[Colloquium] Statistics Visiting PhD Presentation: MARTIN WENDLER, Tuesday, March 1, 2011, at 3:00 in Eckhart 110

[Katie Casey]

MARTIN WENDLER
Ruhr-Universitat Bochum, Germany
Visiting Student, University of Chicago


Generalized Linear Statistics of Dependent Data

TUESDAY, March 1, 2011, at 3:00 PM
110 Eckhart Hall, 5734 S. University Ave.

ABSTRACT

Generalized linear (GL) statistics are a unifying class that contains U-statistics, U-quantiles, L-statistics as well as trimmed and winsorized U-statistics. For example, many commonly used estimators of scale fall into this class. GL-statistics can be described as linear combinations of generalized quantiles. GL-statistics only have been studied under independence; in my talk, I will present an asymptotic theory for GL-statistics of sequences which are strongly mixing or L1 near epoch dependent on an absolutely regular process. For this purpose, we prove an almost sure approximation of the empirical U-process by a Gaussian process. With the help of a generalized Bahadur representation, it follows that such a strong invariance principle also holds for the empirical U-quantile process and consequently for GL-statistics. We obtain the functional central limit theorem and the law of the iterated logarithm for GL-statistics as straightforward corollaries.

Information about building access for persons with disabilities may be obtained in advance by 
calling Sandra Romero at 773.702-0541 or by email (sandra at galton.uchicago.edu). 
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