Inverse gamma kernel density estimation for nonnegative data

This paper considers a varying asymmetric kernel estimation of the density f for nonnegative data. Regardless of f(0)=0 or f(0)>0, it is important to give a good varying shape/scale parameter for the inverse gamma (IGam) kernel, due to the problem of f̂(0)=0 in some existing literature. After reformulating the IGam kernel density estimator, asymptotic properties like mean integrated squared error, mean integrated absolute error, strong consistency, and asymptotic normality are investigated in detail, under some conditions on the target density f. Simulation studies are conducted to compare the proposed IGam kernel density estimators with the existing gamma kernel density estimators.