Lucio De Capitani

University of Milano-Bicocca

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Antonio Punzo

University of Catania

Luca Bagnato

Università Cattolica del Sacro Cuore

Leo Pasquazzi

University of Milano-Bicocca

Daniele De Martini

University of Genoa

Alessandro Zini

National Agency for New Technologies, Energy and Sustainable Economic Development

Federica Nicolussi

Politecnico di Milano

M Zenga

University of Milano-Bicocca

Cristina Giannattasio

University of Milano-Bicocca

Alberto Cereda

Ospedale San Paolo

Claudio Giovanni Borroni

University of Milano-Bicocca

Cooperative Institutions

University of Milano-Bicocca

University of Milan

Ospedale Maggiore

Azienda Socio Sanitaria Territoriale Grande Ospedale Metropolitano Niguarda

University of the Arts Utrecht

Utrecht University

Aalborg University

Università Cattolica del Sacro Cuore

Fondazione IRCCS Ca' Granda Ospedale Maggiore Policlinico

Politecnico di Milano

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Some measures of kurtosis and their inference on large datasets

AStA Advances in Statistical Analysis (2022)

Claudio Giovanni Borroni Lucio De Capitani

Abstract 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.

Kurtosis

Statistical Inference

10.1007/s10182-022-00442-y

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Citations (7)

SDD: AnRPackage for Serial Dependence Diagrams

Journal of Statistical Software (2015)

Luca Bagnato Lucio De Capitani Angelo Mazza Antonio Punzo

Detecting and measuring lag-dependencies is very important in time-series analysis. This study is commonly carried out by focusing on the linear lag-dependencies via the well-known autocorrelogram. However, in practice, there are many situations in which the autocorrelogram fails because of the nonlinear structure of the serial dependence. To cope with this problem, in this paper the R package SDD is introduced. Among the available approaches to analyze the lag-dependencies in an omnibus way, the SDD package considers the autodependogram and some of its variants. The autodependogram, defined by computing the classical Pearson χ2 -statistic at various lags, is a graphical device recently proposed in the literature to analyze lag-dependencies. The concept of reproducibility probability, and several density-based measures of divergence, are considered to define the variants of the autodependogram. An application to daily returns of the Swiss Market Index is also presented to exemplify the use of the package.

Statistic

Divergence (linguistics)

R package

10.18637/jss.v064.c02

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Citations (11)

On stochastic orderings of the Wilcoxon Rank Sum test statistic—With applications to reproducibility probability estimation testing

Statistics & Probability Letters (2011)

Lucio De Capitani Daniele De Martini

Statistic

Rank (graph theory)

Location parameter

Stochastic ordering

10.1016/j.spl.2011.04.001

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Citations (26)

Testing Serial Independence via Density-Based Measures of Divergence

Methodology And Computing In Applied Probability (2013)

Luca Bagnato Lucio De Capitani Antonio Punzo

Hellinger distance

Independence

Divergence (linguistics)

Kullback–Leibler divergence

10.1007/s11009-013-9320-4

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Citations (16)

A new estimator for a finite population cdf in presence of auxiliary information

Leo Pasquazzi Lucio De Capitani

In this work we propose a new estimator for the finite population cdf of a study variable that combines the two approaches to exploit knowledge about an auxiliary variable used in the Chambers and Dunstan ([2]) and the Kuo ([5]) estimators. As both the latter estimators, the new estimator is based on a superpopulation model where the population values of the study variable are generated independently from a model-cdf that is allowed to depend smoothly on an auxiliary variable. Like the Chambers and Dunstan estimator, the new estimator is based on estimates for the model-cdf of the study variable that are obtained by estimating the model-mean regression function and the model-cdf of the error terms separately. In the new estimator however both estimation steps are performed by non parametric regression in order to account for superpopulation models with smooth mean regression function and error term distribution that depends smoothly on the auxiliary variable. The non parametric regression for estimating model-cdf of the error terms resembles the one used in the Kuo estimator to estimate the model-cdf of the study variable directly, without considering the model-mean regression function. We will present a simulation study which shows that the new estimator outperforms several well known estimators from literature when the error terms are independently but not identically distributed. Leo Pasquazzi Department of Statistics and Quantitative Methods, University of Milano-Bicocca, Via Bicocca degli Arcimboldi 8, 20126 Milan, e-mail: leo.pasquazzi@unimib.it Lucio De Capitani Department of Statistics and Quantitative Methods, University of Milano-Bicocca, Via Bicocca degli Arcimboldi 8, 20126 Milan, e-mail: lucio.decapitani1@unimib.it

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Interval estimation for the Sharpe Ratio when returns are not i.i.d. with special emphasis on the GARCH(1,1) process with symmetric innovations

Statistical Methods & Applications (2012)

Lucio De Capitani

10.1007/s10260-012-0198-z

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Citations (4)

Quantile Estimation with Auxiliary Information: Simulation Results

Lucio De Capitani Leo Pasquazzi

Quantile