Document Zbl 0424.62020

Two errors in statistical model fitting. (English) Zbl 0424.62020

Ann. Inst. Stat. Math. 29, 131-152 (1977).

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MSC:

62F10	Point estimation
62J07	Ridge regression; shrinkage estimators (Lasso)
62J05	Linear regression; mixed models
62B10	Statistical aspects of information-theoretic topics

Keywords:

risk function; statistical model fitting; Kullback-Leibler information measures; ridge estimator

Citations:

Zbl 0202.172

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Full Text: DOI

References:

[1]	Aitchison, J. and Silvey, S. D. (1958). Maximum-likelihood estimation of parameters subject to restraints,Ann. Math. Statist. 29, 813–828. · Zbl 0092.36704 · doi:10.1214/aoms/1177706538
[2]	Akaike, H. (1972). Information theory and an extension of the maximum likelihood principle,Proc. 2nd Intl. Symp. on Information Theory, Supplement to Problems of Control and Information Theory, 267–281.
[3]	Hoerl, A. E. and Kennard, R. W. (1970). Ridge regression: Biased estimation for non-orthogonal problems,Technometrics,12, 55–67. · Zbl 0202.17205 · doi:10.2307/1267351
[4]	Ibragimov, I. A. and Khas’minskii, R. Z. (1972). Asymptotic behavior of statistical estimators in the smooth case,Theory Prob. Appl. 17, 443–460.
[5]	Ibragimov, I. A. and Khas’minskii, R. Z. (1973). Asymptotic behavior of some statistical estimators II. Limit theorems for the a posteriori density and Bayes’ estimators,Theory Prob. Appl.,18, 76–91. · Zbl 0283.62038 · doi:10.1137/1118006
[6]	Inagaki, N. and Ogata, Y. (1975). The weak convergence of likelihood ratio random fields and its applications,Ann. Inst. Statist. Math.,27, 391–419. · Zbl 0381.62023 · doi:10.1007/BF02504659
[7]	Inagaki, N. and Ogata, Y. (1975). The weak convergence of likelihood ratio random fields for Markov observation,Research Memorandum, No. 79, The Institute of Statistical Mathematics. · Zbl 0381.62023
[8]	LeCam, L. (1970). On the assumptions used to prove asymptotic normality of maximum likelihood estimates,Ann. Math. Statist.,41, 802–828. · Zbl 0246.62039 · doi:10.1214/aoms/1177696960
[9]	Lindley, D. V. (1968). The choice of variables in multiple regression,J. R. Statist. Soc. B,30, 31–53. · Zbl 0155.26702
[10]	Lindley, D. V. and Smith, A. F. M. (1972). Bayes estimates for linear model,J. R. Statist. Soc. B,34, 1–18. · Zbl 0246.62050
[11]	Mallows, C. L. (1973). Some comments onC p ,Technometics,15, 661–675. · Zbl 0269.62061 · doi:10.2307/1267380

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