"Condence Intervals for Geoadditive Expectile Regression Models"
Fabian Sobotka (Institut für Mathematik, Carl von Ossietzky Universität Oldenburg, Germany)
30/08/2011 - 13:00-14:00
1-19 Torrington Place, Galton LT
Department of Statistical Science, UCL
ALL WELCOME
Abstract:
While a simple mean regression attempts to describe the expectation of a response as a function of the covariates, the results of a quantile or expectile regression offer a much broader view. In principle, a dense set of expectiles or quantiles allows for an analysis of the complete conditional distribution of the response. This can lead to new insight in the dependency between the response and its covariates.
The results of a quantile regression can be acquired by minimising the asymmetrically weighted sum of the absolute residuals and in analogy an expectile regression is computed from the least asymmetrically weighted squares (LAWS) of the residuals. Hence the computation of expectile regression is much easier, though its interpretation is more complex than for a quantile. But only in expectile regression, one can build flexible additive models that contain different kinds of effects. For continuous univariate covariates, smooth regression curves can be fitted using penalised splines. Additionally the model can include spatial effects based on Markov random fields and tensor product splines, for example.
In our work, we construct pointwise confidence intervals for each fitted expectile. These give an insight into the precision of the estimated expectile curve and therefore into the amount of information that can be drawn from the expectiles. For the construction of the confidence intervals we use the asymptotic normality of the regression coefficients. We compare this method to the results of bootstrap percentile intervals, which are generally computationally intensive.
(joint work with Thomas Kneib, University Oldenburg, and Göran Kauermann, Linda Schulze Waltrup, University Bielefeld, Germany)
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