Estimation of the Parameters of Mixtures via Distance between Densities or Characteristic Functions

摘要

The integrated weighted distance between the sample characteristic function and the assumed characteristic function, or equivalently, the integrated distance between the smoothed assumed density and its kernel-estimate, is shown to be affective procedure for estimation of mixing proportions and for estimating all parameters of a modified compound Poisson distribution. These procedures are compared against their competitors in terms of efficiency, mean square error, and computational time. The characteristic function-based procedures are generally superior in terms of computation time for each of two types of procedures. The procedure introduced for the modified compound distribution is widely applicable since it is basically nonlinear modified x squared minimum. THe role of the sampling interval in estimating the parameters of the modified compound distribution is discussed and recommendations are made. Information matrices associated with this distribution are given for a spectrum of parameter values.