Bernoulli

Nonparametric regression with filtered data

Oliver Linton, Enno Mammen, Jens Perch Nielsen, and Ingrid Van Keilegom

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Abstract

We present a general principle for estimating a regression function nonparametrically, allowing for a wide variety of data filtering, for example, repeated left truncation and right censoring. Both the mean and the median regression cases are considered. The method works by first estimating the conditional hazard function or conditional survivor function and then integrating. We also investigate improved methods that take account of model structure such as independent errors and show that such methods can improve performance when the model structure is true. We establish the pointwise asymptotic normality of our estimators.

Article information

Source
Bernoulli, Volume 17, Number 1 (2011), 60-87.

Dates
First available in Project Euclid: 8 February 2011

Permanent link to this document
https://projecteuclid.org/euclid.bj/1297173833

Digital Object Identifier
doi:10.3150/10-BEJ260

Mathematical Reviews number (MathSciNet)
MR2797982

Zentralblatt MATH identifier
1284.62227

Keywords
censoring counting process theory hazard functions kernel estimation local linear estimation truncation

Citation

Linton, Oliver; Mammen, Enno; Nielsen, Jens Perch; Van Keilegom, Ingrid. Nonparametric regression with filtered data. Bernoulli 17 (2011), no. 1, 60--87. doi:10.3150/10-BEJ260. https://projecteuclid.org/euclid.bj/1297173833


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