Asymptotic properties of the EM algorithm estimate for normal mixture models with component specific variances

Nityasuddhi, Dechavudh; Böhning, Dankmar

doi:10.1016/s0167-9473(02)00176-7

Cited by 29 publications

(22 citation statements)

References 4 publications

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“…Letŷ be the estimator for the treatment effects in the patients truly with the molecular target obtained from the EM algorithm. Nityasuddhi and Bo¨hning [13] show that the estimator obtained under the EM algorithm is asymptotic unbiased. Let S 2 B denote the estimator of the variance ofŷ obtained by the bootstrap procedure as demonstrated in the Appendix.…”

Section: The Proposed Proceduresmentioning

confidence: 99%

Inference on treatment effects for targeted clinical trials under enrichment design

Liu¹,

Lin²,

Chow³

2009

Pharmaceutical Statistics

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After completion of a human genome project, the disease targets at molecular level can be identified. As a result, treatment modality for molecular targets can be developed. In practice, targeted clinical trials are usually conducted for evaluation of the possibility and feasibility of the individualized treatment of patients. However, the accuracy of diagnostic devices for identification of such molecular targets is usually not perfect. Therefore, some of the patients enrolled in targeted clinical trials with a positive result by the diagnostic device might not have the specific molecular targets and hence the treatment effects of the targeted drugs estimated from targeted clinical trials could be biased for the patient population truly with the molecular targets. Under an enrichment design for targeted clinical trials, we propose to use the EM algorithm and bootstrap method for obtaining the inference of the treatment effects of the targeted drugs in the patient population truly with molecular targets. A simulation study was conducted to empirically investigate the bias and variability of the proposed estimator and the size and power of the proposed testing method. Simulation results demonstrate that the proposed estimator is unbiased with adequate precision and the confidence interval can provide satisfactory coverage probability. In addition, the proposed testing procedure can adequately control the size with sufficient power. A practical example illustrates the utility of the proposed method.

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Section: The Proposed Proceduresmentioning

confidence: 99%

Inference on treatment effects for targeted clinical trials under enrichment design

Liu¹,

Lin²,

Chow³

2009

Pharmaceutical Statistics

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“…As recommended in the literature, in practical applications, it is helpful to run the EM algorithm several times using different starting values to obtain more stable estimates (see Muthen & Shedden (1999), Nityasuddhi & Bohning (2003) and Yao (2013), etc).…”

Section: The Proposed Estimationmentioning

confidence: 99%

Parameters Estimation for Mixed Generalized Inverted Exponential Distributions with Type-II Progressive Hybrid Censoring

Tian¹,

Yang²,

Li³

et al. 2016

HJMS

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The type-II progressive hybrid censoring scheme, which is a mixture of type-II progressive and hybrid censoring schemes, has become substantially fashionable due to its flexibility of allowing for random removals of the remaining survival units at each failure time and terminating the experiment at a pre-specified time. In the literature, this censoring scheme has been used to analyze lifetime data for general population distributions such as exponential distributions and Weibull distributions. However, we seldom focus on parameter estimations for the mixture distribution, which is an important class of models in reliability analysis. This paper aims to investigate the estimation problem of mixed generalized inverted exponential distribution (MGIED) under the type-II progressive hybrid censoring scheme. The maximum likelihood estimators (MLEs) of the model are obtained via EM algorithm. Some simulations are implemented and a case of analysis is provided to illustrate the proposed method.

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“…We consider a mixture of k normal densities

f_{j} (y | θ_{j}) (j = 1, \dots, k)

with parameters

θ = (μ_{1}, \dots, μ_{k}, σ_{1}, \dots, σ_{k})

and unknown mixing proportions

p = (p_{1}, \dots, p_{k})

f (y | θ) = \sum_{j = 1}^{k} p_{j} f_{j} (y | μ_{j}, σ_{j})

with

\sum_{j = 1}^{k} p_{j} = 1 .

In the case of normal mixtures with component‐specific variances, the log‐likelihood is unbounded and attains

+ \infty

for certain values of the parameter space (Nityasuddhi and Böhning, ). Therefore, standard deviation is held constant, so that

σ = σ_{j} (j = 1, \dots, k)

.…”

Section: Finite Mixture Model Without Missing Datamentioning

confidence: 99%

Treatment of nonignorable missing data when modeling unobserved heterogeneity with finite mixture models

Lehmann,

Schlattmann

2016

Biometrical J

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Multiple imputation has become a widely accepted technique to deal with the problem of incomplete data. Typically, imputation of missing values and the statistical analysis are performed separately. Therefore, the imputation model has to be consistent with the analysis model. If the data are analyzed with a mixture model, the parameter estimates are usually obtained iteratively. Thus, if the data are missing not at random, parameter estimation and treatment of missingness should be combined. We solve both problems by simultaneously imputing values using the data augmentation method and estimating parameters using the EM algorithm. This iterative procedure ensures that the missing values are properly imputed given the current parameter estimates. Properties of the parameter estimates were investigated in a simulation study. The results are illustrated using data from the National Health and Nutrition Examination Survey.

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Asymptotic properties of the EM algorithm estimate for normal mixture models with component specific variances

Cited by 29 publications

References 4 publications

Inference on treatment effects for targeted clinical trials under enrichment design

Inference on treatment effects for targeted clinical trials under enrichment design

Parameters Estimation for Mixed Generalized Inverted Exponential Distributions with Type-II Progressive Hybrid Censoring

Treatment of nonignorable missing data when modeling unobserved heterogeneity with finite mixture models

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