Akaike H. (1974). A new look at the statistical model identification IEEE Trans Appl Comp. 19
Anders U, Korn O. (1999). Model selection in neural networks. Neural networks : the official journal of the International Neural Network Society. 12 [PubMed]
Cherkassky V, Shao X, Mulier FM, Vapnik VN. (1999). Model complexity control for regression using VC generalization bounds. IEEE transactions on neural networks. 10 [PubMed]
Deo CM. (1972). Some limit theorems for maxima of absolute values of gaussian sequences Sankhy. 34
Erdos P, Darling DA. (1956). A limit theorem for the maximum of normalized sums of independent random variables Duke Math J. 23
Fukumizu K. (1996). A Regularity Condition of the Information Matrix of a Multilayer Perceptron Network. Neural networks : the official journal of the International Neural Network Society. 9 [PubMed]
Hagiwara K. (2002). On the problem in model selection of neural network regression in overrealizable scenario. Neural computation. 14 [PubMed]
Hagiwara K, Hayasaka T, Toda N, Usui S, Kuno K. (2001). Upper bound of the expected training error of neural network regression for a Gaussian noise sequence. Neural networks : the official journal of the International Neural Network Society. 14 [PubMed]
Leadbetter MR, Rootzen H. (1988). Extremal theory for stochastic processes Ann Prob. 16
Moody J. (1992). The effective number of parameters: An analysis of generalization and regularization in nonlinear learning systems Advances in neural information processing systems.
Murata N, Yoshizawa S, Amari S. (1994). Network information criterion-determining the number of hidden units for an artificial neural network model. IEEE transactions on neural networks. 5 [PubMed]
Phillips PCB. (1989). Partially identified econometric models Econometric Theory. 5
Rao CR. (2002). Linear statistical inference and its application (2nd ed).
Resnick SI. (1987). Extreme values, regular variation, and point processes.
Usui S, Hagiwara K, Hayasaka T, Toda N. (1996). On the least square error and prediction square error of function representation with discrete variable basis Proceedings of the 1996 IEEE Signal Processing Society Workshop.
Usui S, Hagiwara K, Toda N. (1993). On the problem of applying AIC to determine the structure of a layered feed-forward neural network Proceedings Of IJCNN. 3
Usui S, Hayasaka T, Toda N, Kitahara M. (2001). On the probability distribution of estimators of regression model using 3-layered neural networks Proceedings Of 2001 International Symposium On Nonlinear Theory And Its Applications. 2
Watanabe S. (2001). Algebraic analysis for nonidentifiable learning machines. Neural computation. 13 [PubMed]
White H. (1989). Learning in artificial neural networks: A statistical perspective Neural Comput. 1
de_Haan L. (1976). Sample extremes: An elementary introduction Statist Neelandica. 30