Optimal expectile smoothing

Schnabel, S., Eilers, P. H. C.

Computational Statistics and Data Analysis, 53:12, 4168-4177 (2009)


Quantiles are computed by optimizing an asymmetrically weighted L1 norm, i.e. the sum of absolute values of residuals. Expectiles are obtained in a similar way when using an L2 norm, i.e. the sum of squares. Computation is extremely simple: weighted regression leads to the global minimum in a handful of iterations. Least asymmetrically weighted squares are combined with P-splines to compute smooth expectile curves. Asymmetric cross-validation and the Schall algorithm for mixed models allow efficient optimization of the smoothing parameter. Performance is illustrated on simulated and empirical data.