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LINEAR MODEL SELECTION BASED ON RISK ESTIMATION

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J. H. VENTER^{ 1} AND J. L. J.
SNYMAN^{ 2}

^{1} *Department of Statistics, Potchefstroom
University, Potchefstroom 2520, South Africa*

^{2} *Department of Statistics, Rand Afrikaans
University, Aucklandpark 2006, South Africa*
(Received November 6, 1995; revised April 15, 1996)

**Abstract.**
The problem of selecting one model from a
family of linear models to describe a normally distributed
observed data vector is considered. The notion of the model of
given dimension nearest to the observation vector is introduced
and methods of estimating the risk associated with such a nearest
model are discussed. This leads to new model selection criteria
one of which, called the ``partial bootstrap'', seems
particularly promising. The methods are illustrated by
specializing to the problem of estimating the non-zero components
of a parameter vector on which noisy observations are available.

**Key words and phrases:**
Linear model selection, risk
estimation, little bootstrap estimator, Stein estimation,
selection criteria.

**Source**
( TeX ,
DVI ,
PS )