A Family of Estimators of a Density Using Concomitant Variable and Additional Data

In this paper we have suggested a family of estimators of a density f(y) of a random variable Y based upon a set of observations taken from a bivariate joint density β(x, y) of Y and a suitably chosen concomitant random variable X so that f(y) = ∫ β(x, y)dx. It is shown that the estimator envisaged by Ahmad and Singh (1989) is a particular member of the proposed family. Asymptotic expressions for bias and variance of the proposed family are obtained. Asymptotically optimum estimator (AOE) in the class is also identified.