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Ridge Parameters Optimization based on Minimizing Model Selection Criterion in Multivariate Generalized Ridge Regression

大石 峰暉 広島大学

2021.03.23

概要

We consider n pairs of data {yi , xi } (i = 1, . . . , n), where yi is a p-dimensional
vector of response variables, xi is a k-dimensional vector of explanatory variables, and n satisfies n > max{p, k + 1}. A multivariate linear regression model
is a statistical model for multiple response variables (e.g., Srivastava [19], Chap.
9; Timm [22], Chap. 4). Let Y = (y1 , . . . , yn )′ be an n × p matrix of response
variables, X = (x1 , . . . , xn )′ be an n × k matrix of explanatory variables, and
E = (ε1 , . . . , εn )′ be an n × p matrix of error variables. ...

参考文献

[1] H. Akaike, Information theory and an extension of the maximum likelihood principle, In:

B. N. Pretrov, F. Cs´

aki (Eds.), 2nd International Symposium on Information Theory,

Akad´

emiai Kiad´

o, Budapest, 26 (1973), 267–281.

[2] T. W. Anderson, An Introduction to Multivariate Statistical Analysis, John Wiley &

Sons, Inc., New Jersey, 2003.

[3] A. C. Atkinson, A note on the generalized information criterion for choice of a model,

Biometrika, 67 (1980), 413–418.

[4] K. A. Bollen, Structural Equations with Latent Variables, John Wiley & Sons, Inc., New

York, 1989.

[5] P. Craven & G. Wahba, Smoothing noisy data with spline functions: estimating the

correct degree of smoothing by the method of generalized cross-validation, Numer. Math.,

31 (1979), 377–403.

[6] A. C. David, Galois Theory, John Wiley & Sons, Inc., New Jersey, 2004.

[7] D. L. Donoho & I. M. Johnstone, Ideal spatial adaptation by wavelet shrinkage,

Biometrika, 81 (1994), 425–455.

[8] Y. Fujikoshi & K. Satoh, Modified AIC and Cp in multivariate linear regression,

Biometrika, 84 (1997), 707–716.

[9] E. J. Hannan & B. G. Quinn, The determination of the order of an autoregression, J. R.

Stat. Soc. Ser. B. Stat. Methodl., 41 (1979), 190–195.

[10] A. E. Hoerl & R. W. Kennard, Ridge regression: biased estimation for nonorthogonal

problems, Technometrics, 12 (1970), 55–67.

44

Mineaki Ohishi

[11] C. M. Hurvich & C.-L. Tsai, Regression and time series model selection in small samples,

Biometrika, 76 (1989), 297–307.

[12] C. L. Mallows, Some comments on Cp , Technometrics, 15 (1973), 661–675.

[13] Y. Mori & T. Suzuki, Generalized ridge estimator and model selection criteria in multivariate linear regression, J. Multivariate Anal., 165 (2018), 243–261.

[14] I. Nagai, H. Yanagihara & K. Satoh, Optimization of ridge parameters in multivariate

generalized ridge regression by plug-in methods, Hiroshima Math. J., 42 (2012), 301–324.

[15] R. Nishii, Asymptotic properties of criteria for selection of variables in multiple regression,

Ann. Statist., 12 (1984), 758–765.

[16] M. Ohishi, H. Yanagihara & Y. Fujikoshi, A fast algorithm for optimizing ridge parameters

in a generalized ridge regression by minimizing a model selection criterion, J. Statist.

Plann. Inference, 204 (2020), 187–205.

[17] M. Ohishi, H. Yanagihara & S. Kawano, Equivalence between adaptive-Lasso and generalized ridge estimators in linear regression with orthogonal explanatory variables after

optimizing regularization parameters, Ann. Inst. Statist. Math., 72 (2020), 1501–1516.

[18] G. Schwarz, Estimating the dimension of a model, Ann. statist., 6 (1978), 461–464.

[19] M. S. Srivastava, Methods of Multivariate Statistics, John Wiley & Sons, Inc., New York,

2002.

[20] R. Tibshirani, Regression shrinkage and selection via the Lasso, J. R. Stat. Soc. Ser. B.

Stat. Methodl., 58 (1996), 267–288.

[21] J.-P. Tignol, Galois’ Theory of Algebraic Equations, World Scientific Publishing, Singapore, 2001.

[22] N. H. Timm, Applied Multivariate Analysis, Springer-Verlag, New York, 2002.

[23] X. Xin, J. Hu & L. Liu, On the oracle property of a generalized adaptive elastic-net

for multivariate linear regression with a diverging number of parameters, J. Multivariate

Anal., 162 (2017), 16–31.

[24] H. Yanagihara, Explicit solution to the minimization problem of generalized crossvalidation criterion for selecting ridge parameters in generalized ridge regression, Hiroshima Math. J., 48 (2018), 203–222.

[25] H. Yanagihara, I. Nagai & K. Satoh, A bias-corrected Cp criterion for optimizing ridge

parameters in multivariate generalized ridge regression, J. Appl. Statist., 38 (2009), 151–

172 (in Japanese).

[26] H. Zou, The adaptive Lasso and its oracle properties, J. Amer. Statist. Assoc., 101 (2006),

1418–1429.

Mineaki Ohishi

Department of Mathematics

Graduate School of Science

Hiroshima University

Higashi-Hiroshima 739-8526 JAPAN

E-mail : mineaki-ohishi@hiroshima-u.ac.jp

...

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