Maximum likelihood estimation in the multiplicative intensity model via sieves

DOI10.1214/aos/1176350356zbMath0628.62086OpenAlexW2042656961MaRDI QIDQ1093292

Alan F. Karr

Publication date: 1987

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aos/1176350356

zbMATH Keywords

local asymptotic normalitycentral limit theoremmaximum likelihood estimatorssieve estimatorsmethod of sievesstrong and weak consistencymultiplicative intensity processmartingale estimatorsMartingale limit theoremsunbounded log-likelihood functions

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Asymptotic distribution theory in statistics (62E20) Central limit and other weak theorems (60F05) Non-Markovian processes: estimation (62M09) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

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Nonparametric inference for a doubly stochastic Poisson process ⋮ Maximum likelihood identification of neural point process systems ⋮ A counting process approach to the regression analysis of grouped survival data ⋮ Histogram maximum likelihood estimator in the multiplicative intensity model ⋮ A penalty method for nonparametric estimation of the intensity function of a counting process ⋮ Time-dependent coefficients in a Cox-type regression model ⋮ Stochastic calculus as a tool in survival analysis: A review ⋮ Stochastic calculus as a tool in survival analysis: A review ⋮ A General Approach To Nonparametric Histogram Estimation ⋮ Convergence rates for the minimum complexity estimator of counting process intensities^∗

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