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Title: Nonparametric circular regression estimation with spatially correlated errors Authors:  Andrea Meilan-Vila - Universidade da Coruna (Spain) [presenting]
Mario Francisco-Fernandez - Universidade da Coruna (Spain)
Rosa Crujeiras - University of Santiago de Compostela (Spain)
Agnese Panzera - University of Florence (Italy)
Abstract: Circular data can be regarded as points whose support is on a circle (with unit radius) measured in degrees or radians and with periodic nature. Examples of circular data arise in many applied fields such as biology (animal orientation), meteorology (wind direction) or oceanography (ocean currents), among others. These data may exhibit an important feature: close observations tend to be more similar than those that are far apart. Therefore, such observations cannot be treated as independent and the dependence structure should be taken into account in the estimation process. The aim is to propose and study nonparametric procedures to estimate the circular regression function, assuming a multivariate linear-circular regression model (circular responses and multivariate linear predictors) with spatially correlated circular errors. The new approaches consist in computing the inverse tangent function of the ratio between kernel estimators of the conditional expectation of the sine and cosine of the response, respectively. Nadaraya-Watson and local polynomial type estimators are considered. The asymptotic bias and variance of the proposed nonparametric estimators are derived. Additionally, some guidelines to select asymptotically local optimal matrix bandwidths are given. Simulation studies are carried out to check the finite sample performance of the considered estimators. The methodology is illustrated with a real data set.