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Variable selection through CART

Marie Sauve, Christine Tuleau-Malot (2014)

ESAIM: Probability and Statistics

This paper deals with variable selection in regression and binary classification frameworks. It proposes an automatic and exhaustive procedure which relies on the use of the CART algorithm and on model selection via penalization. This work, of theoretical nature, aims at determining adequate penalties, i.e. penalties which allow achievement of oracle type inequalities justifying the performance of the proposed procedure. Since the exhaustive procedure cannot be realized when the number of variables...

Variance function estimation via model selection

Teresa Ledwina, Jan Mielniczuk (2010)

Applicationes Mathematicae

The problem of estimating an unknown variance function in a random design Gaussian heteroscedastic regression model is considered. Both the regression function and the logarithm of the variance function are modelled by piecewise polynomials. A finite collection of such parametric models based on a family of partitions of support of an explanatory variable is studied. Penalized model selection criteria as well as post-model-selection estimates are introduced based on Maximum Likelihood (ML) and Restricted...

Why L 1 view and what is next?

László Györfi, Adam Krzyżak (2011)

Kybernetika

N. N. Cencov wrote a commentary chapter included in the Appendix of the Russian translation of the Devroye and Györfi book [15] collecting some arguments supporting the L 1 view of density estimation. The Cencov’s work is available in Russian only and it hasn’t been translated, so late Igor Vajda decided to translate the Cencov’s paper and to add some remarks on the occasion of organizing the session “25 Years of the L 1 Density Estimation” at the Prague Stochastics 2010 Symposium. In this paper we...

Wild bootstrap in RCA(1) model

Zuzana Prášková (2003)

Kybernetika

In the paper, a heteroskedastic autoregressive process of the first order is considered where the autoregressive parameter is random and errors are allowed to be non-identically distributed. Wild bootstrap procedure to approximate the distribution of the least-squares estimator of the mean of the random parameter is proposed as an alternative to the approximation based on asymptotic normality, and consistency of this procedure is established.

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