Nonparametric multiple regression estimation for circular response
- PDF / 949,159 Bytes
- 23 Pages / 439.37 x 666.142 pts Page_size
- 12 Downloads / 248 Views
Nonparametric multiple regression estimation for circular response Andrea Meilán-Vila1 Agnese Panzera3
· Mario Francisco-Fernández1
· Rosa M. Crujeiras2
·
Received: 20 February 2020 / Accepted: 29 September 2020 © Sociedad de Estadística e Investigación Operativa 2020
Abstract Nonparametric estimators of a regression function with circular response and Rd valued predictor are considered in this work. Local polynomial estimators are proposed and studied. Expressions for the asymptotic conditional bias and variance of these estimators are derived, and some guidelines to select asymptotically optimal local bandwidth matrices are also provided. The finite sample behavior of the proposed estimators is assessed through simulations, and their performance is also illustrated with a real data set. Keywords Linear–circular regression · Multiple regression · Local polynomial estimators Mathematics Subject Classification 62G05 · 62G08 · 62G20 · 62H11
1 Introduction New challenges on regression modeling appear when trying to describe relations between variables and some of them do not belong to an Euclidean space. This is
Electronic supplementary material The online version of this article (https://doi.org/10.1007/s11749020-00736-w) contains supplementary material, which is available to authorized users.
B
Andrea Meilán-Vila [email protected]
1
Research Group MODES, CITIC, Department of Mathematics, Faculty of Computer Science, Universidade da Coruña, Campus de Elviña s/n, 15071 A Coruña, Spain
2
Department of Statistics, Mathematical Analysis and Optimization, Faculty of Mathematics, Universidade de Santiago de Compostela, Rúa Lope Gómez de Marzoa s/n, 15782 Santiago de Compostela, Spain
3
Dipartimento di Statistica, Informatica, Applicazioni “G. Parenti”, Università degli Studi di Firenze, Viale Morgagni, 59, 50134 Firenze, Italy
123
A. Meilán-Vila et al.
the case for regression problems where some or all of the involved variables are circular ones. The special nature of circular data (points on the circumference of the unit circle; angles in T = [0, 2π )) relies on their periodicity, which requires ad hoc statistical methods to analyze them. Circular statistics is an evolving discipline, and several statistical techniques for linear data now may claim their circular analogues. Comprehensive reviews on circular statistics (or more general, directional data) are provided in Fisher (1995), Jammalamadaka and SenGupta (2001) or Mardia and Jupp (2000). Some recent advances in directional statistics are collected in Ley and Verdebout (2017). Examples of circular data arise in many scientific fields such as biology, studying animal orientation (Batschelet 1981), environmental applications (SenGupta and Ugwuowo 2006) or oceanography (as in Wang et al. 2015, among others). When the circular variable is supposed to vary with respect to other covariates and the goal is to model such a relation, regression estimators for circular responses must be designed and analyzed. Parametric regression approaches were original
Data Loading...
