Nonparametric estimation of directional highest density regions

Highest density regions (HDRs) are defined as level sets containing sample points of relatively high density. Although Euclidean HDR estimation from a random sample, generated from the underlying density, has been widely considered in the statistical literature, this problem has not been contemplated for directional data yet. In this work, directional HDRs are formally defined and plug-in estimators based on kernel smoothing and associated confidence regions are proposed. We also provide a new suitable bootstrap bandwidth selector for plug-in HDRs estimation based on the minimization of an error criteria that involves the Hausdorff distance between the boundaries of the theoretical and estimated HDRs. An extensive simulation study shows the performance of the resulting estimator for the circle and for the sphere. The methodology is applied to analyze two real data sets in animal orientation and seismologyOpen Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. R.M. Crujeiras and P. Saavedra-Nieves acknowledge the financial support of Ministerio de Economía y Competitividad and Ministerio de Ciencia e Innovación of the Spanish government under grants MTM2016-76969P, MTM2017-089422-P, PID2020-118101GB-I00 and PID2020-116587GB-I00 and ERDF. Authors also thank Elena Vázquez Abal for her help, Prof. Felicita Scapini for providing the sandhoppers data (collected under the support of the European Project ERB ICI8-CT98-0270), the computational resources of the CESGA Supercomputing Center and the referees for the constructive comments which have improved the paperS

Processos de canonizaçom e margens sistémicas no sistema literário galego: estudo comparativo das trajetórias de Teresa Moure e Susana Sanches Arins

[Resumo] Este trabalho pretende identificar e analisar os processos de canonizaçom operantes nas margens reintegracionistas do sistema literário galego, através do estudo comparativo das trajetórias de duas agentes do mesmo: umha autora que, trás atingir certo grau de consagraçom no centro sistémico, transita para o subsistema reintegracionista (Teresa Moure) e outra que participa apenas desse subsistema ao longo de toda a sua trajetória (Susana Sanches Arins). Para isto, som demarcados os seguintes objetivos: a precisom dos estados sucessivos do campo literário em que as agentes desenvolvem a sua trajetória, as tomadas de posiçom efetuadas polas agentes, assim como qualquer outra mostra do seu nível de consagraçom (repertórios atualizados, campos em que participam, prémios literários ganhados, etc.). Esta proposta combina a metodologia sociológica com o estudo de caso demonstra a influência dos processos de atribuiçom de valor centrais na periferia reintegracionista do SLG.Traballo fin de mestrado (UDC.FIL). Literatura, cultura e diversidade. Curso 2018/201

Inferencia estatística

Titulación: Grao en Enxeñaría Informática -- Materia: EstatísticaAs bases da probabilidade e a estatística, segundo a Association for Computing Machinery e a IEEE Computer Society, subxacen aos conceptos de fiabilidade, seguridade e dependencia, factores fundamentais no ámbito da Enxeñaría en xeral e da Enxeñaría Informática, en particular. Con esta premisa, as devanditas asociacións elaboraron unhas guías para o deseño dos currículos formativos nos Graos en Enxeñaría Informática, onde se establece como obxectivo fundamental que o alumnado destes títulos adquira coñecementos dos modelos de probabilidade discretos e continuos, das distribucións na mostraxe, dos métodos de estimación e contraste e do modelado a través da regresión. No currículo do Grao en Enxeñaría Informática da Universidade de Santiago de Compostela (USC), a Estatística é unha materia do segundo semestre do primeiro curso, pertencente ao módulo de Matemáticas xunto con Álxebra, Fundamentos de Matemáticas, Matemática Discreta (primeiro semestre) e Cálculo e Análise Numérica (segundo semestre). Todas estas son materias básicas e polo tanto de carácter xeral, nas que se debe realizar unha tarefa de nivelación dos coñecementos do alumnado, proporcionando asemade os alicerces metodolóxicos para desenvolvementos posteriores noutras áreas como a representación gráfica ou a xestión empresarial. Nesta unidade didáctica presentaranse inicialmente os obxectivos da UD III (Inferencia Estatística), detallando a continuación os contidos máis relevantes da mesma considerando á súa vez tres bloques temáticos diferenciados (introdución á Inferencia Estatística, estimación de parámetros e contraste de hipóteses). Para unha selección adecuada dos contidos a incluír na UD, debe terse presente que o obxectivo final da Inferencia Estatística é tirar conclusións sobre una poboación (conxunto homoxéneo de individuos sobre os que se estudan características observables). Estas conclusións sobre o comportamento da poboación poden referirse a aspectos paramétricos, a comportamentos globais da distribución ou a comparativas con outras poboacións ou entre grupos dentro da mesma. Así, as técnicas da Inferencia Estatística poderían clasificarse en dous tipos, atendendo ao seu obxectivo final, se ben ambos os dous están estreitamente relacionados: a estimación de parámetros, de maneira puntual ou mediante intervalos, e o contraste de hipóteses. Abordar estes problemas dende un enfoque xeral presenta unha gran dificultade matemática, que excedería os coñecementos do alumnado de primeiro curso, polo que os contidos desta UD restrinxiranse, nun primeiro termo, a poboacións normais e ao estudo de proporcións. Malia a imposibilidade dun tratamento amplo do problema da estimación de parámetros, incluiranse algunhas breves mencións ás metodoloxías xerais de estimación, rematando esta UD con algunhas nocións sobre contrastes non paramétricos. Os contidos desta UD atópanse distribuídos en tres bloques temáticos, consecutivos no tempo, dado que cada un deles senta as bases do seguinte. As gráficas presentadas foron elaboradas co software estatístico R. No Anexo, inclúese unha breve presentación da libraría rpanel, en concreto, da utilidade rpcartoons que permite realizar algunhas ilustracións gráficas relacionadas cos contidos desta UD.Universidade de Santiago de Compostela. Servizo de Normalización Lingüístic

A circular nonhomogeneous hidden Markov field for the spatial segmentation of wildfire occurrences

This is the pre-peer reviewed version of the following article: Ameijeiras‐Alonso, J, Lagona, F, Ranalli, M, Crujeiras, RM. A circular nonhomogeneous hidden Markov field for the spatial segmentation of wildfire occurrences. Environmetrics. 2019; 30:e2501. https://doi.org/10.1002/env.2501, which has been published in final form at https://doi.org/10.1002/env.2501. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived VersionsMotivated by studies of wildfire seasonality, we propose a nonhomogeneous hidden Markov random field to model the spatial distribution of georeferenced fire occurrences during the year, by representing occurrence times as circular data. The model is based on a mixture of Kato–Jones circular densities, whose parameters vary across space according to a latent nonhomogeneous Potts model, modulated by georeferenced covariates. It allows us to segment fire occurrences according to a finite number of latent classes that represent the conditional distributions of the data under specific periods of the year, simultaneously accounting for unobserved heterogeneity and spatial autocorrelation. Further, it parsimoniously accommodates specific features of wildfire occurrence data such as multimodality, skewness, and kurtosis. Due to the numerical intractability of the likelihood function, estimation of the parameters is based on composite likelihood methods. It reduces to a computationally efficient expectation–maximization algorithm that iteratively alternates the maximization of a weighted composite likelihood function with weights updating. The proposal is illustrated in a study of wildfire occurrences in the Iberian Peninsula during a decadeJose Ameijeiras‐Alonso and Rosa M. Crujeiras gratefully acknowledge the support of Project MTM2016‐76969‐P (Spanish State Research Agency, AEI), co‐funded by the European Regional Development Fund (ERDF), IAP network from Belgian Science Policy. Part of the research was carried out by Jose Ameijeiras‐Alonso during his visit to University of Roma Tre, supported by Grants BES‐2014‐071006 and EEBB‐I‐17‐12716 from the Spanish Ministry of Economy, Industry and Competitiveness. Francesco Lagona is supported by the 2015 PRIN supported project “Environmental processes and human activities: capturing their interactions via statistical methods”, funded by the Italian Ministry of Education, University and Scientific ResearchNO

An introduction to statistical methods for circular data

Angles, directions, events, occurrences along time... all of them can be viewed as data on a circle (circular data). The particular nature of this type of data requires specific and adapted inferential and modelling procedures. Although there are quite a few references on this topic, and despite circular data are quite common in many applied sciences, they are frequently overlooked. This brief introduction aims to give the reader just some basic ideas on circular data analysis (with some mentions to the general case of spherical or directional data), providing some relevant references and tools for their application in practiceS

Mode testing, critical bandwidth and excess mass

This is a post-peer-review, pre-copyedit version of an article published in TEST. The final authenticated version is available online at: https://doi.org/10.1007/s11749-018-0611-5The identification of peaks or maxima in probability densities, by mode testing or bump hunting, has become an important problem in applied fields. For real random variables, this task has been approached in the statistical literature from different perspectives, with the proposal of testing procedures which are based on kernel density estimators or on the quantification of excess mass. However, none of the existing proposals for testing the number of modes provides a satisfactory performance in practice. In this work, a new procedure which combines the previous approaches (smoothing and excess mass) is presented together with a revision on the previous proposals. The new method is compared with the existing ones in an extensive simulation study, showing a superior behaviour, with good calibration and power results. Theoretical justification for its performance is also obtained. A real data example on philatelic data is also included for illustration purposes, revising previous approaches and discussing the results with the new procedureThe authors gratefully acknowledge the support of Projects MTM2016-76969-P (Spanish State Research Agency, AEI) and MTM2013-41383-P (Spanish Ministry of Economy, Industry and Competitiveness), both co-funded by the European Regional Development Fund (ERDF), IAP network from Belgian Science Policy. Work of J. Ameijeiras-Alonso has been supported by the Ph.D. Grant BES-2014-071006 from the Spanish Ministry of Economy, Industry and CompetitivenessS

Nonparametric estimation of circular trend surfaces with application to wave directions

Versión final aceptada de: https://doi.org/10.1007/s00477-020-01919-5This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1007/s00477-020-01919-5In oceanography, modeling wave fields requires the use of statistical tools capable of handling the circular nature of the data measurements. An important issue in ocean wave analysis is the study of height and direction waves, being direction values recorded as angles or, equivalently, as points on a unit circle. Hence, reconstruction of a wave direction field on the sea surface can be approached by the use of a linear–circular regression model, viewing wave directions as a realization of a circular spatial process whose trend should be estimated. In this paper, we consider a spatial regression model with a circular response and several real-valued predictors. Nonparametric estimators of the circular trend surface are proposed, accounting for the (unknown) spatial correlation. Some asymptotic results about these estimators as well as some guidelines for their practical implementation are also given. The performance of the proposed estimators is investigated in a simulation study. An application to wave directions in the Adriatic Sea is provided for illustration.The authors acknowledge the support from the Xunta de Galicia Grant ED481A-2017/361 and the European Union (European Social Fund—ESF). This research has been partially supported by MINECO Grants MTM2016-76969-P and MTM2017-82724-R, and by the Xunta de Galicia (Grupos de Referencia Competitiva ED431C-2016-015, ED431C-2017-38 and ED431C-2020-14, and Centro de Investigación del SUG ED431G 2019/01), all of them through the ERDF. The authors thank Prof. Agnese Panzera, from the University of Florence, for her help in the theoretical developments of the paper and her general comments about this work. The authors also thank an Associate Editor and two anonymous referees for numerous useful comments that significantly improved this article.Xunta de Galicia; ED481A-2017/361Xunta de Galicia; ED431C-2016-015Xunta de Galicia; ED431C-2017-38Xunta de Galicia; ED431C-2020-14Xunta de Galicia; ED431G 2019/0

Goodness-of-fit tests for multiple regression with circular response

Versión final aceptada de: https://doi.org/10.1080/00949655.2021.2015597This is an Accepted Manuscript of an article published by Taylor & Francis in Journal of Statistical Computation and Simulation on 2022, available at: https://doi.org/10.1080/00949655.2021.2015597[Abstract]: Testing procedures for assessing a parametric regression model with a circular response and an Rd-valued covariate are proposed and analysed in this work. The test statistics are based on a circular distance comparing a (non-smoothed or smoothed) parametric circular regression estimator and a nonparametric one. Two bootstrap procedures for calibrating the tests in practice are also presented. Finite sample performance of the tests in different scenarios is analysed by simulations and illustrated with real data examples.The authors thank Prof. Felicita Scapini and her research team who kindly provided the sand hoppers data that are used in this work. Data were collected within the Project ERB ICI8-CT98-0270 from the European Commission, Directorate General XII Science. The authors also thank the Associate Editor and two anonymous referees for numerous useful comments that significantly improved this article. This research has been partially supported by MINECO (Grants MTM2016-76969-P and MTM2017-82724-R), MICINN (Grant PID2020-113578RB-I00) and by Xunta de Galicia (Grant ED481A-2017/361, through the ESF. Grupos de Referencia Competitiva ED431C-2016-015, ED431C-2017-38 and ED431C-2020-14, and Centro de Investigación del SUG ED431G 2019/01, through the ERDF).Xunta de Galicia; ED481A-2017/361Xunta de Galicia; ED431C-2016-015Xunta de Galicia; ED431C-2017-38Xunta de Galicia; ED431C-2020-14Xunta de Galicia; ED431G 2019/0

On the second order properties of the multidimensional periodogram for regularly spaced data

Recently there is growing interest in improving the level of knowledge of spatial and spatio-temporal processes using spectral techniques. The properties of the estimator of the spectral density, the periodogram, have been broadly studied under different asymptotic assumptions that imply a valuable loss of information about the behavior of the underlying process that is often observed on a grid of small size and with sparse data. In this scheme, neither increasing domain nor shrinking asymptotics applies. The goal of this paper is to study the properties of the multidimensional periodogram, under both cases of tapering and no tapering, and the assumption of finite dimensionality of the regular lattice where the process is observed. We present some theoretical results regarding the second order properties of the multidimensional periodogram. Furthermore, we show that, independent of the tapering procedure, periodogram values present a dependence structure which is not stationary and which particularly depends on weights which are proportional to the Bartlett kernel or the chosen taperThis work was supported by the Spanish Ministry of Science and Education project MTM2005-0020 and grants MTM2004-06231 and BES2003-0581, and by Xunta de Galicia projects PGIDIT06PXIB207009PR and PGIDIT03PXIC20702PNS