Modified Cp Criterion for Optimizing Ridge and Smooth Parameters in the MGR Estimator for the Nonparametric GMANOVA Model

References

[1] A. C. Atkinson, “A note on the generalized information criterion for choice of a model,” Biometrika, vol. 67, no. 2, March 1980, pp. 413-418., pp. 291-293.

[2] P. J. Green and B. W. Silverman, “Nonparametric Regression and Generalized Linear Models,” Chapman & Hall/CRC, 1994.

[3] D. A. Harville, “Matrix Algebra from a Statistician’s Perspective,” New York Springer, 1997.

[4] A. E. Hoerl and R. W. Kennard, “Ridge regression: biased estimation for nonorthogonal problems,” Technometrics, vol. 12, No. 1, February 1970, pp. 55-67.

[5] A. M. Kshirsagar and W. B. Smith, “Growth Curves,” Marcel Dekker, 1995.

[6] J. F. Lawless, “Mean squared error properties of generalized ridge regression,” Journal of the American Statistical Association, vol. 76, no. 374, 1981, pp. 462-466.

[7] C. L. Mallows, “Some comments on Cp,” Technometrics, vol. 15, no. 1, November 1973, pp. 661-675.

[8] C. L. Mallows, “More comments on Cp,” Technometrics, vol. 37, no. 4, November 1995, pp. 362-372.

[9] I. Nagai, H. Yangihara and K. Satoh, “Optimization of Ridge Parameters in Multivariate Generalized Ridge Regression by Plug-in Methods,” TR 10-03, Statistical Research Group, Hiroshima University, 2010.

[10] R. F. Potthoff and S. N. Roy, “A generalized multivariate analysis of variance model useful especially for growth curve problems,” Biometrika, vol. 51, no. 3–4, December 1964, pp. 313-326.

[11] K. S. Riedel and K. Imre, “Smoothing spline growth curves with covariates,” Communications in Statistics – Theory and Methods, vol. 22, no. 7, 1993, pp. 1795-1818.

[12] F. J. Richard, “A flexible growth function for empirical use,” Journal of Experimental Botany, vol. 10, no. 2, 1959, pp. 290–301.

[13] K. Satoh and H. Yanagihara, “Estimation of varying coefficients for a growth curve model,” American Journal of Mathematical and Management Sciences, 2010 (in press).

[14] M. Siotani, T. Hayakawa and Y. Fujikoshi, “Modern Multivariate Statistical Analysis: A Graduate Course and Handbook,” American Sciences Press, Columbus, Ohio, 1985.

[15] R. S. Sparks, D. Coutsourides and L. Troskie, “The multivariate ,” Communications in Statistics - Theory and Methods, vol. 12, no. 15, 1983, pp. 1775-1793.

[16] Y. Takane, K. Jung and H. Hwang, “Regularized reduced rank growth curve models,” Computational Statistics and Data Analysis, vol. 55, no. 2, February 2011, pp. 1041-1052.

[17] H. Yanagihara and K. Satoh, “An unbiased Cp criterion for multivariate ridge regression,” Journal of Multivariate Analysis, vol. 101, no. 5, May 2010, pp. 1226-1238.

[18] H. Yanagihara, I. Nagai and K. Satoh, “A bias-corrected Cp criterion for optimizing ridge parameters in multivariate generalized ridge regression,” Japanese Journal of Applied Statistics, vol. 38, no. 3, October 2009, pp. 151-172 (in Japanese).