The Annals of Statistics

Statistical Inference for Conditional Curves: Poisson Process Approach

M. Falk and R.-D. Reiss

Full-text: Open access

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.

Article information

Source
Ann. Statist., Volume 20, Number 2 (1992), 779-796.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176348656

Digital Object Identifier
doi:10.1214/aos/1176348656

Mathematical Reviews number (MathSciNet)
MR1165592

Zentralblatt MATH identifier
0760.62035

JSTOR
links.jstor.org

Subjects
Primary: 62J99: None of the above, but in this section
Secondary: 60G55: Point processes

Keywords
Regression functionals Poisson process empirical process Hellinger distance

Citation

Falk, M.; Reiss, R.-D. Statistical Inference for Conditional Curves: Poisson Process Approach. Ann. Statist. 20 (1992), no. 2, 779--796. doi:10.1214/aos/1176348656. https://projecteuclid.org/euclid.aos/1176348656


Export citation