论文信息 - Model selection criteria and the orthogonal series method for function estimation

Model selection criteria and the orthogonal series method for function estimation

Closed-form solutions are presented for function estimation using the orthogonal series method and various model selection criteria. While Akaike's (1974) AIC criterion does not lead to consistent estimates, a family of criteria that includes minimum description length operates within a logarithmic factor of the minimax rate in a range of Sobolev smoothness classes.

Pierre Moulin

[1] H. Akaike. A new look at the statistical model identification , 1974 .

[2] Ker-Chau Li,et al. Asymptotic Optimality for $C_p, C_L$, Cross-Validation and Generalized Cross-Validation: Discrete Index Set , 1987 .

[3] R. Shibata. An optimal selection of regression variables , 1981 .

[4] Naoki Saito,et al. Simultaneous noise suppression and signal compression using a library of orthonormal bases and the minimum-description-length criterion , 1994, Defense, Security, and Sensing.

[5] Andrew R. Barron,et al. Minimum complexity density estimation , 1991, IEEE Trans. Inf. Theory.

[6] I. Johnstone,et al. Ideal spatial adaptation by wavelet shrinkage , 1994 .