NONPARAMETRIC-INFERENCE FOR GEOMETRIC PROCESSES

A stochastic process {X(n), n = 1,2,...} is a geometric process if there exists a > 0 so that {a(n-1)X(n), n = 1,2,...0} is a renewal process. This is a stochastically monotone process, and can be used for modelling a point process with trend. In this paper, we study the statistical inference for geometric processes by nonparametric methods. Two statistics and a graphical technique are suggested for testing whether a process is a geometric process. Further, we can estimate the parameters a, lambda and sigma-2 of the geometric process by using linear regression method, where lambda and sigma-2 are the mean and variance of X1 respectively.