A Common Model Selection Criterion

N. R. Draper and I. Guttman
Additional contact information
N. R. Draper: University of Wisconsin
I. Guttman: University of Wisconsin

A chapter in Probability and Bayesian Statistics, 1987, pp 139-150 from Springer

Abstract: Abstract We consider the linear model situation (1.1) $$ {\rm{}} = {{\rm{}}_{\rm{t}}}{{\rm{\beta }}_{\rm{t}}} + {{\rm{}}_{\rm{t}}} $$ where y = (y1,y2,…,yn)′ is an n × 1 vector of response observations, Xt is an n × pt matrix of predictor variable values, $$ {\rm{n}} > {{\rm{p}}_{\rm{t}}}{\rm{,}}{{\rm{}}_{\rm{t}}} $$ is a pt × 1 vector of regression parameters to be estimated and $$ {{\rm{}}_{\rm{t}}} $$ is distribt uted $$ {\rm{N}}({{\rm{}}_{\rm{t}}}{\rm{.}}{{\rm{\sigma }}^{\rm{2}}}{{\rm{I}}_{\rm{n}}}) $$ . We shall distinguish between problems in which (a) $$ {{\rm{}}_{\rm{t}}} = $$ for all t, and (b) $$\mathop{\delta }\limits_{{ \sim t}} = {{\left( {\mathop{{0'}}\limits_{ \sim } ,\mathop{{a'}}\limits_{{ \sim t}} } \right)}^{\prime }} $$ , for all t, where the elements of the $$ {{\rm{}}_{\rm{t}}} $$ are non-zero and each $$ {{\rm{}}_{\rm{t}}} $$ vector is size k × 1 where, typically, k ≪ n/2. The generic notation t denotes a general indexing which will be made specific for particular problems to be discussed below. Each choice of t will provide a model Mt, say, defined by (1.1). The general problem, given a specific indexing system for t, is to decide, from data made available on $$\mathop{y}\limits_{ \sim } $$ and the $$ {{\rm{}}_{\rm{t}}}^\prime {\rm{s}} $$ , which Mt “best represents” the data.

Keywords: Prior Information; Estimation Space; Bayesian Variable Selection; Outlier Problem; Change Point Problem (search for similar items in EconPapers)
Date: 1987
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:978-1-4613-1885-9_14

Ordering information: This item can be ordered from
http://www.springer.com/9781461318859

DOI: 10.1007/978-1-4613-1885-9_14

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 ().