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HERNIWAT, H.
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Mathematics

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CONSISTENCY OF KERNEL-TYPE ESTIMATORS FOR THE FIRST AND SECOND DERIVATIVES OF A PERIODIC POISSON INTENSITY FUNCTION MANGKU, I W.; SYAMSURI, S.; HERNIWAT, H.
MILANG Journal of Mathematics and Its Applications Vol. 6 No. 2 (2007): Journal of Mathematics and Its Applications
Publisher : School of Data Science, Mathematics and Informatics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29244/jmap.6.2.47-55

Abstract

We construct and investigate consistent kernel-type estimators for the first and second derivatives of a periodic Poisson intensity function when the period is known. We do not assume any particular parametric form for the intensity function. More- over, we consider the situation when only a single realization of the Poisson process is available, and only observed in a bounded interval. We prove that the proposed estimators are consistent when the length of the interval goes to infinity. We also prove that the mean-squared error of the estimators converge to zero when the length of the interval goes to infinity.1991 Mathematics Subject Classification: 60G55, 62G05, 62G20.
Co-Authors MANGKU, I W. SYAMSURI, S.