Estimation of Distance Functionals between Density Functions

Nonparametric kernel estimators of the type of quasi-$U$-statistics are proposed for the class of functionals describing various distance measures, such as $\chi^2$, Kullback–Leibler, Hellinger, Bhattacharya, etc. The functional estimators are shown to be asymptotically unbiased and the exact asymptotic variances are determined. The distances listed above are considered as examples.