Estimation of the Intensity Function of a Periodic Poisson Process with Power Function Trend

In this paper, we construct the estimation for periodic component of the intensity function of a periodic Poisson process in the presence of power function trend by using general kernel function. It is considered the worst case where there is only available a single realization of the Poisson process having intensity which consist of a periodic component and a power function trend, observed in interval [0,n]. It is assumed that the period of the periodic component is known and the slope of the power function trend is unknown. It has been formulated the consistent estimator for the slope and the estimator for the periodic component.