Publications

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Book
Lita da Silva, J., F. Caeiro, I. Natário, and C. A. Braumann Advances in Regression, Survival Analysis, Extreme Values, Markov Processes and Other Statistical Applications. Berlin Heidelberg: Springer, 2013.productflyer_978-3-642-34903-4.pdf
Book Chapter
Caeiro, Frederico, and Dora Susana Raposo Prata Gomes. "Adaptive estimation of a tail shape second order parameter." International Conference of Computational Methods in Sciences and Engineering 2015 (ICCMSE 2015). AIP Conference Proceedings. American Institute of Physics Inc., 2015. Abstract

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.

F., Caeiro, Gomes, and M.I. "Asymptotic Comparison at Optimal Levels of Minimum-Variance Reduced-Bias Tail-Index Estimators." Advances in Regression, Survival Analysis, Extreme Values, Markov Processes and Other Statistical Applications. Studies in Theoretical and Applied Statistics. Springer Berlin Heidelberg, 2013. 83-91. Abstract
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Gomes, Ivette M., Frederico Caeiro, Lígia Henriques-Rodrigues, and B. g Manjunath. "Bootstrap Methods in Statistics of Extremes." Extreme Events in Finance. John Wiley & Sons, Inc., 2016. 117-138. Abstract
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F., Caeiro, and Gomes M.I. "A Class of Semi-parametric Probability Weighted Moment Estimators." Recent Developments in Modeling and Applications in Statistics. Studies in Theoretical and Applied Statistics. Springer Berlin Heidelberg, 2013. 139-147. Abstract
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Mateus, Ayana Maria Xavier Furtado, and Frederico Almeida Gião Gonçalves Caeiro. "The difference-sign randomness test." NTERNATIONAL CONFERENCE OF COMPUTATIONAL METHODS IN SCIENCES AND ENGINEERING 2015. Vol. 1702. AIP Conference Proceedings, 1702. American Institute of Physics Inc., 2015. Abstract

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.

Caeiro, Frederico Almeida Gião Gonçalves, Ayana Maria Xavier Furtado Mateus, and Luís Pedro Carneiro Ramos. "Extreme value analysis of the sea levels in Venice." PROCEEDINGS OF THE INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2014. AIP Conference Proceedings. American Institute of Physics Inc., 2015. Abstract

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.

Caeiro, Frederico, Ana P. Martins, and Inês J. Sequeira. "Finite sample behaviour of classical and quantile regression estimators for the Pareto distribution." Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014. Vol. 1648. American Institute of Physics Inc., 2015. Abstract

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.

Caeiro, Frederico, and Dora Susana Raposo Prata Gomes. "A log probability weighted moment estimator of extreme quantiles." Theory and Practice of Risk Assessment - ICRA5 2013. Vol. 136. Springer New York LLC, 2015. 293-303. Abstract

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.

Caeiro, Frederico, Filipe J. Marques, Ayana Mateus, and Serra Atal. "A note on the Jackson exponentiality test." International Conference of Computational Methods in Sciences and Engineering 2016, ICCMSE 2016. Vol. 1790. American Institute of Physics Inc., 2016. Abstract

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.

Caeiro, F., and M. I. Gomes. "Probability weighted moments bootstrap estimation: a case study in the field of insurance." Risk and Extreme Values in Insurance and Finance: Book of Abstracts. Lisbon: CEAUL, 2011. 27-30.rev2011_caeiro_gomes.pdf
Caeiro, Frederico Almeida Gião Gonçalves, and Ayana Maria Xavier Furtado Mateus. "An R implementation of several randomness tests." AIP Conference Proceedings. 2014. 531-534. Abstract

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.

Cabral, Ivanilda, Frederico Caeiro, and Ivette M. Gomes. "Redução do viés do estimador de Hill: uma nova abordagem." Estatística: Progressos e Aplicações. 2016. 73-84. Abstract
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Cabral, Ivanilda, Frederico Caeiro, and Ivette M. Gomes. "Reduced bias Hill estimators." International Conference of Computational Methods in Sciences and Engineering 2016, ICCMSE 2016. Vol. 1790. American Institute of Physics Inc., 2016. Abstract

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.

M.I., Gomes, Henriques-Rodrigues L., and Caeiro F. "Refined Estimation of a Light Tail: An Application to Environmental Data." Advances in Theoretical and Applied Statistics. Ed. Fortunato; Bar-Hen Avner(Eds.) Torelli, Nicola; Pesarin. Studies in Theoretical and Applied Statistics. Springer Berlin Heidelberg, 2013. 143-153. Abstract
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Caeiro, F., and M. I.: Gomes. "A semi-parametric estimator of a shape second order parameter." New Advances in Statistical Modeling and Applications. Eds. Pacheco, A., Santos, R., M. Rosário Oliveira, and C. D. Paulino. Studies in Theoretical and Applied Statistics. Springer, 2014. 137-144. Abstract

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Mateus, Ayana, Frederico Caeiro, Dora Prata Gomes, and Inês J. Sequeira. "Statistical analysis of extreme river flows." International Conference of Computational Methods in Sciences and Engineering 2016, ICCMSE 2016. Vol. 1790. AIP Conference Proceedings, 1790. American Institute of Physics Inc., 2016. Abstract

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.

Caeiro, Frederico, and Ivette M. Gomes. "Threshold Selection in Extreme Value Analysis." Extreme Value Modeling and Risk Analysis. Chapman and Hall/CRC 2007, 2016. 69-86. Abstract

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.

Conference Proceedings
Caeiro, F., M. I. Gomes, and D. Pestana Alguns resultados adicionais sobre a variância de um estimador de viés reduzido do índice de cauda.. Eds. Correia Ferreira Dias Braumann E. F. S. e Oliveira, I. Actas do XVI Congresso Anual da Sociedade Portuguesa de Estatística - "Arte de Explicar o Acaso"., 2009. Abstract2009spe_art016.pdf

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Caeiro, F., and M. I. Gomes Caudas pesadas: t de Student e variante assimétrica versus metodologia semi-paramétrica.. Actas do XV Congresso Anual da Sociedade Portuguesa de Estatística - “Da Teoria à Prática”. Lisboa, 2008.art053.pdf
Gomes, M. I., and F. Caeiro Eficiency of partially reduced-bias mean-of-order-p versus minimum-variance reduced-bias extreme value index estimation. COMPSTAT 2014: 21th International Conference on Computational Statistics. Geneve, 2014. Abstractgomes_caeiro_compstat2014_reprint.pdf

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Caeiro, F., and M. I. Gomes Estimação de quantis elevados em estatística de extremos. Actas do XIII Congresso Anual da Sociedade Portuguesa de Estatística - "Ciência Estatística"., 2006.2006spe217-228.pdf
Caeiro, F., and M. I. Gomes On the bootstrap methodology for the estimation of the tail sample fraction. COMPSTAT 2014: 21th International Conference on Computational Statistics. Geneve, 2014.caeiro_gomes_compstat2014_reprint.pdf