Am Freitag, 08. März 2002, spricht Prof. Ludger Rüschendorf über
"Adaptives Schätzen mit Schätzern vom neuronalen Netztyp".
Termin: Freitag, 08. März 2002, 11:15 Uhr
Ort: Technische Universität Wien
1040 Wien, Wiedner Hauptstraße 8-10
Freihaus, Turm C (grüner Bereich), 6. Stock,
Seminarraum 107
WWW:
http://www.fam.tuwien.ac.at/schedule
Abstract:
We obtain consistency results and determine convergence rates for neural
nets type estimators. In detail we consider the estimation of the
log-hazard function in random censoring models with covariates. Our
results are based on a general approach to sieved maximum likelihood
estimators (or minimum contrast estimators) including an adaptive version
of the estimators based on the method of structural risk estimation. A
related approach was developed recently in Birge Massart(1998) and Barron
Birge Massart(1999). In comparison we obtain upper bounds for the
estimation error involving more simple covering numbers. We discuss two
types of applications of the general results. For smoothness classes we
establish an adaptive version of the tensor product spline estimator as
introduced in Kooperberg Stone Truong(1995a). The minimax optimal rate of
convergence is not achieved for the standard sigmoidal neural net
estimator but is attained approximatively for some other activation
functions as e.g. for the threshold function. Assuming the existence of a
certain integral representation of the log-hazard function which is
related to some smoothness conditions, we obtain improved convergence
rates for net sieves type estimators as neural nets, radial basis function
nets and wavelet nets. Similar convergence rate results have been
established before for regression estimation in Barron(1993) and for
density estimation in Modha Masry(1996). Our improvement of the
convergence rate is based on an improved approximation result for
functions of this type by finite net classes.
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|christopher summer ||tu vienna, financial and actuarial mathematics
|tel +43 1 58801 10522 ||http://www.fam.tuwien.ac.at/~csummer
|fax +43 1 58801 10599 ||csummer(a)fam.tuwien.ac.at