DENSITY DECONVOLUTION OF DIFFERENT CONDITIONAL DISTRIBUTIONS

MARIANNA PENSKY AND AHMED I. ZAYED

Department of Mathematics, University of Central Florida, Orlando, FL 32816, U.S.A.

(Received November 1, 2000; revised May 28, 2001)

Abstract. Recently, a new technique to circumvent the ill-posedness of the deconvolution problem has been suggested. This technique is based on what is known as multi-channel convolution system. In this paper, we modify and develop this technique in order to adapt it for statistical use. We then apply it to the problem of estimation of deconvolution density in the case of different conditional densities. This method enables us to combine equations efficiently for any set of conditional densities and to construct estimators in cases where the characteristic functions of the conditional distributions vanish at some points, as it happens in the case of uniform and triangular distributions.

Key words and phrases: Deconvolution, ill-posed problem, probability density.