ASYMPTOTIC APPROXIMATIONS TO THE BIAS AND VARIANCE OF A KERNEL-TYPE ESTIMATOR OF THE INTENSITY OF THE CYCLIC POISSON PROCESS WITH THE LINEAR TREND

Abstract

From the previous research, a kernel-type estimator of the intensity ofthe cyclic Poisson process with the linear trend has been constructed using a singlerealization of the Poisson process observed in a bounded interval. This proposedestimator has been proved to be consistent as the size of the observation intervaltends to innity. In this paper, asymptotic approximations to its bias, variance andMSE (Mean-Squared-Error) are computed. Asymptotically optimal bandwidth isalso derived.

DOI : http://dx.doi.org/10.22342/jims.17.1.8.1-9