Nonparametric Inference for Regression Models with Spatially Correlated Errors

Programa Oficial de Doutoramento en Estatística e Investigación Operativa. 5017V01[Abstract] Regression estimation can be approached using nonparametric procedures, producing exible estimators and avoiding misspeci cation problems. Alternatively, parametric methods may be preferable to nonparametric approaches if the regression function belongs to the assumed parametric family. However, a bad speci cation of this family can lead to wrong conclusions. Regression function misspeci cation problems can be somewhat tackled by applying a goodness-of- t test. For data presenting some kind of complexity, for example, circular data, the approaches used in regression estimation or in goodness-of- t tests have to be conveniently adapted. Moreover, it might occur that the variables of interest can present a certain type of dependence. For example, they can be spatially correlated, where observations which are close in space tend to be more similar than observations that are far apart. The goal of this thesis is twofold, rst, some inference problems for regression models with Euclidean response and covariates, and spatially correlated errors are analyzed. More speci - cally, a testing procedure for parametric regression models in the presence of spatial correlation is proposed. The second aim is to design and study new approaches to deal with regression function estimation and goodness-of- t tests for models with a circular response and an Rd-valued covariate. In this setting, nonparametric proposals to estimate the circular regression function are provided and studied, under the assumption of independence and also for spatially correlated errors. Moreover, goodness-of- t tests for assessing a parametric regression model are presented in these two frameworks. Comprehensive simulation studies and application of the different techniques to real datasets complete this dissertation.[Resumo] A estimación da regresión pode ser abordada empregando técnicas non paramétricas, dando lugar a estimadores exibles e evitando problemas de mala especi ficación. Alternativamente, os métodos paramétricos poden ser preferibles se a función de regresión pertence á familia paramétrica asumida. Porén, unha mala especi ficación desta familia pode levar a conclusións equivocadas. Os problemas de especi cación incorrecta da función de regresión poden ser abordados aplicando un contraste de bondade de axuste. Para datos que presentan algún tipo de complexidade, por exemplo, datos circulares, os métodos empregados na estimación ou nos contrastes, deben adaptarse convenientemente. Ademais, pode ocorrer que as variables de interese poidan presentar un certo tipo de dependencia. Por exemplo, poden estar espacialmente correladas, onde as observacións que están preto no espazo tenden a ser máis similares que as observacións que están lonxe. O obxectivo desta tese é dobre, primeiro, analízanse problemas de inferencia para modelos de regresión con resposta e covariables Euclídeas, e erros espacialmente correlados. Máis concretamente, contrástase se a función de regresión pertence a unha familia paramétrica, en presenza de correlación espacial. O segundo obxectivo é deseñar e estudar novos procedementos para abordar estimación e contrastes da función regresión para modelos con resposta circular e covariable con valores en Rd. Neste contexto, preséntanse e estúdanse propostas non paramétricas para estimar a función de regresión circular, baixo o suposto de independencia e tamén para erros espacialmente correlados. Ademais, nestes dous contextos, preséntanse contrastes para avaliar un modelo de regresión paramétrico. Esta memoria complétase con estudos de simulación exhaustivos e aplicacións a conxuntos de datos reais.[Resumen] La estimación de la regresión puede ser abordada usando técnicas no paramétricas, dando lugar a estimadores flexibles y evitando problemas de mala especificación. Alternativamente, los métodos paramétricos pueden ser preferibles si la función de regresión pertenece a la familia paramétrica asumida. Sin embargo, una mala especificación de esta familia puede llevar a conclusiones equivocadas. Los problemas de especificación incorrecta de la función de regresión pueden ser abordados aplicando un contraste de bondad de ajuste. Para datos que presentan algún tipo de complejidad, por ejemplo, datos circulares, los métodos utilizados en la estimación o en los contrastes, deben adaptarse convenientemente. Además, puede ocurrir que las variables de interés puedan presentar un cierto tipo de dependencia. Por ejemplo, pueden estar espacialmente correladas, donde las observaciones que están cerca en el espacio tienden a ser más similares que las observaciones que están lejos. El objetivo de esta tesis es doble, primero, se analizan problemas de inferencia para modelos de regresión con respuesta y covariables Euclídeas, y errores espacialmente correlados. Más concretamente, se contrasta si la función de regresión pertenece a una familia paramétrica, en presencia de correlación espacial. El segundo objetivo es diseñar y estudiar nuevos procedimientos para abordar estimación y contrastes de la función regresión para modelos con respuesta circular y covariable con valores en J.Rd. En este contexto, se presentan y estudian propuestas no paramétricas para estimar la función de regresión, bajo el supuesto de independencia y también para errores espacialmente correlados. Además, en estos dos contextos, se presentan contrastes para evaluar un modelo de regresión paramétrico. Esta memoria se completa con estudios de simulación exhaustivos y aplicaciones a conjuntos de datos reales. Palabras clave: contraste de bondad de ajuste, estadística circular, estimación no paramétrica, regresión lineal-circular, dependencia espacia

Self-tuning model predictive control for wake flows

This study presents a noise-robust closed-loop control strategy for wake flows employing model predictive control. The proposed control framework involves the autonomous offline selection of hyperparameters, eliminating the need for user interaction. To this purpose, Bayesian optimization maximizes the control performance, adapting to external disturbances, plant model inaccuracies, and actuation constraints. The noise robustness of the control is achieved through sensor data smoothing based on local polynomial regression. The plant model can be identified through either theoretical formulation or using existing data-driven techniques. In this work, we leverage the latter approach, which requires minimal user intervention. The self-tuned control strategy is applied to the control of the wake of the fluidic pinball, with the plant model based solely on aerodynamic force measurements. The closed-loop actuation results in two distinct control mechanisms: boat tailing for drag reduction and stagnation point control for lift stabilization. The control strategy proves to be highly effective even in realistic noise scenarios, despite relying on a plant model based on a reduced number of sensors

Nonparametric estimation of circular trend surfaces with application to wave directions

In 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.Comment: 34 pages, 8 figure

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

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

Nonparametric Regression Estimation for Circular Data

[Abstract] Non-parametric regression with a circular response variable and a unidimensional linear regressor is a topic which was discussed in the literature. In this work, we extend the results to the case of multivariate linear explanatory variables. Nonparametric procedures to estimate the circular regression function are formulated. A simulation study is carried out to study the sample performance of the proposed estimators.Ministerio de Economía y Competitividad; MTM2016-76969-PMinisterio de Economía y Competitividad; MTM2017-82724-RXunta de Galicia; ED481A-2017/361Grupos de Referencia Competitiva; ED431C-2016-015Centro Singular de Investigación de Galicia; ED431G/0

A goodness-of-fit test for regression models with spatially correlated errors

Versión final aceptada de: https://doi.org/10.1007/s11749-019-00678-yThis 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/s11749-019-00678-yThe problem of assessing a parametric regression model in the presence of spatial correlation is addressed in this work. For that purpose, a goodness-of-fit test based on a -distance comparing a parametric and nonparametric regression estimators is proposed. Asymptotic properties of the test statistic, both under the null hypothesis and under local alternatives, are derived. Additionally, a bootstrap procedure is designed to calibrate the test in practice. Finite sample performance of the test is analyzed through a simulation study, and its applicability is illustrated using a real data example.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 MTM2014-52876-R, MTM2016-76969-P and MTM2017-82724-R, and by the Xunta de Galicia (Grupos de Referencia Competitiva ED431C-2016-015 and ED431C-2017-38, and Centro Singular de Investigación de Galicia ED431G/01), all of them through the ERDF. We also thank two reviewers and the Associate Editor for their helpful comments and suggestions that significantly improved this article.Xunta de Galicia; ED431G/01Xunta de Galicia; ED481A 2017/361Xunta de Galicia; ED431C-2016-015Xunta de Galicia; ED431C-2017-3