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Title: Quantile regression estimation in varying coefficient models Authors:  Irene Gijbels - Katholieke Universiteit Leuven (Belgium) [presenting]
Abstract: Quantile regression is an important tool for describing the characteristics of conditional distributions. In both, mean and quantile regression, flexible models are often needed to capture the complexity of the underlying stochastic phenomenon. Among flexible models encountered in a multivariate covariate regression setting are varying coefficient models. These models introduce additional flexibility as compared to multiple linear regression models by allowing the coefficients to vary with, for example, another covariate. Coefficients are no longer real parameters but unknown functions. We focus on estimating conditional quantile functions in varying coefficient models. As a major tool we use B-spline approximations for the unknown coefficient functions. We distinguish between homoscedastic and heteroscedastic modeling, and discuss also estimation of the variability function in the latter setting. We summarize the theoretical results obtained and briefly discuss practical implementation issues. The finite-sample performances of the estimation methods have been investigated via simulation studies and their practical use has been illustrated in real data analysis.