Jun 03, 2011
from 04:00 PM to 05:00 PM
|Where||MR12, CMS, Wilberforce Road, Cambridge, CB3 0WB|
|Contact Name||Richard Nickl|
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Tatyana Krivobokova (Goettingen)
Title: Smoothing parameter selection for spline estimators
In contrast to other nonparameteric regression techniques, smoothing parameter selection for spline estimators can be performed not only by employing criteria that approximate the average mean squared error (e.g. generalized cross validation), but also by making use of the maximum likelihood (or empirical Bayes) paradigm. In the later case, the function to be estimated is assumed to be a realization of some stochastic process, rather than from a certain class of smooth functions. Under this assumption both smoothing parameter selectors for spline estimators are well-studied and known to perform similar. A more interesting problem is the properties of smoothing parameter estimators in the frequentist framework, that is if the underlying function is non-random. In this talk we discuss the asymptotic properties of both smoothing parameter selection criteria for general low-rank spline smoothers in the frequentist framework and give also insights into their small sample performance.