Overfitting Probabilities using Dependent F-tests in Regression

  • Park, Chan-Keun (Full-time Instructor, Divistion of Applied Science, Korea, Maritime University, Pusan, 606-791)
  • 발행 : 2001.12.01

초록

Probabilities of overfilling for model selection criteria are derived for several different situations. First, one candidate model with one extra variable is compared to the current model. This is expanded to m candidate models. We show that these comparisons are not independent and discuss ovefitting probabilities. Correlation between two F-tests is derived. Finally, probabilities are computed using the dependent F distributions and F distributions based on order statistics of independent Chi-squares.

키워드

참고문헌

  1. in 2nd International symposium on Information Theory Information theory and an extension of the maximum likelihood principle Akaike,H.;B.N.Petrov(ed.);F.Csaki(ed.);Akademia Kiado(ed.)
  2. Annals of the Institute of Statistical Mathematics v.30 A bayesian analysis of the minimum AIC procedure Akaike,H.
  3. Order Statistics David,H.A.
  4. Journal for the Royal Statistical Society v.B 41 The determination of the order of an autoregression Hannan,E.J.;Quinn,B.G.
  5. Biometrika v.76 Regression and time series model selection in small samples Hurvich,C.M.;Tsai,C.L.
  6. Annals of Mathematical Statistics v.22 On information and sufficiency Kullback,S.;Leibler,R.A.
  7. Statistics & Probability Letters v.44 A small-sample correlation for the Schwarz SIC model selection criterion Mcquarrie,A.D.
  8. Statistics & Probability Letters v.34 The model selection criterion AICu Mcquarrie,A.D.;Shumway,R.H.;Tsai,C.L.
  9. Annals of Statistics v.12 no.2 Asymptotic properties of criteria for selection of variables in multiple regression Nishii,R.
  10. Annals of Statistics v.6 Estimating the dimension of a model Schwarz,G.
  11. The Annals of Statistics v.8 Asymptotically effcient selection of the order of the model for estimating parameters of linear process Shibata,R.
  12. Biometrika v.68 An optimal selection of regression variables Shibata,R.
  13. Journal of Applied Probability v.23A Consistency of model selection and parameter estimation. In Essays in time series and applied processes Shibata,R.