Model selection for least absolute deviations regression in small samples

We develop a small sample criterion (L1cAIC) for the selection of least absolute deviations regression models. In contrast to AIC (Akaike, 1973), L1cAIC provides an exactly unbiased estimator for the expected Kullback--Leibler information, assuming that the errors have a double exponential distribution and the model is not underfitted. In a Monte Carlo study, L1cAIC is found to perform much better than AIC and AICR (Ronchetti, 1985). A small sample criterion developed for normal least squares regression (cAIC, Hurvich and Tsai, 1988) is found to perform as well as L1cAIC. Further, cAIC is less computationally intensive than L1cAIC.