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June, 1987 Maximum Likelihood Estimation in the Multiplicative Intensity Model via Sieves
Alan F. Karr
Ann. Statist. 15(2): 473-490 (June, 1987). DOI: 10.1214/aos/1176350356

Abstract

For point processes comprising i.i.d. copies of a multiplicative intensity process, it is shown that even though log-likelihood functions are unbounded, consistent maximum likelihood estimators of the unknown function in the stochastic intensity can be constructed using the method of sieves. Conditions are given for existence and strong and weak consistency, in the $L^1$-norm, of suitably defined maximum likelihood estimators. A theorem on local asymptotic normality of log-likelihood functions is established, and applied to show that sieve estimators satisfy the same central limit theorem as do associated martingale estimators. Examples are presented. Martingale limit theorems are a principal tool throughout.

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Alan F. Karr. "Maximum Likelihood Estimation in the Multiplicative Intensity Model via Sieves." Ann. Statist. 15 (2) 473 - 490, June, 1987. https://doi.org/10.1214/aos/1176350356

Information

Published: June, 1987
First available in Project Euclid: 12 April 2007

zbMATH: 0628.62086
MathSciNet: MR888421
Digital Object Identifier: 10.1214/aos/1176350356

Subjects:
Primary: 62M09
Secondary: 60G55, 62F12, 62G05

Rights: Copyright © 1987 Institute of Mathematical Statistics

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Vol.15 • No. 2 • June, 1987
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