Journal ArticleDOI
Non-regular maximum likelihood problems
Russell C. H. Cheng,L. Traylor +1 more
TLDR
In this paper, the authors reviewed and discussed four non-regular estimation problems and compared modified likelihood and spacings methods with the Box-Cox shifted power transform (BCPT).Abstract:
Four non-regular estimation problems are reviewed and discussed. One (the unbounded likelihood problem) involves distributions with infinite spikes, for which maximum likelihood can fail to give consistent estimators. A comparison is made with modified likelihood and spacings methods which do give efficient estimators in this case. An application to the Box-Cox shifted power transform is given. The other three problems occur when the true parameter lies in some special subregion. In one (the constrained parameter problem) the subregion is a boundary. The other two (the embedded model and the indeterminate parameters problems) occur when the model takes on a special form in the subregion. These last two problems have previously been investigated separately. We show that they are equivalent in some situations. Both often arise in non-linear models and we give a directed graph approach which allows for their occurrence in nested model building. It is argued that many non-regular problems can be handled systematically without having to resort to elaborate technical assumptions. Relatively uncomplicated methods may be used provided that the underlying nature of the non-regularity is understoodread more
Citations
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Journal ArticleDOI
Bayesian analysis of stochastic volatility models with fat-tails and correlated errors
TL;DR: In this article, the authors extend the basic univariate stochastic volatility model to allow for a so-called leverage effect via correlation between the volatility and mean innovations, and for fat-tails in the mean equation innovation.
Journal ArticleDOI
Quasi-likelihood and its application : a general approach to optimal parameter estimation
TL;DR: In this article, an alternative approach is proposed: E-sufficiency, asymptotic confidence zones of minimum size, bypassing the Likelihood, and by hypothesis testing.
Journal ArticleDOI
A modified likelihood ratio test for homogeneity in finite mixture models
TL;DR: In this article, a modified LRT for homogeneity in finite mixture models with a general parametric kernel distribution family is proposed, which has a X2-type of null limiting distribution and is asymptotic most powerful under local alternatives.
Journal ArticleDOI
QMPE: estimating Lognormal, Wald, and Weibull RT distributions with a parameter-dependent lower bound.
TL;DR: This work describes and test quantile maximum probability estimator (QMPE), an open-source ANSI Fortran 90 program for response time distribution estimation that enables users to estimate parameters for the ex-Gaussian and Gumbel (1958) distributions, along with three “shifted” distributions.
Journal ArticleDOI
Testing for a finite mixture model with two components
TL;DR: In this article, a modified likelihood ratio (MLR) test is proposed for finite mixture models with normal, binomial and Poisson kernels, where the estimates of the parameters are obtained from a modified probability function.
References
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Book
Statistical analysis of finite mixture distributions
TL;DR: This course discusses Mathematical Aspects of Mixtures, Sequential Problems and Procedures, and Applications of Finite Mixture Models.
Journal ArticleDOI
Mixture densities, maximum likelihood, and the EM algorithm
TL;DR: This work discusses the formulation and theoretical and practical properties of the EM algorithm, a specialization to the mixture density context of a general algorithm used to approximate maximum-likelihood estimates for incomplete data problems.
Journal ArticleDOI
Asymptotic Properties of Maximum Likelihood Estimators and Likelihood Ratio Tests under Nonstandard Conditions
Steven G. Self,Kung Yee Liang +1 more
TL;DR: In this article, the authors derived the asymptotic distribution of maximum likelihood estimators and likelihood ratio statistics, which is the same as the distribution of the projection of the Gaussian random variable.
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Hypothesis testing when a nuisance parameter is present only under the alternative
TL;DR: In this article, the authors used a test derived from the corresponding family of test statistics appropriate for the case when 0 is given and applied to the two-phase regression problem in the normal case.