Nonparametric estimation of a trend based upon sampled continuous processes

Details Nonparametric estimation of a trend based upon sampled continuous processes Nonparametric estimation of a trend based upon sampled continuous processes

2008-12-15

arxiv.org/abs/0812.2749v2

Comptes Rendus Mathematiques de l'Academie des Sciences, Serie I 347 (2009) 191--194

Mathematics

Statistics Theory

Published at Comptes Rendus Mathematiques de l'Academie des Sciences

Scientific paper

10.1016/j.crma.2008.12.016

Let X be a second order random process indexed by a compact interval [0,T]. Assume that n independent realizations of X are observed on a fixed grid of p time points. Under mild regularity assumptions on the sample paths of X, we show the asymptotic normality of suitable nonparametric estimators of the trend function mu = EX in the space C([0,T]) as n, p go to infinity and, using Gaussian process theory, we derive approximate simultaneous confidence bands for mu.

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