Nonparametric regression with filtered data

Details Nonparametric regression with filtered data Nonparametric regression with filtered data

2011-02-09

arxiv.org/abs/1102.1857v1

Bernoulli 2011, Vol. 17, No. 1, 60-87

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.3150/10-BEJ260 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

10.3150/10-BEJ260

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.

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