Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Quality & Quantity
Erschienen in: Quality & Quantity 6/2014

01.11.2014

Ridge regression and its degrees of freedom

verfasst von: Theo K. Dijkstra

Erschienen in: Quality & Quantity | Ausgabe 6/2014

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

For ridge regression the degrees of freedom are commonly calculated by the trace of the matrix that transforms the vector of observations on the dependent variable into the ridge regression estimate of its expected value. For a fixed ridge parameter this is unobjectionable. When the ridge parameter is optimized on the same data, by minimization of the generalized cross validation criterion or Mallows \(\hbox {C}_{L}\), additional degrees of freedom are used however. We give formulae that take this into account. This allows of a proper assessment of ridge regression in competitions for the best predictor.
Vorheriger Artikel Exploring competitiveness in banking sector of a small island economy: a study of Fiji
Nächster Artikel The policy delphi method: contribution to policy and strategy within energy organisations: a 2013 Malaysian case study with global implications

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Jetzt informieren
Fußnoten
1
If \(z\) is a Gausssian variable and \(f\left( z\right) \) a smooth function of \( z\), then the slope of the best linear fit (regression) to \(f\left( z\right) \) is the average derivative of \(f\left( z\right) \). This property characterizes the Gaussian distribution.
 
2
See e.g. Dhrymes (1978), appendix 4, on matrix differentiation; \(vec\left( .\right) \) stacks the columns of the matrix argument in the natural order, and \(\otimes \) is the Kronecker product.
 
3
I am grateful to the authors of the publications referred to for allowing me to use their data.
 
4
Anand et al. (2009) suggest this split, which appears to be rather reasonable. The Economist of December 18th 2010 featured an article titled “The joy of growing old (or why life begins at 46)”. Reference is made to the ‘U-curve’ in reported well-being as a function of age that reaches a nadir at a global average of 46 years.
 
5
This is the ‘leave-one-out’ version of cross-validation. See Stone’s comments on Shao (1997), and Burman (1989) for a justification to use leave-one-out instead of v-fold cross-validation.
 
Literatur
Anand, P., Hunter, G., Dowding, K., Guala, F., van Hees, M.: The development of capability indicators. J. Hum. Dev. Capab. 10(1), 125–152 (2009)
Berk, R.A.: Statistical Learning from a Regression Perspective. Springer, New York (2008)
Burman, P.: A comparative study of ordinary cross-validation, v-fold cross-validation and the repeated learning-testing methods. Biometrika 76(3), 503–514 (1989)CrossRef
Dhrymes, P.J.: Introductory Econometrics. Springer, San Francisco (1978)CrossRef
Efron, B.: The estimation of prediction error: covariance penalties and cross-validation. J. Am. Stat. Assoc. 467, 619–632 (2004)CrossRef
Golub, G.H., Heath, M., Wahba, G.: Generalized cross-validation as a method for choosing a good ridge parameter. Technometrics 21(2), 215–223 (1979)CrossRef
Hastie, T., Tibshirani, R., Friedman, J.: The Elements of Statistical Learning, 2nd edn. Springer, New York (2009)CrossRef
Izenman, A.J.: Modern Multivariate Statistical Techniques. Springer, New York (2008)CrossRef
Li, K.-C.: Asymptotic optimality of \(C_{L}\) and generalized cross-validation in ridge regression with application to spline-smoothing. Ann. Stat. 14(3), 1101–1112 (1986)CrossRef
McDonald, G.C., Schwing, R.C.: Instabilities of regression estimates relating air pollution to mortality. Technometrics 15(3), 463–481 (1973)CrossRef
McDonald, G.C.: Ridge regression. Wiley Interdiscip. Rev. Comput. Stat. 1, 93–100 (2009)CrossRef
McDonald, G.C.: Tracing ridge regression coefficients. Wiley Interdiscip. Rev. Comput. Stat. 2, 695–703 (2010)CrossRef
Shao, J.: An asymptotic theory for linear model selection (with discussion). Stat. Sinica 7, 221–264 (1997)
Metadaten
Titel
Ridge regression and its degrees of freedom
verfasst von
Theo K. Dijkstra
Publikationsdatum
01.11.2014
Verlag
Springer Netherlands
Erschienen in
Quality & Quantity / Ausgabe 6/2014
Print ISSN: 0033-5177
Elektronische ISSN: 1573-7845
DOI
https://doi.org/10.1007/s11135-013-9949-7

Weitere Artikel der Ausgabe 6/2014

Quality & Quantity 6/2014 Zur Ausgabe

OriginalPaper

Quality and quantity in the construction and validation of a psychological test for the assessment and selection of aspiring volunteer rescuers: the action-research in an Italian health association

OriginalPaper

Specifying and assessing a formative measure for Hofstede’s cultural values: a Malaysian study

OriginalPaper

A data mining algorithm for fuzzy transaction data

OriginalPaper

Perceived crisis management and its effect on re-election: the case of local government in Israel under the Second Lebanon War

OriginalPaper

Do missing values exist? Incomplete data handling in cross-national longitudinal studies by means of continuous time modeling

OriginalPaper

Exploring the root causes of terrorism in South Asia: everybody should be concerned