Goodness-of-Fit Tests Based on Kullback-Leibler Information

Şenoğlu, Birdal; Sürücü, Barış

doi:10.1109/tr.2004.833319

Cited by 14 publications

(10 citation statements)

References 40 publications

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“…A goodness-of-fit statistic can be readily obtained by transforming the KullbackLeibler distance D j to test the null hypothesis that the transcriptome of a given tissue is statistically equal to a given distribution (24). Another issue is the estimation of confidence intervals for H j , D j , ␦ j , and S i that can be obtained by the bootstrap method and will be presented elsewhere.…”

Section: Analysis Of Human Datamentioning

confidence: 99%

Defining diversity, specialization, and gene specificity in transcriptomes through information theory

Martínez

Reyes-Valdés

2008

Proc. Natl. Acad. Sci. U.S.A.

114

130

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The transcriptome is a set of genes transcribed in a given tissue under specific conditions and can be characterized by a list of genes with their corresponding frequencies of transcription. Transcriptome changes can be measured by counting gene tags from mRNA libraries or by measuring light signals in DNA microarrays. In any case, it is difficult to completely comprehend the global changes that occur in the transcriptome, given that thousands of gene expression measurements are involved. We propose an approach to define and estimate the diversity and specialization of transcriptomes and gene specificity. We define transcriptome diversity as the Shannon entropy of its frequency distribution. Gene specificity is defined as the mutual information between the tissues and the corresponding transcript, allowing detection of either housekeeping or highly specific genes and clarifying the meaning of these concepts in the literature. Tissue specialization is measured by average gene specificity. We introduce the formulae using a simple example and show their application in two datasets of gene expression in human tissues. Visualization of the positions of transcriptomes in a system of diversity and specialization coordinates makes it possible to understand at a glance their interrelations, summarizing in a powerful way which transcriptomes are richer in diversity of expressed genes, or which are relatively more specialized. The framework presented enlightens the relation among transcriptomes, allowing a better understanding of their changes through the development of the organism or in response to environmental stimuli.biological complexity ͉ gene expression ͉ microarrays ͉ serial analysis of gene expression (SAGE) ͉ Shannon entropy

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Section: Analysis Of Human Datamentioning

confidence: 99%

Defining diversity, specialization, and gene specificity in transcriptomes through information theory

Martínez

Reyes-Valdés

2008

Proc. Natl. Acad. Sci. U.S.A.

114

130

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“…These plots can only be drawn for tests based on the distance between the theoretical distribution function specified in the null hypothesis and the empirical distribution function, while other tests designed for equivalent situations, such as the quadratic-type tests or the goodness-of-fit tests based on Kullback-Leibler information (see Senoglu and Sürücü, 2004), have acceptance regions that cannot be drawn on probability plots. The test proposed in this article can be extended to other distributions belonging to location and scale families when the parameters are unknown, but in this situation each case should be independently analyzed.…”

Section: Discussionmentioning

confidence: 99%

A New Goodness-of-Fit Test for Censored Data with an Application in Monitoring Processes

Castro-Kuriss

Kelmansky

Leiva

et al. 2009

Communications in Statistics - Simulation and Computation

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In this article, we propose a new goodness-of-fit test for Type I or Type II censored samples from a completely specified distribution. This test is a generalization ofMichael's test for censored data, which is based on the empirical distribution and a variance stabilizing transformation. Using Monte Carlo methods, the distributions of the test statistics are analyzed under the null hypothesis. Tables of quantiles of these statistics are also provided. The power of the proposed test is studied and compared to that of other well-known tests also using simulation. The proposed test is more powerful in most of the considered cases. Acceptance regions for the PP, QQ, and Michael's stabilized probability plots are derived, which enable one to visualize which data contribute to the decision of rejecting the null hypothesis. Finally, an application in quality control is presented as illustration.

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“…For example, Vasicek [8] compares his entropy-based test with several well-known tests, including that of Kolmogorov-Smirnov and the Shapiro-Wilk W test and concludes that the power of the entropy-based test is very competitive and, in many cases, superior to the others. In a somewhat contradictory claim,Şenoǧlu and Sürücü [20] compare Vasicek's to Shapiro-Wilk's W test and conclude that the W test is more powerful 'on the whole. ' We propose a simulation methodology and corresponding graphical presentation of power results for tests of normality.…”

Section: Methods Of Comparisonmentioning

confidence: 99%

“…Several recent papers build on Vasicek's entropy-based test, such as work by Esteban et al [18], Song [19], andŞenoǧlu and Sürücü [20]. Finally, a number of tests of normality based on order statistics have appeared recently, including the work of Glen et al [21] and of Balakrishnan et al [22].…”

Section: Related Literaturementioning

confidence: 99%

A tool for systematically comparing the power of tests for normality

Breton

DeVore

Brown

2008

Journal of Statistical Computation and Simulation

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In this article, we describe a new approach to compare the power of different tests for normality. This approach provides the researcher with a practical tool for evaluating which test at their disposal is the most appropriate for their sampling problem. Using the Johnson systems of distribution, we estimate the power of a test for normality for any mean, variance, skewness, and kurtosis. Using this characterization and an innovative graphical representation, we validate our method by comparing three well-known tests for normality: the Pearson χ 2 test, the Kolmogorov-Smirnov test, and the D'Agostino-Pearson K 2 test. We obtain such comparison for a broad range of skewness, kurtosis, and sample sizes.We demonstrate that the D'Agostino-Pearson test gives greater power than the others against most of the alternative distributions and at most sample sizes. We also find that the Pearson χ 2 test gives greater power than Kolmogorov-Smirnov against most of the alternative distributions for sample sizes between 18 and 330.

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Goodness-of-Fit Tests Based on Kullback-Leibler Information

Cited by 14 publications

References 40 publications

Defining diversity, specialization, and gene specificity in transcriptomes through information theory

Defining diversity, specialization, and gene specificity in transcriptomes through information theory

A New Goodness-of-Fit Test for Censored Data with an Application in Monitoring Processes

A tool for systematically comparing the power of tests for normality

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