Estimation of Probability Densities of the Absolute Value and Argument of Complex Random Variables

We particularize criteria proposed by one of the authors for estimating the probability densities of a random vector of size N to the case of even N. For the presentation convenience in this case, two-dimensional vectors are treated as complex random variables and the probability densities of their absolute values and arguments are estimated. The estimation algorithms are synthesized on the basis of the obtained criteria under conditions of both presence and absence of complete a priori information on the sample statistic. A number of examples are given to prove that the obtained algorithms are optimal in the statistical sense. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 48, No. 7, pp. 616–627, July 2005.