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arXiv · 0812.2749

Nonparametric estimation of a trend based upon sampled continuous processes

David Degras
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Abstract

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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David Degras. 2011-05-24. Nonparametric estimation of a trend based upon sampled continuous processes. https://doi.org/10.1016/j.crma.2008.12.016

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