文章基本信息

标题：Maximum likelihood estimation for stationary point processes
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作者：Madan L. Puri ; Pham D. Tuan
期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：1986
卷号：83
期号：3
页码：541-545
DOI：10.1073/pnas.83.3.541
语种：English
出版社：The National Academy of Sciences of the United States of America
摘要：In this paper we derive the log likelihood function for point processes in terms of their stochastic intensities by using the martingale approach. For practical purposes we work with an approximate log likelihood function that is shown to possess the usual asymptotic properties of a log likelihood function. The resulting estimates are strongly consistent and asymptotically normal (under some regularity conditions). As a by-product, a strong law of large numbers and a central limit theorem for martingales in continuous times are derived.
关键词：compensator ; stochastic intensity ; martingale ; natural increasing process ; point process ; predictable process