[Statlist] Next talk: Friday, June 01, 2012 with Bodhisattva Sen, Columbia University New York, Cambridge University, UK

[Cecilia Rey]

> ETH and University of Zurich

> Proffs. P. Buehlmann -  L. Held - H.R. Kuensch -
> M. Maathuis -  S. van de Geer - M. Wolf
>
>
> *******************************************************************************
> We are glad to announce the following talk
>
> Friday, June 01, 2012, 15.15h, HG G 19.1
>
> ******************************************************************************
> by Bodhisattva Sen, Columbia University New York, Cambridge  
> University, UK
>
>
> Title:
> Inference and estimation using nonprametric shape restricted functions
>
> Absract:
>                  The talk will introduce nonparametric function  
> estimation under known shape constraints. In the first part of the ta 
> lk, I focus on construction of confidence intervals (CIs) for an  
> unknown non-increasing density function on the positive real line  
> based on the Grenander estimator, the nonparametric maximum  
> likelihood estimator. This estimator, a prototypical example of a  
> class of shape constrained estimators in one dimension, converges at  
> rate cube-root n to a non-normal limit distribution. I investigate  
> the consistency and performance of different bootstrap schemes for  
> constructing point-wise CIs in this setup.
> In the second part of the talk I consider the nonparametric least  
> squares estimation of a convex regression function when the  
> dimension of the covariate can be greater than one. I characterize  
> and discuss the computation of such an estimator via the solution of  
> certain quadratic and linear programs. I prove that under mild  
> regularity conditions the estimator and its subdiff-erentials are  
> consistent in both fixed and stochastic design regression settings.
>
> ___________________________________________________________________________
>
> The abstract is also to be found here:  http://stat.ethz.ch/events/research_seminar
>
>


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