Speaker: Andrea Meilan Vila (Department of Statistics, Universidad Carlos III de Madrid)

Title: Kernel regression estimation for a circular response and different types of covariates

Abstract:

The analysis of a variable of interest that depends on other variable(s) is a typical issue appearing in many practical problems. Regression analysis provides the statistical tools to address this type of problem. This topic has been deeply studied, especially when the variables in the study are of Euclidean type. However, there are situations where the data present certain kinds of complexities, for example, the involved variables are of circular or functional type, and the classical regression procedures designed for Euclidean data may not be appropriate. In these scenarios, these techniques would have to be conveniently modified to provide useful results. 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 that are close in space tend to be more similar than observations that are far apart. This work aims to design and study new approaches to deal with regression function estimation for models with a circular response and different types of covariates. For an R^d-valued covariate, nonparametric proposals to estimate the circular regression function are provided and studied, under the assumption of independence and also for spatially correlated errors. These estimators are also adapted for regression models with a functional covariate. In the above-mentioned frameworks, the asymptotic bias and variance of the proposed estimators are calculated. Some guidelines for their practical implementation are provided, checking their sample performance through simulations. Finally, the behavior of the estimators is also illustrated with real data sets.