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June, 1992 Statistical Inference for Conditional Curves: Poisson Process Approach
M. Falk, R.-D. Reiss
Ann. Statist. 20(2): 779-796 (June, 1992). DOI: 10.1214/aos/1176348656

Abstract

A Poisson approximation of a truncated, empirical point process enables us to reduce conditional statistical problems to unconditional ones. Let $(\mathbf{X,Y})$ be a $(d + m)$-dimensional random vector and denote by $F(\cdot\mid\mathbf{x})$ the conditional d.f. of $\mathbf{Y}$ given $\mathbf{X} = \mathbf{x}$. Applying our approach, one may study the fairly general problem of evaluating a functional parameter $T(F(\cdot\mid\mathbf{x}_1),\ldots,F(\cdot\mid\mathbf{x}_p))$ based on independent replicas $(\mathbf{X}_1,\mathbf{Y}_1),\ldots,(\mathbf{X}_n,\mathbf{Y}_n)$ of $(\mathbf{X,Y})$. This will be exemplified in the particular cases of nonparametric estimation of regression means and regression quantiles besides other functionals.

Citation

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M. Falk. R.-D. Reiss. "Statistical Inference for Conditional Curves: Poisson Process Approach." Ann. Statist. 20 (2) 779 - 796, June, 1992. https://doi.org/10.1214/aos/1176348656

Information

Published: June, 1992
First available in Project Euclid: 12 April 2007

zbMATH: 0760.62035
MathSciNet: MR1165592
Digital Object Identifier: 10.1214/aos/1176348656

Subjects:
Primary: 62J99
Secondary: 60G55

Rights: Copyright © 1992 Institute of Mathematical Statistics

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Vol.20 • No. 2 • June, 1992
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