Nonparametric inference for geometric processes

Abstract

A stochastic process {Xn,n = 1,2,...} is a geometric n process if there exists a > 0 so that is a n 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, λ and σ2 of the geometric process by using linear regression 2 method, where λ and σ2 are the mean and variance of X1 respectively.