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A review of 20 years of naive tests of significance for high-dimensional mean vectors and covariance matrices

Consistency of the penalized MLE for two-parameter gamma mixture models

Robust U-type test for high dimensional regression coefficients using refitted cross-validation variance estimation

Penalized least squares estimation with weakly dependent data

On high-dimensional change point problem

Identifying the limiting distribution by a general approach of Stein’s method

Time-varying latent model for longitudinal data with informative observation and terminal event times

Random difference equations with subexponential innovations

Joint modeling of longitudinal proportional measurements and survival time with a cure fraction

Functional singular component analysis based functional additive models

On nonparametric change point estimator based on empirical characteristic functions

Degrees of freedom in low rank matrix estimation

Exponential inequalities under the sub-linear expectations with applications to laws of the iterated logarithm

Sure feature screening for high-dimensional dichotomous classification

Overlapped groupwise dimension reduction

Dynamic single-index model for functional data

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Consistency of the penalized MLE for two-parameter gamma mixture models

Content Provider	Springer Nature Link
Author	Chen, JiaHua Li, ShaoTing Tan, XianMing
Copyright Year	2016
Abstract	Two-parameter gamma distributions are widely used in liability theory, lifetime data analysis, financial statistics, and other areas. Finite mixtures of gamma distributions are their natural extensions, and they are particularly useful when the population is suspected of heterogeneity. These distributions are successfully employed in various applications, but many researchers falsely believe that the maximum likelihood estimator of the mixing distribution is consistent. Similarly to finite mixtures of normal distributions, the likelihood function under finite gamma mixtures is unbounded. Because of this, each observed value leads to a global maximum that is irrelevant to the true distribution. We apply a seemingly negligible penalty to the likelihood according to the shape parameters in the fitted model. We show that this penalty restores the consistency of the likelihoodbased estimator of the mixing distribution under finite gamma mixture models. We present simulation results to validate the consistency conclusion, and we give an example to illustrate the key points.
Starting Page	2301
Ending Page	2318
Page Count	18
File Format	PDF
ISSN	16747283
Journal	Science in China Series A: Mathematics
Volume Number	59
Issue Number	12
e-ISSN	18691862
Language	English
Publisher	Science China Press
Publisher Date	2016-07-29
Publisher Place	Beijing
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	constrained MLE identifiability finite mixture penalized likelihood Stirling formula Applications of Mathematics
Content Type	Text
Resource Type	Article
Subject	Mathematics

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