Penalized maximum likelihood estimation for a function of the intensity of a Poisson point process

被引：0

作者：

Dias R. ^{[1
]}

Ferreira C.S. ^{[1
]}

Garcia N.L. ^{[1
]}

机构：

[1] Departamento de Estatística, IMECC, UNICAMP, 13.081-970 Campinas, SP

来源：

Statistical Inference for Stochastic Processes | 2008年 / 11卷 / 1期

基金：

巴西圣保罗研究基金会;

关键词：

H-splines; Nonparametric estimation; Poisson processes;

D O I：

10.1007/s11203-006-9005-5

中图分类号：

学科分类号：

摘要：

Let f: [a,b] → ℝ be an unknown 2 times differentiable function and consider M to be an α- homogeneous Poisson process on Graf(f). The goal is to estimate f having a sample of the inhomogeneous Poisson process N constructed by dislocating each point of M perpendicularly to Graf(f) by a normal random variable with zero mean and constant variance σ2. The exact formulas for the mean measure and the intensity function of N are obtained. Then, the function f is estimated directly using a hybrid spline approach to penalized maximum likelihood. Simulation results indicate the procedure to be consistent as α → ∞ and σ2 → 0. © 2006 Springer Science+Business Media, LLC.

引用

页码：11 / 34

页数：23

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