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 of the 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
infinity. In this paper, asymptotic approximations to its bias, variance and MSE
(Mean-Squared-Error) are computed. Asymptotically optimal bandwidth is also
derived.
Key words: Cyclic Poisson
process, intensity function, linear trend, asymptotic bias, asymptotic variance
Author: I Wayan Mangku,
Siswadi and Retno Budiarti
Journal Code: jpmatematikagg110017
