Frederico Caeiro

Reduced-bias tail index estimators under a third order framework

In this article, 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 γ. 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.

Bias reduction of a tail index estimator through an external estimation of the second-order parameter

In this paper, we first consider a class of consistent semi-parametric estimators of a positive tail index γ, parameterised in a tuning or control parameter α. Such a control parameter enables us to have access, for any available sample, to an estimator of the tail index γ with a null dominant component of asymptotic bias, and consequently with a reasonably flat mean squared error pattern, as a function of k, the number of top-order statistics considered. Such a control parameter depends on a second-order parameter ρ, which will be adequately estimated so that we may achieve a high efficiency relative to the classical Hill estimator, provided we use a number of top-order statistics larger than the one usually required for the estimation through the Hill estimator. An illustration of the behaviour of the estimators is provided, through the analysis of the daily log-returns on the Euro–US

A Class of Asymptotically Unbiased Semi-parametric Estimators of the Tail Index

exchange rates.

A Semi-parametric Estimator of a Shape Second-Order Parameter

In this paper we consider a class of consistent semi-parametric estimators of a positive tail index γ, parameterized in atuning orcontrol parameter α. Such a control parameter enables us to have access, for any available sample, to an estimator of γ with a null dominant component of asymptotic bias, and with a reasonably flatMean Squared Error pattern, as a functional ofk, the number of top order statistics considered. Moreover, we are able to achieve a high efficiency relatively to the classical Hill estimator, provided we may have access to a larger number of top order statistics than the number needed for optimal estimation through the Hill estimator.

Bias reduction in the estimation of a shape second-order parameter of a heavy-tailed model

In extreme value theory, any second-order parameter is an important parameter that measures the speed of convergence of the sequence of maximum values, linearly normalized, towards its limit law. In this paper we study a new estimator of a shape second-order parameter under a third-order framework.

Comparing several tests of randomness based on the difference of observations

In extreme value theory, the shape second-order parameter is a quite relevant parameter related to the speed of convergence of maximum values, linearly normalized, towards its limit law. The adequate estimation of this parameter is vital for improving the estimation of the extreme value index, the primary parameter in statistics of extremes. In this article, we consider a recent class of semi-parametric estimators of the shape second-order parameter for heavy right-tailed models. These estimators, based on the largest order statistics, depend on a real tuning parameter, which makes them highly flexible and possibly unbiased for several underlying models. In this article, we are interested in the adaptive choice of such tuning parameter and the number of top order statistics used in the estimation procedure. The performance of the methodology for the adaptive choice of parameters is evaluated through a Monte Carlo simulation study.

A location-invariant probability weighted moment estimation of the Extreme Value Index

In this work, we consider the problem of testing randomness. After reviewing several non-parametric randomness tests based on the sign of the difference of observations we shall compare their performance through a Monte Carlo simulation study.

Revisiting the Maximum Likelihood Estimation of a Positive Extreme Value Index

The peaks over random threshold (PORT) methodology and the Pareto probability weighted moments (PPWM) of the largest observations are used to build a class of location-invariant estimators of the Extreme Value Index (EVI), the primary parameter in statistics of extremes. The asymptotic behaviour of such a class of EVI-estimators, the so-called PORT-PPWM EVI-estimators, is derived, and an alternative class of location-invariant EVI-estimators, the generalized Pareto probability weighted moments (GPPWM) EVI-estimators is considered as an alternative. These two classes of estimators, the PORT-PPWM and the GPPWM, jointly with the classical Hill EVI-estimator and a recent class of minimum-variance reduced-bias estimators are compared for finite samples, through a large-scale Monte-Carlo simulation study. An adaptive choice of the tuning parameters under play is put forward and applied to simulated and real data sets.

Advances in Regression, Survival Analysis, Extreme Values, Markov Processes and Other Statistical Applications

In this article, we revisit Feuerverger and Hall’s 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.

A new partially reduced-bias mean-of-order p class of extreme value index estimators

Part I Invited Sessions: Youden Square with Split Units (Stanislaw Franciszek Mejza and Shinji Kuriki).- Likelihood and PLS Estimators for Structural Equation Modeling: an Assessment of Sample Size, Skewness and Model Misspecification Effects (Manuel J. Vilares and Pedro S. Coelho).- Part II Communications: A Parametric Cure Model with Covariates (Ana M. Abreu and Cristina S. Rocha).- Survival Analysis Applied to the Study of Time from Diagnosis of HIV-1 Infection to AIDS in Portugal (Marta Alves, Cristina S. Rocha and Maria Teresa Paixao).- A new Independence Test for VaR Violations (P. Araujo Santos and M. I. Fraga Alves).- Discrimination Between Parametric Survival Models for Removal Times of Bird Carcasses in Scavenger Removal Trials at Wind Turbines Sites (Regina Bispo, Joana Bernardino, Tiago A. Marques and Dinis Pestana).- Uniformity (M. F. Brilhante, M. Malva, S. Mendonca, D. Pestana, F. Sequeira and S. Velosa).- Asymptotic Comparison at Optimal Levels of Minimum-Variance Reduced-Bias Tail Index Estimators (Frederico Caeiro and M. Ivette Gomes).- Extremal Behavior of the Generalized Integer-valued Random Coefficient Autoregressive Process (Luisa Canto e Castro, Dulce Gomes and Maria da Graca Temido).- Models of Individual Growth in a Random Environment: Study and Application of First Passage Times (Clara Carlos, Carlos A. Braumann and Patricia A. Filipe).- Generalized Linear Mixed Effects Model in the Analysis of Longitudinal Discrete Data (Eunice Carrasquinha, M. Helena Goncalves and M. Salome Cabral).- Risk Assessment on Campylobacter in Broiler Meat at Slaughter Level in Portugal (Marta Castel-Branco, Marilia Antunes, Patricia Inacio and Miguel Cardo).- Predicting and Treating Missing Data with Boot.EXPOS (Clara Cordeiro and M. Manuela Neves).- Bayesian Genetic Mapping of Binary Trait Loci (Cesar Correia, Nuno Sepulveda and Carlos Daniel Paulino).- Concomitant Latent Class Models Applied to Mathematics Education (Maria Eugenia Ferrao and Jose G. Dias).- Evaluating Discriminant Analysis Results (Ana Sousa Ferreira and Margarida Cardoso).- Distribution of the Number of Losses in Busy-periods of MX /G/1/n Systems (Fatima Ferreira, Antonio Pacheco and Helena Ribeiro).- Misleading Signals in Simultaneous Residual Schemes for the Process Mean and Variance of AR(1) Processes: A Stochastic Ordering Approach (Patricia Ferreira Ramos, Manuel Cabral Morais and Antonio Pacheco).- Conditional EVT for VAR Estimation: Comparison with a new Independence Test (M. I. Fraga Alves and P. Araujo Santos).- Asymptotic Distribution of the Maximum for a Chaotic Economic Model (Ana Cristina Moreira Freitas).- Adaptive Choice of Thresholds and the Bootstrap Methodology: An Empirical Study (M. Ivette Gomes, Fernanda Figueiredo and M. Manuela Neves).- Distributional Properties of Generalized Threshold ARCH Models (E. Goncalves and N. Mendes-Lopes).- Preliminary Results on Confidence Intervals for Open Bonus Malus (Gracinda R. Guerreiro, Joao T. Mexia and Maria F. Miguens).- Study of the Electrocardiographic Fluctuations on Brugada Syndrome Screening (Carla Henriques, Ana Cristina Matos and Luis Ferreira dos Santos).- Circulatory System Diseases and Neoplasms Mortality on Older Portuguese Population: A Spatio-temporal Analysis by Age and Sex (Sandra Lagarto, Carla Nunes, Dulce Gomes and Maria Filomena Mendes).- Absolute Diffusion Process: Sensitivity Measures (Manuela Larguinho, Jose Carlos Dias and Carlos A. Braumann).- Scaling Exponents in Heart Rate Variability (Argentina Leite, Maria Eduarda Silva and Ana Paula Rocha).- Prediction of Dementia Patients: A Comparative Approach Using Parametric vs. non Parametric Classifiers (Joao Maroco, Dina Silva, Manuela Guerreiro, Alexandre de Mendonca and Isabel Santana).- Pareto Scale Mixtures (Miguel Martins Felgueiras).- Fitting Johnsons SB distribution to Forest Tree Diameter (Ayana Mateus and Margarida Tome).- On a Continuous Time Stock Price Model With two Mean Reverting Regimes (Pedro P. Mota).- Generalized F Tests in Models With Random Perturbations: The Truncated Normal Case (Celia Nunes, Dario Ferreira, Sandra Ferreira and Joao T. Mexia).- Generalized Linear Models, Generalized Additive Models and Neural Networks: Comparative Study in Medical Applications (Ana Luisa Papoila, Cristina Rocha, Carlos Geraldes and Patricia Xufre).- Joint Regression Analysis and Incorporation of Environmental Variables in Stochastic Frontier Production Function: An Application to Experimental Data of Winter Rye (Dulce Gamito Pereira and Ana Sampaio).- On the Maximum and Minimum of a Stationary Random Field (Luisa Pereira).- Publication Bias and Meta-analytic Syntheses (D. Pestana, M. L. Rocha, R. Vasconcelos and S. Velosa).- Self-perception of Health Status and Socio-economic Differences in the Use of Health Services (Alexandra Pinto, Victor Lobo, Fernando Bacao and Helena Bacelar-Nicolau).- Comparison of Modal Variables Using Multivariate Analysis (Isabel Pinto Doria, Aurea Sousa, Helena Bacelar-Nicolau and Georges Le Calve).- Disentangling the Relationship Between Entrepreneurship and Job Creation by Poisson Mixture Regressions (Leandro P. Pontes and Jose G. Dias).-Simulation Study of the Calibration Technique in the Extremal Index Estimation (D. Prata Gomes, Joao T. Mexia and M. Manuela Neves).- Semi-parametric Building of the Optimal Screening Region in Supervised Classification (Sandra Ramos, Maria Antonia Amaral Turkman and Marilia Antunes).- An Application of Statistical Methods of Indirect Estimation and Projection of Internal Migration Flows Within the Portuguese Mainland (Maria FilomenaMendes, Antonio Caleiro, Sandra Lagarto and Filipe Ribeiro).- Robust Clustering Method for the Detection of Outliers: Using AIC to Select the Number of Clusters (Carla M. Santos-Pereira and Ana M. Pires).- HLA Allele and Haplotype Frequencies of the Portuguese Bone Marrow Donors Registry (Ricardo Sao Joao, Ana Luisa Papoila, Dario Ligeiro and Helder Trindade).- Independent Component Analysis for Extended Time Series in Climate Data (Fernando Sebastiao and Irene Oliveira).- Life Satisfaction: a MIMIC Approach With a Discrete Latent Variable (Patricia Serra, Jose G. Dias and Maria de Fatima Salgueiro).- An Application of MRMC ROC Curves on Radiology (Carina Silva-Fortes, Maria Antonia Amaral Turkman, Luis Lanca, Ricardo Silva and Goncalo Marques).- Some Remarks About Gibbs Variable Selection Performance (Julia Teles and Maria Antonia Amaral Turkman).- Dependence of Multivariate Extremes (C. Viseu, L. Pereira, A.P. Martins and H. Ferreira).