[Statlist] Talk on Statistics: Friday, December 12, 2008

[Cecilia Rey]

We are glad to announce the following talk

Friday December 12, 2008, 15.15 - 17.00
in LEO C6, Leonhardstrasse 27, 8092 Zurich

Prof. Tilmann Gneiting, University of Washington, Seattle

Mean, Median, Mode, More

Suppose that we are to predict a future quantity of interest.  Our
favorite statistical technique provides a predictive probability
distribution, say F.  However, as it turns out, we are required to
issue a single-valued point forecast.  How are we going to proceed?
Of course, our strategy will depend on the loss structure.  If the
loss function is quadratic, the mean of F is the unique optimal point
predictor.  Under linear loss, we pick the median of F, under zero-one
loss its mode.

Are standard loss functions realistic?  Typically, no.  Are standard
predictors, such as quantiles, compatible with realistic loss
structures?  Perhaps surprisingly, typically, yes.  Indeed, quantiles
arise as optimal point predictors under a general class of
economically relevant loss functions, to which we refer as generalized
piecewise linear (GPL).  The level of the quantile depends on a
generic asymmetry parameter that reflects the possibly distinct costs
of under-prediction and over-prediction.  A loss function for which
quantiles are optimal point predictors is necessarily GPL, similarly
to the classical fact that a loss function for which the mean is
optimal is necessarily a Bregman function.

These results are both of theoretical and empirical relevance, as will
be illustrated using the Bank of England's density forecasts of United
Kingdom inflation rates, and probabilistic predictions of wind speed
at a Pacific Northwest wind energy site.

The abstract kann also be found under the following link: 
http://stat.ethz.ch/talks/research_seminar

-- 
ETH Zürich
Cecilia Rey-Lutz	          rey using stat.math.ethz.ch
Seminar für Statistik
Leonhardstr. 27, LEO D11	  phone: +41 44 632 34 38
CH-8092 Zurich, Switzerland	  fax  : +42 44 6321228