A Constrained Formulation of Maximum-Likelihood Estimation for Normal Mixture Distributions

Hathaway, Richard J.

doi:10.1214/aos/1176349557

Cited by 340 publications

(266 citation statements)

References 9 publications

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“…Based on the plot of p(k) versus k, one can also clearly see how the cut point C in (6) affects the constrained MLE (Hathaway 1985(Hathaway , 1986). We will demonstrate this using examples in Section 3.…”

Section: Mixtures Of Two Componentsmentioning

confidence: 99%

“…Instead, when the likelihood is unbounded, we define the MLE as the maximum interior/local mode. Hathaway (1985) provided some theoretical support of using the maximum interior/local mode.…”

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confidence: 98%

“…See Hathaway (1985Hathaway ( , 1986 and Bezdak, Hathaway, and Huggins (1985) for more detail. However, a big challenge for this method is to choose the appropriate cut point C. If C is too large, it is possible that the consistent local maxima does not belong to the constrained parameter space Ω C and thus the found estimate will be misleading.…”

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confidence: 99%

“…Unlike the constrained EM algorithm (Hathaway, 1985(Hathaway, , 1986, our proposed method does not need to specify a cut point C. In addition, based on our proposed method, we can clearly check whether there are some other minor interior modes and see how the choice of C in (2) affects the constrained global MLE.…”

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confidence: 99%

“…Using the simulation study and a real data application, we demonstrate the effectiveness of our proposed method and show how the selection of cut point C affects the constrained MLE (Hathaway, 1985(Hathaway, , 1986.…”

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confidence: 99%

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A profile likelihood method for normal mixture with unequal variance

Yao

2010

Journal of Statistical Planning and Inference

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How to cite this manuscriptIf you make reference to this version of the manuscript, use the following information: AbstractIt is well known that the normal mixture with unequal variance has unbounded likelihood and thus the corresponding global maximum likelihood estimator (MLE) is undefined. One of the commonly used solutions is to put a constraint on the parameter space so that the likelihood is bounded and then one can run the EM algorithm on this constrained parameter space to find the constrained global MLE. However, choosing the constraint parameter is a difficult issue and in many cases different choices may give different constrained global MLE. In this article, we propose a profile log likelihood method and a graphical way to find the maximum interior mode. Based on our proposed method, we can also see how the constraint parameter, used in the constrained EM algorithm, affects the constrained global MLE. Using two simulation examples and a real data application, we demonstrate the success of our new method in solving the unboundness of the mixture likelihood and locating the maximum interior mode.

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Section: Mixtures Of Two Componentsmentioning

confidence: 99%

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confidence: 98%

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confidence: 99%

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confidence: 99%

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confidence: 99%

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A profile likelihood method for normal mixture with unequal variance

Yao

2010

Journal of Statistical Planning and Inference

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Global soil moisture bimodality in satellite observations and climate models

Vilasa¹,

Miralles

Dolman³

2017

JGR Atmospheres

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A new diagnostic metric based on soil moisture bimodality is developed in order to examine and compare soil moisture from satellite observations and Earth System Models. The methodology to derive this diagnostic is based on maximum likelihood estimator encoded into an iterative algorithm, which is applied to the soil moisture probability density function. This metric is applied to satellite data from the Advanced Microwave Scanning Radiometer for the Earth Observing System and global climate models data from the Coupled Model Intercomparison Project Phase 5 (CMIP5). Results show high soil moisture bimodality in transitional climate areas and high latitudes, potentially associated with land‐atmosphere feedback processes. When comparing satellite versus climate models, a clear difference in their soil moisture bimodality is observed, with systematically higher values in the case of CMIP5 models. These differences appear related to areas where land‐atmospheric feedback may be overestimated in current climate models.

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2011

Maximum Likelihood Estimation and Inference

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A Constrained Formulation of Maximum-Likelihood Estimation for Normal Mixture Distributions

Cited by 340 publications

References 9 publications

A profile likelihood method for normal mixture with unequal variance

A profile likelihood method for normal mixture with unequal variance

Global soil moisture bimodality in satellite observations and climate models

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