Frederico Caeiro

In Statistics of Extremes, the tail shape second order parameter is a relevant parameter whenever we want to improve the estimation of first order parameters. We shall consider two semi-parametric estimators of the shape second order parameter, parameterized with a tuning parameter. We provide a Monte Carlo comparative simulation study of several algorithms for the choice of such tuning parameter and for an adaptive estimation of the shape second order parameter.In Statistics of Extremes, the tail shape second order parameter is a relevant parameter whenever we want to improve the estimation of first order parameters. We shall consider two semi-parametric estimators of the shape second order parameter, parameterized with a tuning parameter. We provide a Monte Carlo comparative simulation study of several algorithms for the choice of such tuning parameter and for an adaptive estimation of the shape second order parameter.

In this paper we review the properties of the difference-sign randomness test. First we analyse the exact andasymptotic distribution of the test statistic and provide a table with values for the exact distribution function, for samples ofsize n ≤ 32. Then, we also present several moments of the statistic test, under the null hypothesis of randomness and underthe hypothesis of the existence of a linear trend. Finally, we present an illustration of the test difference-sign to a real data set.In this paper we review the properties of the difference-sign randomness test. First we analyse the exact andasymptotic distribution of the test statistic and provide a table with values for the exact distribution function, for samples ofsize n ≤ 32. Then, we also present several moments of the statistic test, under the null hypothesis of randomness and underthe hypothesis of the existence of a linear trend. Finally, we present an illustration of the test difference-sign to a real data set.

The number of floods in the city of Venice has increased substantially in the last decades and can be explained bythe sea level rise and land subsidence. Using Statistics of Extremes we shall model the extreme behaviour of the sea level inVenice and quantify risk through the estimation of important parameters such as return periods of high levels.The number of floods in the city of Venice has increased substantially in the last decades and can be explained bythe sea level rise and land subsidence. Using Statistics of Extremes we shall model the extreme behaviour of the sea level inVenice and quantify risk through the estimation of important parameters such as return periods of high levels.

The Pareto distribution is a well known and important model in Statistics. It has been used to study large incomes, city population size, size of losses, stock price fluctuations, number of citations received by papers and other similar phenomena. In this work we compare the finite sample performance of several estimation methods, namely the Moment, Maximum Likelihood and Quantile Regression methods. The comparison will be made through a Monte-Carlo simulation study.The Pareto distribution is a well known and important model in Statistics. It has been used to study large incomes, city population size, size of losses, stock price fluctuations, number of citations received by papers and other similar phenomena. In this work we compare the finite sample performance of several estimation methods, namely the Moment, Maximum Likelihood and Quantile Regression methods. The comparison will be made through a Monte-Carlo simulation study.

In this paper we consider the semi-parametric estimation of extreme quantiles of a right heavy-tail model. We propose a new Probability Weighted Moment estimator for extreme quantiles, which is obtained from the estimators of the shape and scale parameters of the tail. Under a second-order regular variation condition on the tail, of the underlying distribution function, we deduce the non degenerate asymptotic behaviour of the estimators under study and present an asymptotic comparison at their optimal levels. In addition, the performance of the estimators is illustrated through an application to real data.In this paper we consider the semi-parametric estimation of extreme quantiles of a right heavy-tail model. We propose a new Probability Weighted Moment estimator for extreme quantiles, which is obtained from the estimators of the shape and scale parameters of the tail. Under a second-order regular variation condition on the tail, of the underlying distribution function, we deduce the non degenerate asymptotic behaviour of the estimators under study and present an asymptotic comparison at their optimal levels. In addition, the performance of the estimators is illustrated through an application to real data.

In this paper we revisit the Jackson exponentiality test. We study and provide functions in R language to compute theoretical moments, the distribution function and quantiles of the statistic test. Approximations to the exact distribution function and quantiles are also provided and their precision discussed. In addition, we provide an application of the Jackson test to real data.In this paper we revisit the Jackson exponentiality test. We study and provide functions in R language to compute theoretical moments, the distribution function and quantiles of the statistic test. Approximations to the exact distribution function and quantiles are also provided and their precision discussed. In addition, we provide an application of the Jackson test to real data.

In many statistic methods, including distribution-free methods, we assume to work with random samples. In this note, we present randtests: an R package implementation of several nonparametric randomness tests. After a brief description of the tests included in the package, we present an application to real data sets in the field of Agricultural.In many statistic methods, including distribution-free methods, we assume to work with random samples. In this note, we present randtests: an R package implementation of several nonparametric randomness tests. After a brief description of the tests included in the package, we present an application to real data sets in the field of Agricultural.

For heavy tails, classical extreme value index estimators, like the Hill estimator, are usually asymptotically biased. Consequently those estimators are quite sensitive to the number of top order statistics used in the estimation. The recent minimum-variance reduced-bias extreme value index estimators enable us to remove the dominant component of asymptotic bias and keep the asymptotic variance of the new estimators equal to the asymptotic variance of the Hill estimator. In this paper a new minimum-variance reduced-bias extreme value index estimator is introduced, and its non degenerate asymptotic behaviour is studied. A comparison with another important minimum-variance reduced-bias extreme value index estimator is also provided.For heavy tails, classical extreme value index estimators, like the Hill estimator, are usually asymptotically biased. Consequently those estimators are quite sensitive to the number of top order statistics used in the estimation. The recent minimum-variance reduced-bias extreme value index estimators enable us to remove the dominant component of asymptotic bias and keep the asymptotic variance of the new estimators equal to the asymptotic variance of the Hill estimator. In this paper a new minimum-variance reduced-bias extreme value index estimator is introduced, and its non degenerate asymptotic behaviour is studied. A comparison with another important minimum-variance reduced-bias extreme value index estimator is also provided.

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Floods are recurrent events that can have a catastrophic impact. In this work we are interested in the analysis of a data set of gauged daily flows from the Whiteadder Water river, Scotland. Using statistic techniques based on extreme value theory, we estimate several extreme value parameters, including extreme quantiles and return periods of high levels.Floods are recurrent events that can have a catastrophic impact. In this work we are interested in the analysis of a data set of gauged daily flows from the Whiteadder Water river, Scotland. Using statistic techniques based on extreme value theory, we estimate several extreme value parameters, including extreme quantiles and return periods of high levels.

The main objective of statistics of extremes is the prediction of rare events, and its primary problem has been the estimation of the extreme value index (EVI). Whenever we are interested in large values, such estimation is usually performed on the basis of the largest k + 1 order statistics in the sample or on the excesses over a high level u. The question that has been often addressed in practical applications of extreme value theory is the choice of either k or u, and an adaptive EVI-estimation. Such a choice can be either heuristic or based on sample paths stability or on the minimization of a mean squared error estimateas a function of k. Some of these procedures will be reviewed. Despite of thefact that the methods provided can be applied, with adequate modifications, to any real EVI and not only to the adaptive EVI-estimation but also to the adaptive estimation of other relevant right-tail parameters, we shall illustrate the methods essentially for the EVI and for heavy tails, i.e., for a positive EVI.The main objective of statistics of extremes is the prediction of rare events, and its primary problem has been the estimation of the extreme value index (EVI). Whenever we are interested in large values, such estimation is usually performed on the basis of the largest k + 1 order statistics in the sample or on the excesses over a high level u. The question that has been often addressed in practical applications of extreme value theory is the choice of either k or u, and an adaptive EVI-estimation. Such a choice can be either heuristic or based on sample paths stability or on the minimization of a mean squared error estimateas a function of k. Some of these procedures will be reviewed. Despite of thefact that the methods provided can be applied, with adequate modifications, to any real EVI and not only to the adaptive EVI-estimation but also to the adaptive estimation of other relevant right-tail parameters, we shall illustrate the methods essentially for the EVI and for heavy tails, i.e., for a positive EVI.

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