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When a distributional model is chosen, the analytic relation between its shape parameters and the values taken by some kurtosis indexes, especially if they are unconventional, is rarely known. In addition, different indexes may provide contrasting evidence about the level of global kurtosis, when the parameters of the model are varied. That happens because just few parameters act "plainly" on kurtosis, namely so as to produce consistent modifications of the shape of the graph on both its sides. Many parameters, instead, affect kurtosis along with a change of the skewness of the distribution, that is by "inflating" a single side of the graph (usually a tail) at the expense of the other. Thanks to some relevant examples, this paper tries to provide general indications to recognize the two kinds of parameters above and to interpret their effect on the classical Pearson's standardized fourth moment and on some lesser known kurtosis indexes. Specifically, it is shown that only a decomposed analysis of indexes can help to understand their apparent contradictions, especially when some of them are too sensitive to changes in the tails. Finally, some applications are provided. [ABSTRACT FROM AUTHOR]

This paper deals with the estimation of kurtosis on large datasets. It aims at overcoming two frequent limitations in applications: first, Pearson's standardized fourth moment is computed as a unique measure of kurtosis; second, the fact that data might be just samples is neglected, so that the opportunity of using suitable inferential tools, like standard errors and confidence intervals, is discarded. In the paper, some recent indexes of kurtosis are reviewed as alternatives to Pearson's standardized fourth moment. The asymptotic distribution of their natural estimators is derived, and it is used as a tool to evaluate efficiency and to build confidence intervals. A simulation study is also conducted to provide practical indications about the choice of a suitable index. As a conclusion, researchers are warned against the use of classical Pearson's index when the sample size is too low and/or the distribution is skewed and/or heavy-tailed. Specifically, the occurrence of heavy tails can deprive Pearson's index of any meaning or produce unreliable confidence intervals. However, such limitations can be overcome by reverting to the reviewed alternative indexes, relying just on low-order moments. [ABSTRACT FROM AUTHOR]

The paper develops a general and flexible toolbox for implementing multi-criteria evaluation processes and for computing synthetic indicators and rankings, on multi-dimensional systems of ordinal variables. It integrates partial order theory and fuzzy logic, into a general procedure that can be tuned to different application domains and evaluation problems, fully respecting the non-numerical and multi-faceted nature of the data. The toolbox is shown in action in the domain of multi-dimensional deprivation assessment, on real data pertaining to poverty in Belize. [ABSTRACT FROM AUTHOR]

Experimental results are often interpreted through statistical tests, where the alternative hypothesis represents the theory to be evinced; if the experimental results lead to the rejection of the null hypothesis, the theory is supported by empirical evidence. In these cases, the reproducibility of this empirical evidence can be measured by the Reproducibility Probability (RP) of the test, which coincides with the probability of rejecting the null hypothesis. The terminology "Reproducibility" Probability stems from the fact that it is usually computed when an experiment provides a significant result to evaluate the probability that a further identical and independent experiment confirms the statistical significance. In recent literature, some RP estimators have been proposed. They are useful for two reasons: they allow us to evaluate the reliability of the obtained statistical significance and some estimates can be used as a test statistic, owing to the so-called "RP-testing" decision rule (reject the null hypothesis if and only if the RP estimate is greater than 1/2). Unfortunately, the usually adopted RP estimators are affected by a high mean squared error. In this paper, a new class of RP estimators is introduced and examined to improve their estimation precision. Specifically, the performances of the new RP estimators have been compared with those of the existing estimators and a 30% greater reduction in the mean squared error (on average) was observed. Moreover, the new estimator with the best performance allowed the use of the RP-testing decision rule. Hence, this work achieves the double goal of improving Reproducibility Probability estimation and preserving RP-testing. [ABSTRACT FROM AUTHOR]

The Ljung-Box test is typically used to test serial independence even if, by construction, it is generally powerful only in presence of pairwise linear dependence between lagged variables. To overcome this problem, Bagnato et al. recently proposed a simple statistic defining a serial independence test which, differently from the Ljung-Box test, is powerful also under a linear/nonlinear dependent process characterized by pairwise independence. The authors also introduced a normalized bar diagram, based on p-values from the proposed test, to investigate serial dependence. This paper proposes a balanced normalization of such a diagram taking advantage of the concept of reproducibility probability. This permits to study the strength and the stability of the evidence about the presence of the dependence under investigation. An illustrative example based on an artificial time series, as well as an application to a transport time series, are considered to appreciate the usefulness of the proposal. [ABSTRACT FROM AUTHOR]

This article reviews some nonparametric serial independence tests based on measures of divergence between densities. Among others, the well-known Kullback-Leibler, Hellinger, Tsallis, and Rosenblatt divergences are analyzed. Moreover, their copula-based version is taken into account. Via a wide simulation study, the performances of the considered serial independence tests are compared under different settings. Both single-lag and multiple-lag testing procedures are investigated to find out the best 'omnibus' solution. [ABSTRACT FROM AUTHOR]

The autodependogram is a graphical device recently proposed in the literature to analyze autodependencies. This paper proposes a normalization of this diagram taking into consideration the concept of reproducibility probability (RP). The result is a novel tool, named RP-autodependogram, which permits to study the strength and the stability of the evidence about the presence of lag-dependence. A simulation study on well-established time-series models is carried out to investigate the behavior of the RP-autodependogram also in comparison with other diagrams studying autodependencies. An application to financial data is finally considered to appreciate its usefulness in the identification of parametric/nonparametric models. [ABSTRACT FROM AUTHOR]

In this paper, assuming that returns follows a stationary and ergodic stochastic process, the asymptotic distribution of the natural estimator of the Sharpe Ratio is explicitly given. This distribution is used in order to define an approximated confidence interval for the Sharpe ratio. Particular attention is devoted to the case of the GARCH(1,1) process. In this latter case, a simulation study is performed in order to evaluate the minimum sample size for reaching a good coverage accuracy of the asymptotic confidence intervals. [ABSTRACT FROM AUTHOR]