This paper proposes a density estimation technique whereby a momentbased adjustment is applied to the saddlepoint approximation as determined from the empirical cumulant-generating function associated with a given set of observations. When two variables are involved, the product of saddlepoint density estimates of the marginal distributions is adjusted by means of a bivariate polynomial. Unlike kernel density estimates, the modified saddlepoint density estimates have simple functional representations that readily lend themselves to algebraic manipulations. Since the proposed methodology relies essentially on a determinate number of sample moments, it is particularly well suited for modeling massive data sets. As well, it should lead to improved density estimates in connection with the countless current applications arising in various fields of scientific investigation. For illustrative purposes, the density estimation approach being advocated herein is applied to two univariate and two bivariate data sets.
Keywords and Phrases
Saddlepoint approximation; density estimation; moments; empirical cumulant-generating function; big data; bivariate density estimate
A.M.S. subject classiﬁcation
62G07; 62E17; 62H10.