Pendugaan komponen periodik fungsi intensitas berbentuk fungsi periodik kali tren kuadratik suatu proses Poisson non-homogen

Abstract

This manuscript is concerned with estimation of periodic component of the intensity function of form periodic function multiplied by quadratic trend of a non-homogeneous Poisson process. It is considered the worst case, where there is only a single realization of a Poisson process with intensity function of form periodic component multiplied by a quadratic trend were observed in the interval [0,n]. It is assumed that the period of the periodic component is known. An estimator of the periodic component of the intensity function has been formulated and its Mean Square Error (MSE) has been proved converges to zero as n   . In addition, asymptotic approximations to the bias, variance, and the Mean Square Error (MSE) of the estimator have been formulated. An asymptotically optimal bandwidth for this estimator is also determined.