Inference procedures based on the polar coordinates of the empirical characteristic function

Abstract

A general procedure of parametric estimation is proposed for distributions having characteristic function with polar coordinates in closed form. The procedure generalizes the method of Koutrouvelis (1982a) for estimating the parameters in the special case of Cauchy distributions. The resulting estimators are asymptotically equivalent to the estimators proposed by Feuerverger and McDunnough (1981b) and serve as a basis for chi-squared goodness-of-fit tests. For symmetric families the employment of polar coordinates of the empirical characteristic function is shown to have definite advantages in both estimation and testing.