Calculate tuning parameters based on given leave-one-out Cross Validation.
tuning_loocv(Y, X, K_mat, lambda)(matrix, n*1) The vector of response variable.
(matrix, n*d_fix) The fixed effect matrix.
(list of matrices) A nested list of kernel term matrices, corresponding to each kernel term specified in the formula for a base kernel function in kern_func_list.
(numeric) A numeric string specifying the range of tuning parameter to be chosen. The lower limit of lambda must be above 0.
(numeric) The estimated tuning parameter.
leave-one-out Cross Validation
$$\lambda_{n-CV}={argmin}_{\lambda \in \Lambda}\;\Big\{log\;y^{\star T}[I-diag(A_\lambda)-\frac{1}{n}I]^{-1}(I-A_\lambda)^2[I-diag(A_\lambda)- \frac{1}{n}I]^{-1}y^\star \Big\}$$
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Trevor Hastie, Robert Tibshirani, and Jerome Friedman. The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Second Edition. Springer Series in Statistics. Springer- Verlag, New York, 2 edition, 2009.
Hirotogu Akaike. Information Theory and an Extension of the Maximum Likelihood Principle. In Selected Papers of Hirotugu Akaike, Springer Series in Statistics, pages 199<U+2013>213. Springer, New York, NY, 1998.
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Hurvich Clifford M., Simonoff Jeffrey S., and Tsai Chih-Ling. Smoothing parameter selection in nonparametric regression using an improved Akaike information criterion. January 2002.