Nonparametric estimation of circular trend surfaces with application to wave directions
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ORIGINAL PAPER
Nonparametric estimation of circular trend surfaces with application to wave directions Andrea Meila´n-Vila1
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Rosa M. Crujeiras2
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Mario Francisco-Ferna´ndez1
Accepted: 23 October 2020 Ó Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract 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. Keywords Angular risk Circular data Local polynomial regression Spatial correlation Wave orientation
1 Introduction In many scientific fields, such as oceanography, meteorology or biology, data are angular measurements (points on the circumference of the unit circle), exhibiting in some cases a spatial dependence structure which should be accounted for in any modeling approach. For instance, Casson and Coles (1998) provided a spatial analysis about the direction of maximum wind speed at locations on the Gulf and Atlantic coasts of the United States. On a series of simulated hurricane wind speeds, the authors aim to model the stochastic behavior of the extreme wind speeds jointly with their associated directions. In other scenarios, circular measurements are also accompanied by observations of
& Andrea Meila´n-Vila [email protected] 1
Research Group MODES, CITIC, Department of Mathematics, Faculty of Computer Science, Universidade da Corun˜a, Campus de Elvin˜a s/n, 15071 A Corun˜a, Spain
2
Department of Statistics, Mathematical Analysis and Optimization, Faculty of Mathematics, Universidade de Santiago de Compostela, Ru´a Lope Go´mez de Marzoa s/n, 15782 Santiago de Compostela, Spain
real-valued random variables, as in Garcı´a-Portugue´s et al. (2014), who analyzed the relation between orientation and size of wildfires in Portugal; or Mastrantonio et al. (2018), who proposed a Markov model for multivariate circular– linear data to forecast the wind speed and direction in the city of Taranto (Italy). Alternative approaches using copulas have been also considered in similar contexts. For instance, Carnicero et al. (2013), explored the relation between wind direction and
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