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Caeiro, F. (2022).  Preface of the Session ?Computational Statistical Methods?. AIP Conference Proceedings. 2425, Abstract
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Caeiro, F., & Gomes M. I. (2011).  Probability weighted moments bootstrap estimation: a case study in the field of insurance. Risk and Extreme Values in Insurance and Finance: Book of Abstracts. 27-30., Lisbon: CEAULrev2011_caeiro_gomes.pdf
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Caeiro, F. A. G. G., & Mateus A. M. X. F. (2014).  An R implementation of several randomness tests. AIP Conference Proceedings. 531 - 534., 2014/1/1 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.

Caeiro, F., & Gomes M. I. (2006).  Redução de viés na estimação semi-paramétrica de um parâmetro de escala. Actas do XIII Congresso da SPE - "Ciência Estatística". 127-148.2006spe_127-148.pdf
Cabral, I., Caeiro F., & Gomes I. M. (2016).  Redução do viés do estimador de Hill: uma nova abordagem. Estatística: Progressos e Aplicações. 73 - 84., 2016/11 Abstract
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F., C., & M.I. G. (2012).  A Reduced Bias Estimator of a 'Scale' Second Order Parameter. 1114-1117., Jan, Number 1479 Abstract

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Cabral, I., Caeiro F., & Gomes I. M. (2016).  Reduced bias Hill estimators. International Conference of Computational Methods in Sciences and Engineering 2016, ICCMSE 2016. 1790, , 2016/12/6: American Institute of Physics Inc. 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.

Gomes, M. I., Caeiro F., Figueiredo F., Henriques-Rodrigues L., & Pestana D. (2020).  Reduced-bias and partially reduced-bias mean-of-order-p value-at-risk estimation: a Monte-Carlo comparison and an application. Journal of Statistical Computation and Simulation. 90, 1735-1752., Number 10 Abstract
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Caeiro, F., & Henriques-Rodrigues L. (2019).  Reduced-bias kernel estimators of a positive extreme value index. Mathematical Methods in the Applied Sciences. 42, 5867-5880., Number 17 Abstract
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Caeiro, F., Gomes M. I., & Rodrigues L. H. (2009).  Reduced-bias tail index estimators under a third-order framework.. Commun. Stat., Theory Methods. 38, 1019-1040., Number 7 Abstract

{Summary: We are interested in the comparison, under a third-order framework, of classes of second-order, reduced-bias tail index estimators, giving particular emphasis to minimum-variance reduced-bias estimators of the tail index $\gamma$. The full asymptotic distributional properties of the proposed classes are derived under a third-order framework and the estimators are compared with other alternatives, not only asymptotically, but also for finite samples through Monte Carlo techniques. An application to the log-exchange rates of the Euro against the USA Dollar is also provided.}

Caeiro, F. (2003).  Redução de viés em estimadores do índice de cauda. Actas do X Congresso Anual da SPE - “Literacia e Estatística”. 187-199., Porto, Portugalspe2002_187-199.pdf
M.I., G., L. H. - R., & F. C. (2013).  Refined Estimation of a Light Tail: An Application to Environmental Data. (Torelli, Nicola; Pesarin, Fortunato; Bar-Hen, Avner (Eds.), Ed.).Advances in Theoretical and Applied Statistics. 143-153., Jan: Springer Berlin Heidelberg Abstract
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Caeiro, F., & Gomes I. M. (2015).  Revisiting the maximum likelihood estimation of a positive extreme value index. Journal Of Statistical Theory And PracticeJournal Of Statistical Theory And Practice. 9(1), 200 - 218., 2015/1/13 AbstractWebsite

In this article, we revisit Feuerverger and Halls maximum likelihood estimation of the extreme value index. Based on those estimators we propose new estimators that have the smallest possible asymptotic variance, equal to the asymptotic variance of the Hill estimator. The full asymptotic distributional properties of the estimators are derived under a general third-order framework for heavy tails. Applications to a real data set and to simulated data are also presented.In this article, we revisit Feuerverger and Halls maximum likelihood estimation of the extreme value index. Based on those estimators we propose new estimators that have the smallest possible asymptotic variance, equal to the asymptotic variance of the Hill estimator. The full asymptotic distributional properties of the estimators are derived under a general third-order framework for heavy tails. Applications to a real data set and to simulated data are also presented.

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Caeiro, F., & Gomes M. I. (2007).  Second-order Reduced-bias Tail Index and High Quantile Estimation. 56th SESSION OF THE INTERNATIONAL STATISTICAL INSTITUTE. 109-116., Lisbon, Portugal2007isi_volume_lxii_proceedings_caeiro_gomes.pdf
Caeiro, F., & Gomes M. I.: (2014).  A semi-parametric estimator of a shape second order parameter.. (Pacheco, A.,, Santos, R.,, Rosário Oliveira, M., Paulino, C.D., Ed.).New Advances in Statistical Modeling and Applications. 137-144., Jan: Springer Abstract

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Caeiro, F., & Gomes M. I. (2009).  Semi-parametric second-order reduced-bias high quantile estimation.. Test. 18, 392-413., Number 2 Abstract

{Summary: In many areas of application, like, for instance, climatology, hydrology, insurance, finance, and statistical quality control, a typical requirement is to estimate a high quantile of probability $1 - p$, a value high enough so that the chance of an exceedance of that value is equal to $p$, small. The semi-parametric estimation of high quantiles depends not only on the estimation of the tail index or extreme value index $\gamma $, the primary parameter of extreme events, but also on the adequate estimation of a scale first order parameter. Recently, apart from new classes of reduced-bias estimators for $\gamma >0$, new classes of the scale first order parameter have been introduced in the literature. Their use in quantile estimation enables us to introduce new classes of asymptotically unbiased high quantiles' estimators, with the same asymptotic variance as the (biased) ``classical'' estimator. The asymptotic distributional properties of the proposed classes of estimators are derived and the estimators are compared with alternative ones, not only asymptotically, but also for finite samples through Monte Carlo techniques. An application to the log-exchange rates of the Euro against the Sterling Pound is also provided.}

Caeiro, F., & Gomes M. I. (2011).  Semi-parametric tail inference through probability-weighted moments.. J. Stat. Plann. Inference. 141, 937-950., Number 2 Abstract

{Summary: For heavy-tailed models, and working with the sample of the $k$ largest observations, we present probability weighted moments (PWM) estimators for the first order tail parameters. Under regular variation conditions on the right-tail of the underlying distribution function $F$ we prove the consistency and asymptotic normality of these estimators. Their performance, for finite sample sizes, is illustrated through a small-scale Monte Carlo simulation.}

Caeiro, F., Henriques-Rodrigues L. {\'ı}gia, & Gomes D. P. (2019).  A simple class of reduced bias kernel estimators of extreme value parameters. Computational and Mathematical Methods. e1025., apr: Wiley AbstractWebsite
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Mateus, A., Caeiro F., Gomes D. P., & Sequeira I. J. (2016).  Statistical analysis of extreme river flows. International Conference of Computational Methods in Sciences and Engineering 2016, ICCMSE 2016. 1790, , 2016/12/6: American Institute of Physics Inc. 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.

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Caeiro, F., & Gomes I. M. (2016).  Threshold Selection in Extreme Value Analysis. Extreme Value Modeling and Risk Analysis. 69 - 86., 2016/1/7: Chapman and Hall/CRC 2007 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.

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Caeiro, F., & Gomes M. I. (2005).  Uma classe de estimadores do parâmetro de escala de segunda ordem.. Actas do XII Congresso Anual da Sociedade Portuguesa de Estatística. 113-124., Évora, Portugalcaeirof-spe2004.pdf
Caeiro, F., Henriques-Rodrigues L. {\'ı}gia, & Gomes I. M. (2022).  The Use of Generalized Means in the Estimation of the Weibull Tail Coefficient. (Anil Kumar, Ed.).Computational and Mathematical Methods. 2022, 1–12., jun: Hindawi Limited AbstractWebsite
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