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

I Wayan Mangku

doi:10.22342/jims.17.1.8.1-9

I Wayan Mangku ⁽¹⁾

(1) Bogor Agricultural University, Indonesia

https://doi.org/10.22342/jims.17.1.8.1-9

Issue
Volume 17 Number 1 (April 2011)

Submitted
February 12, 2012

Accepted
February 13, 2012

Published
February 13, 2011

Keywords:

Cyclic Poisson process, intensity function, linear trend, asymptotic bias, asymptotic variance

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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

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Authors

I Wayan Mangku

Bogor Agricultural University

erick_paulus@yahoo.com (Primary Contact)

Mangku, I. W. (2011). ASYMPTOTIC APPROXIMATIONS TO THE BIAS AND VARIANCE OF A KERNEL-TYPE ESTIMATOR OF THE INTENSITY OF THE CYCLIC POISSON PROCESS WITH THE LINEAR TREND. Journal of the Indonesian Mathematical Society, 17(1), 1–9. https://doi.org/10.22342/jims.17.1.8.1-9