ICSA Book Series in Statistics
Volume 9 / 2015
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Article
Open AccessNLRC5 promotes endometrial carcinoma progression by regulating NF-κB pathway-mediated mismatch repair gene deficiency
The innate immune molecule NLR family CARD domain-containing 5 (NLRC5) plays a significant role in endometrial carcinoma (EC) immunosurveillance. However, NLRC5 also plays a protumor role in EC cells. Mismatch...
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Article
Open AccessIdentification of a serum-based microRNA signature that detects recurrent oral squamous cell carcinoma before it is clinically evident
Survival rates for oral squamous cell carcinoma (OSCC) have remained poor for decades, a fact largely attributable to late-stage diagnoses and high recurrence rates. We report analysis of serum miRNA expressio...
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Article
A probabilistic dual hesitant fuzzy multi-attribute decision-making method based on entropy and cross-entropy
The probabilistic dual hesitant fuzzy set (PDHFS), as an extension of generalization of the dual hesitant fuzzy set, contains not only the hesitation values of membership degree (MD) and non-membership degree ...
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Article
Mixture of shifted binomial distributions for rating data
Rating data are a kind of ordinal categorical data routinely collected in survey sampling. The response value in such applications is confined to a finite number of ordered categories. Due to population hetero...
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Book Series
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Chapter
A Few Key Probability Theory Results
The materials presented in this book are undeniably technical in nature. We established numerous theoretical conclusions by relying on classical probability theory results. Although these conclusions are well-...
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Chapter
Maximum Likelihood Estimation Under Finite Mixture Models
Chapter 3 centers our attention on finite mixture models. Within this framework, we establish that the consistent results achieved with the maximum likelihood estimator for nonparametric mixture models remain ...
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Chapter
Order Selection of the Finite Mixture Models
The order selection problem, in contrast to determining whether a lower-ordered finite mixture model should be rejected in favor of a higher-ordered model, seeks to answer the question of what constitutes the ...
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Book
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Chapter
Geometric Properties of Non-parametric MLE and Numerical Solutions
In Chap. 6, our attention turns to numerical solutions for maximum likelihood estimation within the context of nonparametric mixture models. The challenge arises from the infinite dimension of the nonparametri...
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Chapter
Rate of Convergence
The fundamental requirement in data analysis is the consistent estimation of a parameter. As the sample size increases, the precision of the estimator naturally improves, following a rate of
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Chapter
Modified Likelihood Ratio Test
While achieving a profound understanding of the limiting distribution of the likelihood ratio test under mixture models is indeed a grand success, translating this knowledge into concrete data analysis procedu...
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Chapter
em-Test for Homogeneity
The modified likelihood ratio test represents a significant advancement over the limitations of conventional likelihood ratio tests. It is applicable to a specific class of finite mixture models, although its ...
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Chapter
em-Test for Univariate Finite Gaussian Mixture Models
While the success of the EM-test in the previous two chapters was confined to finite mixture models with subpopulation distributions belonging to a one-parameter distribution family, the underlying principle o...
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Chapter
Introduction to Mixture Models
In Chap. 1, we introduce the fundamental concept of a statistical model and provide a detailed definition of both mixture models and finite mixture models. We uncover the latent structure inherent in mixture m...
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Chapter
Consistent Estimation Under Finite Gamma Mixture
The application of finite Gamma mixture models is prevalent when working with strictly positive observations. Surprisingly, the likelihood function within this framework is unbounded, theoretically leading to ...
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Chapter
Finite Mixture MLE and EM Algorithm
The latent structure inherent in mixture models offers a fitting scenario for the renowned EM algorithm. In Chap. 7, we begin by offering a general overview and then get into comprehensive explanations of the ...
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Chapter
Test of Homogeneity
The quest for effective tests of homogeneity within mixture models has a long history. An illustrative example provided by Hartigan shows that the likelihood ratio statistic, unlike its counterpart in regular ...
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Chapter
Likelihood Ratio Test for Homogeneity
Despite the successful application of the C( α \(\alpha \) ) test, statisticians continue to ...
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Chapter
Modified Likelihood Ratio Test for Higher Order
Chapter 12 centers around the modified likelihood test for high-order null hypotheses within the finite mixture model. While the fundamental concept of testing for high-order null hypotheses remains akin to th...
