Bias corrections for some asymmetric kernel estimators

• Additive/nonnegative bias corrections are applied to asymmetric kernel estimators.
• Asymptotic properties of the improved estimators are derived rigorously.
• The finite sample performance of the proposed estimators is studied by simulation.

Several asymmetric kernel (AK) estimators of a density with support [0,∞)[0,∞) have been suggested in the recent fifteen years. In this paper, additive and nonnegative bias correction techniques, originally developed for the standard kernel estimator, are applied to some AK estimators when the underlying density has a fourth order derivative. The major contribution is to study asymptotic properties of new AK estimators corresponding to the limits of improved estimators. Simulation studies are conducted to illustrate the finite sample performance of the proposed estimators.