Abstract
Identifying a model by the penalized contrast procedure, we give an analytical estimation of misfitting subsets in the specific case of a least squares contrast. Then, specifying the statistical model, this allows to determine penalization rates ensuring a consistent identification. Applications are given to time series and geostatistical identification.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abramowitz M, Stegun I (1965) Handbook of mathematical functions. Dover, New York
Akaike H (1969) Fitting autoregressive models for prediction. Ann Inst Statist Math 21:243–247
Amemiya T (1985) Advances econometrics. Blackwell, Hoboken
Bai ZD, Subramanyan K, Zhao LC (1988) On determination of the order of an autoregressive model. J Multivar Anal 27:40–52
Bai ZD, Krishnaiah PR, Sambamoorthi N, Zhao LC (1992) Model selection for non linear models. Sankya Indian J Statist Ser B 54:200–219
Bardet J-M, Doukhan P, Leon J (2008) A functional limit theorem for weakly dependent processes and its applications. Statist Inf Stoch Process 11(3):265–280
Chilès JP, Delfiner P (1999) Geostatistics. Wiley, Hoboken
Cressie N (1993) Statistics for spatial data. Wiley, Hoboken
Doukhan P (1994) Mixing: properties and examples. In Lecture notes in statistics, vol 85. Springer-Verlag, Berlin
Doukhan P, Louhichi S (1999) A new weak dependence condition and applications to moment inequalities. Stoch Proc Appl 84:313–342
Gaetan C, Guyon X (2010) Spatial statistics and modeling. Springer, Berlin
Guyon X, Yao JF (1999) On the underfitting and overfitting sets of models chosen by order selection criteria. J Mult Anal 70:221–249
Lahiri SN, Lee Y, Cressie N (2002) On asymptotic distribution and asymptotic afficiency of least squares estimators of spatial variogram parameters. J Statist Plann Inf 103:65–85
Schwarz G (1978) Estimating the dimension of a model. Ann Statist 6:461–464
Senoussi R (1990) Statistique asymptotique presque sûre des modèles statistiques convexes. Ann Inst H P 26:19–44
Shibata R (1976) Selection of the order of an autoregressive model by Akaike’s information criterion. Biometrika 63:117–126
Yaglom AM (1987) Correlation theory of stationary and related random functions. Basic results. Springer, Berlin
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Guyon, X., Hardouin, C. Misparametrization subsets for penalized least squares model selection. Stat Inference Stoch Process 17, 283–294 (2014). https://doi.org/10.1007/s11203-014-9100-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11203-014-9100-y