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A density based empirical likelihood approach for testing bivariate normality.

ABSTRACT: Sample entropy based tests, methods of sieves and Grenander estimation type procedures are known to be very efficient tools for assessing normality of underlying data distributions, in one-dimensional nonparametric settings. Recently, it has been shown that the density based empirical likelihood (EL) concept extends and standardizes these methods, presenting a powerful approach for approximating optimal parametric likelihood ratio test statistics, in a distribution-free manner. In this paper, we discuss difficulties related to constructing density based EL ratio techniques for testing bivariate normality and propose a solution regarding this problem. Toward this end, a novel bivariate sample entropy expression is derived and shown to satisfy the known concept related to bivariate histogram density estimations. Monte Carlo results show that the new density based EL ratio tests for bivariate normality behave very well for finite sample sizes. In order to exemplify the excellent applicability of the proposed approach, we demonstrate a real data example related to a study of biomarkers associated with myocardial infarction.

SUBMITTER: Gurevich G

PROVIDER: S-EPMC6586021 | biostudies-literature | 2018

REPOSITORIES: biostudies-literature

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A density based empirical likelihood approach for testing bivariate normality.

Gurevich Gregory G Vexler Albert A

Journal of statistical computation and simulation 20180525 13

Sample entropy based tests, methods of sieves and Grenander estimation type procedures are known to be very efficient tools for assessing normality of underlying data distributions, in one-dimensional nonparametric settings. Recently, it has been shown that the density based empirical likelihood (EL) concept extends and standardizes these methods, presenting a powerful approach for approximating optimal parametric likelihood ratio test statistics, in a distribution-free manner. In this paper, we ...[more]

PMID: 31223176

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Project description:BackgroundNormality is both a descriptive and a normative concept. Undoubtedly, the normal often operates normatively as an exclusionary tool of cultural authority. While it has prominently found its way into the field of medicine, it remains rather unclear in what sense it is used. Thus, our study sought to elucidate people's understanding of normality in medicine and to identify concepts that are linked to it.MethodsUsing convenient sampling, we carried out a cross-sectional survey. Since the survey was advertised through social media, we employed an online survey. We performed descriptive and inferential analyses. Predictors were chosen in a theory-driven manner.ResultsIn total, 323 persons from 21 countries completed the survey. Analysis revealed that the overall acceptance of normality in medicine was associated with notions of injustice, authority, discrimination, and with having a medical profession. More precisely, for the field of mental health, injustice insensitivity, genderism and transphobia, and authority were positively associated with a person's acceptance of normality; and, for the field of physical health, injustice insensitivity and having a medical profession were positively associated with a person's acceptance of normality. Finally, participants' acceptance of the use of normality in the area of mental health was lower than in the area of physical health.ConclusionsWhat is considered normal has implications for clinical practice, both at an individual and at a policy-level. Acknowledging its normalistic condition, the discipline of medicine has to confront itself with its own contribution to the augmentation of social inequalities through the excessive reliance on the concept of normality. Research that centers the lived experiences of those who are being systematically marginalized because they are deemed abnormal is needed. By empirically elucidating the conceptual relationships between normality in medicine and other variables, we provide points of leverage to deprive normality of its normative power. For medicine, this is needed to first do no harm.

Project description:BACKGROUND:Standard random-effects meta-analysis methods perform poorly when applied to few studies only. Such settings however are commonly encountered in practice. It is unclear, whether or to what extent small-sample-size behaviour can be improved by more sophisticated modeling. METHODS:We consider likelihood-based methods, the DerSimonian-Laird approach, Empirical Bayes, several adjustment methods and a fully Bayesian approach. Confidence intervals are based on a normal approximation, or on adjustments based on the Student-t-distribution. In addition, a linear mixed model and two generalized linear mixed models (GLMMs) assuming binomial or Poisson distributed numbers of events per study arm are considered for pairwise binary meta-analyses. We extract an empirical data set of 40 meta-analyses from recent reviews published by the German Institute for Quality and Efficiency in Health Care (IQWiG). Methods are then compared empirically as well as in a simulation study, based on few studies, imbalanced study sizes, and considering odds-ratio (OR) and risk ratio (RR) effect sizes. Coverage probabilities and interval widths for the combined effect estimate are evaluated to compare the different approaches. RESULTS:Empirically, a majority of the identified meta-analyses include only 2 studies. Variation of methods or effect measures affects the estimation results. In the simulation study, coverage probability is, in the presence of heterogeneity and few studies, mostly below the nominal level for all frequentist methods based on normal approximation, in particular when sizes in meta-analyses are not balanced, but improve when confidence intervals are adjusted. Bayesian methods result in better coverage than the frequentist methods with normal approximation in all scenarios, except for some cases of very large heterogeneity where the coverage is slightly lower. Credible intervals are empirically and in the simulation study wider than unadjusted confidence intervals, but considerably narrower than adjusted ones, with some exceptions when considering RRs and small numbers of patients per trial-arm. Confidence intervals based on the GLMMs are, in general, slightly narrower than those from other frequentist methods. Some methods turned out impractical due to frequent numerical problems. CONCLUSIONS:In the presence of between-study heterogeneity, especially with unbalanced study sizes, caution is needed in applying meta-analytical methods to few studies, as either coverage probabilities might be compromised, or intervals are inconclusively wide. Bayesian estimation with a sensibly chosen prior for between-trial heterogeneity may offer a promising compromise.

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A density based empirical likelihood approach for testing bivariate normality.

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A density based empirical likelihood approach for testing bivariate normality.

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