[Statlist] Next talks: Friday, November 29, 2013 with Simon Broda (University of Amsterdam) and Thomas Mikosch (University of Copenhagen)

[Cecilia Rey]

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ETH and University of Zurich

Organisers:
Proff. P. Bühlmann - L. Held - T. Hothorn - H.R. Kuensch - M. Maathuis -
N. Meinshausen - S. van de Geer - M. Wolf

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We are glad to announce the following talks

Friday, November 29, 2013

              1) 15.15h to 16.00h   ETH Zurich HG G 19.1 with Simon Broda (University of Amsterdam) 

Titel: 
On distributions of ratios

Abstract: 
A large number of exact inferential procedures in statistics and econometrics involve the sampling distribution of ratios of random variables. If the denominator variable is positive, then tail probabilities of the ratio can be expressed as those of a suitably defined difference of random variables. If in addition, the joint characteristic function of numerator and denominator is known, then standard Fourier inversion techniques can be used to reconstruct the distribution function from it. Most research in this field has been based on this correspondence, but which breaks down when both numerator and denominator are supported on the entire real line. The present manuscript derives inversion formulae and saddlepoint approximations that remain valid in this case, and reduce to known results when the  denominator is almost surely positive. Applications include the IV estimator of a structural parameter in a just-identified equation.

                                         16.00h coffee break

            2) 16.15h to 17.00h     ETH Zurich HG G 19.1 with Thomas Mikosch (University of Copenhagen) 

Title:
Asymptotic theory for the sample covariance matrix of a heavy-tailed multivariate time series

Abstract:
We give an asymptotic theory for the eigenvalues of the sample covariance matrix of a multivariate time series. The time series constitutes a linear process across time and between components. 
The input noise of the linear process has regularly varying tails with index $\alpha\in (0,4)$; in particular, the time series has infinite fourth moment. We derive the limiting behavior for the largest eigenvalues of the sample covariance matrix and show point process convergence of the normalized eigenvalues. 
The limiting process has an explicit form involving points of a Poisson process and eigenvalues of a non-negative definite matrix Based on this convergence we derive limit theory for a host of other continuous functionals of the eigenvalues, including the joint convergence of the largest eigenvalues, the joint convergence of the largest eigenvalue and the trace of the sample covariance matrix, and the ratio of the largest eigenvalue to their sum. 

This is joint work with Richard A. Davis (Columbia NY) and 
Oliver Pfaffel (Munich). 

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These abstracts is also to be found under the following link: http://stat.ethz.ch/events/research_seminar
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