EMPIRICAL LIKELIHOOD‐BASED KERNEL DENSITY ESTIMATION

summary This paper considers the estimation of a probability density function when extra distributional information is available (e.g. the mean of the distribution is known or the variance is a known function of the mean). The standard kernel method cannot exploit such extra information systematically as it uses an equal probability weight n-1 at each data point. The paper suggests using empirical likelihood to choose the probability weights under constraints formulated from the extra distributional information. An empirical likelihood-based kernel density estimator is given by replacing n-1 by the empirical likelihood weights, and has these advantages: it makes systematic use of the extra information, it is able to reflect the extra characteristics of the density function, and its variance is smaller than that of the standard kernel density estimator.