Nonparametric Predictive Inference for Reproducibility of Basic Nonparametric Tests

Coolen, Frank P. A.; Himd, Sulafah Bin

doi:10.1080/15598608.2013.819792

Cited by 27 publications

(38 citation statements)

References 32 publications

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“…From Figure 5 we may observe the same features already described in Marques et al (2018) for Case I, which are: the upper and lower RPs tend to increase and to be closer to each other when the simulated value of the likelihood Prob ratio statistic moves away from the quantile considered. When close to the quantile considered the lower RP is quite small which is a feature present in comparisons of two groups (Coolen and Bin Himd, 2014). As already mentioned the RP is a measure of how likely is to make the same decision if we repeat a test under the same circumstances.…”

Section: Reproducibility Probabilitymentioning

confidence: 85%

“…This problem was first addressed by Goodman (1992) and has received, recently, increasing attention. The nonparametric predictive inference (NPI) for RP was first presented in Coolen and Bin Himd (2014) for two basic nonparametric tests, the one-sample sign test and the one-sample signed-rank test, and in Coolen and Alqifari (2018) RPs were computed for the quantile test and for a precedence test. We consider the NPI method to compute the lower and upper RPs of likelihood ratio tests for simple hypotheses introduced in Marques et al (2018).…”

Section: Reproducibility Probabilitymentioning

confidence: 99%

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Approximations for the Likelihood Ratio Statistic for Hypothesis Testing Between Two Beta Distributions

Marques¹,

Coolen

Coolen‐Maturi

2018

J Stat Theory Pract

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T. (2019) 'Approximations for the likelihood ratio statistic for hypothesis testing between two Beta distributions.', Journal of statistical theory and practice., 13 . p. 17.The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractIn this paper the likelihood ratio to test between two Beta distributions is addressed. The exact distribution of the likelihood ratio statistic, for simple hypotheses, is obtained in terms of Gamma or Generalized Integer Gamma distributions, when the first or the second of the two parameters of the Beta distributions are equal and integers. In the remaining cases addressed, near-exact or asymptotic approximations, are developed for the likelihood ratio statistic. Both the exact, asymptotic or near-exact representations are obtained using a logarithm transformation of the likelihood ratio statistic and by working with the corresponding characteristic function. The numerical studies illustrate the precision of the approximations developed. Simulations are developed to analyse the power and the reproducibility probability of the tests.

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Section: Reproducibility Probabilitymentioning

confidence: 85%

Section: Reproducibility Probabilitymentioning

confidence: 99%

Approximations for the Likelihood Ratio Statistic for Hypothesis Testing Between Two Beta Distributions

Marques¹,

Coolen

Coolen‐Maturi

2018

J Stat Theory Pract

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“…It will be of interest to develop this bivariate method for multiple future observations. NPI has recently been presented for a number of inferential problems, including accuracy of diagnostic tests [10,11], inferences with right-censored observations [9] and reproducibility of basic nonparametric tests [8]. For all such applications, it is of interest to develop predictive methodology for bivariate, and more generally multivariate data.…”

Section: Discussionmentioning

confidence: 99%

Predictive inference for bivariate data: Combining nonparametric predictive inference for marginals with an estimated copula

Coolen‐Maturi

Coolen

Muhammad

2016

Journal of Statistical Theory and Practice

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Additional information:Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractThis paper presents a new method for prediction of an event involving a future bivariate observation. The method combines nonparametric predictive inference (NPI) applied to the marginals with a parametric copula to model and estimate the dependence structure between two random quantities, as such the method is semi-parametric. In NPI, uncertainty is quantified through imprecise probabilities. The resulting imprecision in the marginals provides robustness with regard to the assumed parametric copula. Due to the specific nature of NPI, the estimation of the copula parameter is also quite straightforward. The performance of this method is investigated via simulations, with particular attention to robustness with regard to the assumed copula in case of small data sets. The method is further illustrated via two examples, using small data sets from the literature. This paper presents several novel aspects of statistical inference. First, the link between NPI and copulas is powerful and attractive with regard to computation. Secondly, statistical methods using imprecise probability have gained substantial attention in recent years, where typically imprecision is used on aspects for which less information is available. This paper presents a different approach, namely imprecision mainly being introduced on the marginals, for which there is typically quite sufficient information, in order to provide robustness for the harder part of the inference, namely the * Corresponding author copula assumptions and estimation. Thirdly, the set up of the simulations to evaluate the performance of the proposed method is novel, key to these are frequentist comparisons of the success proportion of predictions with the corresponding data-based lower and upper predictive inferences. All these novel ideas can be applied far more generally to other inferences and models, while also many alternatives can be considered. Hence, this paper presents the starting point of an extensive research programme towards powerful predictive inference methods for multi-variate data.

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“…Further development in RP estimation might concern the application of Bayesian techniques in the nonparametric context, since in the parametric one, they showed promising improvement when uninformative priors have been adopted [27]. Furthermore, prediction intervals may be considered for nonparametric RP estimation (see [28]); in particular, it would be interesting to link prediction intervals, which provide likely results of future RP estimators, once experimental data have been observed, to the RP-testing rule.…”

Section: Discussionmentioning

confidence: 99%

Reproducibility Probability Estimation and RP-Testing for Some Nonparametric Tests

Capitani¹,

Martini²

2016

Entropy

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Several reproducibility probability (RP)-estimators for the binomial, sign, Wilcoxon signed rank and Kendall tests are studied. Their behavior in terms of MSE is investigated, as well as their performances for RP-testing. Two classes of estimators are considered: the semi-parametric one, where RP-estimators are derived from the expression of the exact or approximated power function, and the non-parametric one, whose RP-estimators are obtained on the basis of the nonparametric plug-in principle. In order to evaluate the precision of RP-estimators for each test, the MSE is computed, and the best overall estimator turns out to belong to the semi-parametric class. Then, in order to evaluate the RP-testing performances provided by RP estimators for each test, the disagreement between the RP-testing decision rule, i.e., "accept H 0 if the RP-estimate is lower than, or equal to, 1/2, and reject H 0 otherwise", and the classical one (based on the critical value or on the p-value) is obtained. It is shown that the RP-based testing decision for some semi-parametric RP estimators exactly replicates the classical one. In many situations, the RP-estimator replicating the classical decision rule also provides the best MSE.

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Nonparametric Predictive Inference for Reproducibility of Basic Nonparametric Tests

Cited by 27 publications

References 32 publications

Approximations for the Likelihood Ratio Statistic for Hypothesis Testing Between Two Beta Distributions

Approximations for the Likelihood Ratio Statistic for Hypothesis Testing Between Two Beta Distributions

Predictive inference for bivariate data: Combining nonparametric predictive inference for marginals with an estimated copula

Reproducibility Probability Estimation and RP-Testing for Some Nonparametric Tests

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