A note on Kernel density estimation with auxiliary information

It is well-known that the method of empirical likelihood can be employed to get sharper inferences on many functionals of the population distribution by making effective use of auxiliary information available in a nonparametric model. In this paper, we show that in the context of estimating a population density function, the modified kernel density estimator which makes use of the knowledge of auxiliary information does not sharpen our inferences on the population density function in the sense that the modified kernel density estimator is first order equivalent to the standard kernel density estimator which does not utilize auxiliary information.