Empirical likelihood ratios applied to goodness-of-fit tests based on sample entropy

Vexler, Albert; Gurevich, Gregory

doi:10.1016/j.csda.2009.09.025

Cited by 63 publications

(92 citation statements)

References 24 publications

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“…This problem restricts the applicability of the proposed test statistic to real data applications. To solve this problem, we use the idea of Vexler and Gurevich (2010), and modify our test as follows,…”

Section: The Dbelr Test Statisticmentioning

confidence: 99%

“…Second, the use of the empirical likelihood method enables us to fully employ the information available from the data in an asymptotically efficient way. Vexler and Gurevich (2010) applied the main idea of empirical likelihood method and proposed a density-based empirical likelihood ratio (DBELR) goodness of fit for normality and uniformity. used the same method and construct a DBELR goodness of fit test for the Inverse Gaussian distribution.…”

Section: Introductionmentioning

confidence: 99%

“…Attractive applications of the empirical likelihood method in epidemiology are presented in Vexler (2014a). Vexler and Gurevich (2010) introduced a general test statistic based on ELR and applied it for the special cases of the normal, exponential and uniform distributions. Further, used the DBELR test statistic for the special case of the IG distribution and proposed a DBELR test for the IG distribution.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Testing Skew-Laplace Distribution Using Density-based Empirical Likelihood Approach

Safavinejad¹,

Jomhoori²,

Noughabi³

2016

JSRI

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Abstract. In this paper, we first describe the skew-Laplace distribution and its properties. We then introduce a goodness of fit test for this distribution according to the density-based empirical likelihood ratio concept. Asymptotic consistency of the proposed test is demonstrated. The critical values and Type I error of the test are obtained by Monte Carlo simulations. Moreover, the empirical distribution function (EDF) tests are considered for the skew-Laplace distribution to show they do not have acceptable Type I error in comparison with the proposed test. Results show that the proposed test has an excellent Type I error which does not depend on the unknown parameters. The results obtained from simulation studies designed to investigate the power of the test are presented, too. The applicability of the proposed test in practice is demonstrated by real data examples.

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Section: The Dbelr Test Statisticmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Testing Skew-Laplace Distribution Using Density-based Empirical Likelihood Approach

Safavinejad¹,

Jomhoori²,

Noughabi³

2016

JSRI

View full text Add to dashboard Cite

show abstract

“…Following their method, more test statistics were proposed by Grzegorzewski and Wieczorkowski (1999), Park and Park (2003), Choi et al (2004), Yousefzadeh and Arghami (2008), Gurevich and Davidson (2008), Alizadeh Noughabi and Arghami (2011b) and Zamanzade and Arghami (2011) based on different entropy estimators including estimators of Vasicek (1976), Van-Es (1992), Ebrahimi et al (1994), Correa (1995) and Alizadeh Noughabi (2010). Vexler and Gurevich (2010) and Gurevich and Vexler (2011) developed empirical likelihood ratio tests for goodness of fit and demonstrated that the well-known goodness of fit tests based on sample entropy and KullbackLeibler information are a product of the proposed empirical likelihood methodology.…”

Section: Introductionmentioning

confidence: 99%

Testing Exponentiality Based on Renyi Entropy of Transformed Data

Abbasnejad¹

2012

JSRI

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Abstract. In this paper, we introduce new tests for exponentiality based on estimators of Renyi entropy of a continuous random variable. We first consider two transformations of the observations which turn the test of exponentiality into one of uniformity and use a corresponding test based on Renyi entropy. Critical values of the test statistics are computed by Monte Carlo simulations. Then, we compare powers of the tests for various alternatives and sample sizes with exponentiality tests based on Kullback-Leibler information proposed by Ebrahimi et al. (1992) and Choi et al. (2004). Our simulation results show that the proposed tests have higher powers than the competitor tests.

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“…In practice, statisticians commonly face a variety of distribution-free comparisons and/or evaluations over all distribution functions of complete and incomplete data subject to different types of measurement errors. In these frameworks, the density-based EL methodology is shown to be very efficient [7][8][9][10]. According to the Neyman-Pearson lemma, the most powerful test statistics have structures that are related to density-based likelihood ratios.…”

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confidence: 99%

A Brief Ode to the Empirical Likelihood Concept

Vexler¹

2015

BBIJ

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Submit Manuscript | http://medcraveonline.com robust likelihood-type techniques. Towards this end, the modern biostatistical literature has shifted focus towards robust and efficient nonparametric likelihood methods [2]. The empirical likelihood (EL) methodology employs the likelihood concept in a distribution-free manner, approximating optimal parametric likelihood-based procedures. Since EL techniques and parametric likelihood methods are closely related concepts, one may apply corresponding EL functions to replace their parametric likelihood counterparts in known and well developed parametric procedures, e.g. constructing novel nonparametric Bayesian inference [3] and the confidence interval estimation [4]. This provides the impetus for an impressive expansion in the number of EL developments based on combinations of likelihoods of different types, e.g., when incomplete data should be analyzed, nonparametric likelihood ratio techniques can be combined with parametric likelihoods [5].The classical EL methodology, which is a distribution functionbased approach, has been shown to have attractive properties for testing hypotheses regarding parameters (e.g. moments) of distributions [6]. In practice, statisticians commonly face a variety of distribution-free comparisons and/or evaluations over all distribution functions of complete and incomplete data subject to different types of measurement errors. In these frameworks, the density-based EL methodology is shown to be very efficient [7][8][9][10]. According to the Neyman-Pearson lemma, the most powerful test statistics have structures that are related to density-based likelihood ratios. The density-based EL method can be easily and satisfactorily applied to construct highly efficient test procedures, approximating non-parametrically most powerful NeymanPearson test-rules, given aims of clinical studies. Similarly to the parametric likelihood concept, the EL methodology provides relatively simple strategies to construct powerful statistical tests that can be applied in various complex biostatistical studies. The extreme generality of EL methods and their wide ranges of usefulness partly result from the simple derivation of the EL statistics as components of composite parametric and nonparametric likelihood based systems, efficiently attending to any observed data and relevant information. The EL based methods are employed in much of modern biostatistical practice.

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Empirical likelihood ratios applied to goodness-of-fit tests based on sample entropy

Cited by 63 publications

References 24 publications

Testing Skew-Laplace Distribution Using Density-based Empirical Likelihood Approach

Testing Skew-Laplace Distribution Using Density-based Empirical Likelihood Approach

Testing Exponentiality Based on Renyi Entropy of Transformed Data

A Brief Ode to the Empirical Likelihood Concept

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