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WROCŁAW UNIVERSITY
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TECHNOLOGY

Contents of PMS, Vol. 8, Fasc. ,
pages 103 - 110
 

ESTIMATION OF THE PERIODIC FUNCTION IN THE MULTIPLICATIVE INTENSITY MODEL

Jacek Leśkow

Abstract: Given a point process (N(t),t > 0) with the stochastic intensity c(t) of the form c(t) = a (t)Y (t), 0 it is shown that using the sieves technique one can construct a strongly consistent maximum likelihood estimator of the functional factor a(t). The latter is assumed to be periodic with the known period T = 1, and the ”censoring process” Y (t) fulfills some mild regularity assumptions. As an easy consequence it follows that the maximum likelihood estimator (MLE) can similarly be computed if (N (i)(t),t (- [0,1],i = 1,2,...) are not independent and identically distributed but satisfy some mixing conditions.

This paper extends the results of Karr [13].

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -

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