence in multiple binomial counts of p-values: the…

Asymptotics for likelihood ratio tests under loss of identifiability

- Mathematics
- 2003

This paper describes the large sample properties of the likelihood ratio test statistic (LRTS) when the parameters characterizing the true null distribution are not unique. It is well known that the…

CONSISTENCY OF THE MAXIMUM LIKELIHOOD ESTIMATOR IN THE PRESENCE OF INFINITELY MANY INCIDENTAL PARAMETERS

- Mathematics
- 1956

0 and ai. The parameter 0, upon which all the distributions depend, is called "structural"; the parameters {aiI} are called "incidental". Throughout this paper we shall assume that the Xi, are…