Adaptive orthogonal series density estimation for small samples

Abstract

Adaptive nonnegative orthogonal series estimators are investigated for the case of small sample sizes. The estimators are analyzed via intensive Monte Carlo study and oracle inequalities when an estimator is compared with optimal pseudo-estimators (“oracles”) based on an underlying (estimated) density. The results are favorable to a modified asymptotically efficient estimator. The paper also sheds light on that how to employ results of asymptotic theory for the practically important case of small sample sizes.