Topic: Contributed on On quantiles, expectiles and extremiles Title: Model selection in expectile regression Authors:  Elmar Spiegel - University of Goettingen (Germany) [presenting]
Thomas Kneib - University of Goettingen (Germany)
Fabian Sobotka - University Oldenburg (Germany)
Abstract: Expectile regression can be seen as a mixture of quantile regression and normal linear regression, since an expectile $e_{\tau}$ is the solution of the least asymmetric weighted squared error function $\sum_i{w_{\tau}(y_i)(y_i-e_{\tau})^2}$, with data $y_i$, asymmetry parameter $\tau \in (0,1)$ and weighting function $w_{\tau}(y_i) = (1-\tau) I(y_i < e_{\tau}) + \tau I(y_i \geq e_{\tau})$. So expectile regression estimates the influence of covariates on the whole distribution of the response, but does not assume a specific distribution function. Since expectile regression depends on the $L_2$ norm, it is a generalization of the normal linear regression and inherits its advantages of easily including splines and spatial data. In general, model selection gains greater influence with more complex data and increasing complexity of the models. For expectile regression, model selection is especially interesting, since there are two different perspectives to be considered. On the one hand the best model for the current asymmetry parameter identifies which covariate has relevant influence on this special part of the distribution. On the other side the optimal model to describe the whole distribution is advantageous when comparing the effects of different asymmetries. For both approaches criteria based and shrinkage methods are possible. Finally a simulation study and an application on undernourished children illustrate the approaches.