Boosting Correlation Based Penalization in Generalized Linear Models

Jan Ulbricht () and Gerhard Tutz ()
Additional contact information
Jan Ulbricht: University of Munich, Department of Statistics
Gerhard Tutz: University of Munich, Department of Statistics

A chapter in Recent Advances in Linear Models and Related Areas, 2008, pp 165-180 from Springer

Abstract: Linear models have a long tradition in statistics as nicely summarized in Rao, Toutenburg, Shalabh, Heumann (2008). When the number of covariates is large the estimation of unknown parameters frequently raises problems. Then the interest usually focusses on data driven subset selection of relevant regressors. The sophisticated monitoring equipment which is now routinely used in many data collection processes makes it possible to collect data with a huge amount of regressors, even with considerably more explanatory variables than observations. One example is the analysis of microarray data of gene expressions. Here the typical tasks are to select variables and to classify samples into two or more alternative categories. Binary responses of this type may be handled within the framework of generalized linear models (Neider and Wedderburn (1972)) and are also considered in Rao, Toutenburg, Shalabh, Heumann (2008). In this paper we propose a new regularization method and a boosted version of it, which explicitly focus on the selection of groups. To reach this target we consider a correlation based penalty which uses correlation between variables as data driven weights for penalization. See also Tutz and Ulbricht (2006) for a similar approach to linear models. This new method and some of its main properties are described in Section 2. A boosted version of it that will be presented in Section 3 allows for variable selection. In Section 4 we use simulated and real data sets to compare our new methods with existing ones.

Keywords: Generalize Linear Model; Maximum Likelihood Estimator; Subset Selection; Unknown Parameter Vector; Fisher Matrix (search for similar items in EconPapers)
Date: 2008
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-7908-2064-5_9

Ordering information: This item can be ordered from
http://www.springer.com/9783790820645

DOI: 10.1007/978-3-7908-2064-5_9

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().