Minimax regression estimation for Poisson coprocess

For a Poisson point process X, Itô’s famous chaos expansion implies that every square integrable regression function r with covariate X can be decomposed as a sum of multiple stochastic integrals called chaos. In this paper, we consider the case where r can be decomposed as a sum of δ chaos. In the spirit of Cadre and Truquet [ESAIM: PS 19 (2015) 251–267], we introduce a semiparametric estimate of r based on i.i.d. copies of the data. We investigate the asymptotic minimax properties of our estimator when δ is known. We also propose an adaptive procedure when δ is unknown.

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On Stochastic Integrals with Respect to an Infinite Number of Poisson Point Process and Its Applications

Recent Development in Stochastic Dynamics and Stochastic Analysis - Interdisciplinary Mathematical Sciences ◽

10.1142/9789814277266_0015 ◽

2010 ◽

pp. 237-250

Author(s):

Guanglin Rang ◽

Qing Li ◽

Sheng You

Keyword(s):

Point Process ◽

Infinite Number ◽

Poisson Point Process ◽

Stochastic Integrals

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Nonparametric regression estimation onto a Poisson point process covariate

ESAIM Probability and Statistics ◽

10.1051/ps/2014023 ◽

2015 ◽

Vol 19 ◽

pp. 251-267 ◽

Cited By ~ 1

Author(s):

Benoît Cadre ◽

Lionel Truquet

Keyword(s):

Nonparametric Regression ◽

Point Process ◽

Poisson Point Process ◽

Regression Estimation ◽

Nonparametric Regression Estimation

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Nonparametric Density and Regression Estimation

The Journal of Economic Perspectives ◽

10.1257/jep.15.4.11 ◽

2001 ◽

Vol 15 (4) ◽

pp. 11-28 ◽

Cited By ~ 109

Author(s):

John DiNardo ◽

Justin L Tobias

Keyword(s):

Functional Form ◽

Regression Function ◽

Nonparametric Methods ◽

Actual Data ◽

Attractive Alternative ◽

Regression Estimation ◽

Parametric Methods ◽

Regression Functions

We provide a nontechnical review of recent nonparametric methods for estimating density and regression functions. The methods we describe make it possible for a researcher to estimate a regression function or density without having to specify in advance a particular--and hence potentially misspecified functional form. We compare these methods to more popular parametric alternatives (such as OLS), illustrate their use in several applications, and demonstrate their flexibility with actual data and generated-data experiments. We show that these methods are intuitive and easily implemented, and in the appropriate context may provide an attractive alternative to “simpler” parametric methods.

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