CONSISTENCY OF KERNEL-TYPE ESTIMATORS FOR THE FIRST AND SECOND DERIVATIVES OF A PERIODIC POISSON INTENSITY FUNCTION
| Main Authors: | MANGKU, I W.; Bogor Agricultural University, SYAMSURI, S.; Bogor Agricultural University, HERNIWAT, H.; Bogor Agricultural University |
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| Format: | Article info application/pdf eJournal |
| Bahasa: | eng |
| Terbitan: |
Dept. of Mathematics, Bogor Agricultural University
, 2007
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| Online Access: |
http://journal.ipb.ac.id/index.php/jmap/article/view/20302 http://journal.ipb.ac.id/index.php/jmap/article/view/20302/14022 |
Daftar Isi:
- 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.