Truncation level selection in nonparametric regression using Padé approximation

References

• Baker, G. 1975. Essentials of padé approximants. 1st ed. New York: Academic Press.
   Google Scholar
• Baker, G. A., Jr., and P. Graves-Morris. 1996. Padé approximations. 2nd ed. Cambridge: Cambridge University Press.
   Google Scholar
• Breiman, L. 1996. Bagging predictors. Machine Learning 24 (2):123–40. doi:10.1007/BF00058655.
   Web of Science ®Google Scholar
• Brezinski, C. 1980. Padé-type approximation and general orthogonal polynomials. Basel: Birkhäuser.
   Google Scholar
• Brezinski, C., G. Rodriguez, and S. Seatzu. 2009. Error estimates for the regularization of least squares problems. Numerical Algorithms 51 (1):61–76. doi:10.1007/s11075-008-9243-2.
   Web of Science ®Google Scholar
• Buja, A., T. Hastie, and R. Tibshirani. 1987. Linear smoothers and additive models, Technical report. Vol. 106, University of Washington.
   Google Scholar
• Chen, C. S., and H. C. Huang. 2011. An improved Cp criterion for spline smoothing. Journal of Statistical Planning and Inference 141 (1):445–52. doi:10.1016/j.jspi.2010.06.017.
   Web of Science ®Google Scholar
• Cheney, E. W. 1996. Introduction to approximation theory. 2nd ed. Vermont: Chelsea Publishing Company.
   Google Scholar
• Craven, P., and G. Wahba. 1978. Smoothing noisy data with spline functions. Numerische Mathematik 31 (4):377–403. doi:10.1007/BF01404567.
   Web of Science ®Google Scholar
• Eckart, C., and G. Young. 1936. The approximation of one matrix by another of lower rank. Psychometrika 1 (3):211–8. doi:10.1007/BF02288367.
   Google Scholar
• Eubank, R. 1999. Nonparametric regression and spline smoothing. New York: Marcel Dekker.
   Google Scholar
• Fierro, R. D., G. H. Golub, P. C. Hansen, and D. P. O'Leary. 1997. Regularization by truncated total least squares. SIAM Journal on Scientific Computing 18 (4):1223–41. doi:10.1137/S1064827594263837.
   Web of Science ®Google Scholar
• Golub, G. H., and C. F. Van Loan. 1980. An analysis of the total least squares problem. SIAM Journal on Numerical Analysis 17 (6):883–93. doi:10.1137/0717073.
   Web of Science ®Google Scholar
• Golub, G. H., and C. F. Van Loan. 2013. Matrix computations. Baltimore: The Johns Hopkins University Press.
   Google Scholar
• Green, P. J. and B. W. Silverman. 1994. Nonparametric regression and generalized linear model. Boca Raton: Chapman & Hall.
   Google Scholar
• Hastie, T., R. Tibshirani, and J. Friedman. 2001. The elements of statistical learning. Data mining, inference and prediction. Berlin: Springer.
   Google Scholar
• Henderson, D. J., and C. F. Parmeter. 2015. Applied nonparametric econometrics. New York: Cambridge University Press.
   Google Scholar
• Hurvich, C. M., J. S. Simonoff, and C.-L. Tsai. 1998. Smoothing parameter selection in nonparametric regression using an improved akaike information criterion. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 60 (2):271–93. doi:10.1111/1467-9868.00125.
   Web of Science ®Google Scholar
• Lee, T. C. M. 2004. Improved smoothing spline regression by combining estimates of different smoothness. Statistics & Probability Letters 67:133–40. doi:10.1016/j.spl.2004.01.003.
   Web of Science ®Google Scholar
• Li, Q., and S. Racine. 2007. Nonparametric econometrics, Theory and practice. Princeton NJ: Princeton University Press.
   Google Scholar
• Mallows, C. 1973. Some comments on Cp. Technometrics 15:661–75. doi:10.1080/00401706.1973.10489103.
   Web of Science ®Google Scholar
• Mirsky, L. 1960. Symmetric gauge functions and unitarily invariant norms. The Quarterly Journal of Mathematics 11 (1):50–9. doi:10.1093/qmath/11.1.50.
   Google Scholar
• Nadaraya, E. A. 1964. On estimating regression. Theory of Probability and Its Applications 10 (1):186–90.
   Google Scholar
• Petrushev, P. P., and V. A. Popov. 1987. Rational approximation of real functions. New York: Cambridge University Press.
   Google Scholar
• Ruppert, D. 2002. Selecting the number of knots for penalized splines. Journal of Computational and Graphical Statistics 11 (4):735–57. doi:10.1198/106186002853.
   Web of Science ®Google Scholar
• Reis, P. T., and R. T. Ogden. 2009. Smoothing parameter selection for a class of semiparametric linear models. Journal of the Royal Statistical Society: Series B 71:505–23.
   Google Scholar
• Schimek, G. M. 2000. Smoothing and regression: approaches, computation, and application. New York: John Wiley & Sons, Inc, 19–39.
   Google Scholar
• Schwarz, G. 1978. Estimating the dimension of a model. The Annals of Statistics 6(2):461–4. doi:10.1214/aos/1176344136.
   Web of Science ®Google Scholar
• Sima, D. M., and S. Huffel. 2007. Level choice in truncated total least squares. Computational Statistics and Data Analysis 52: 1208–22. doi:10.1016/j.csda.2007.05.015.
   Web of Science ®Google Scholar
• Tikhonov, A. N. 1963. Solution of incorrectly formulated problems and the regularization method. Soviet Mathematics Doklady 4:1035–8.
   Google Scholar
• Van Huffel, S., and J. Vandewalle. 1991. The total least squares problem, computational aspects and analysis. Philadelphia: SIAM.
   Google Scholar
• Wahba, G. 1983. Bayesian confidence intervals for the cross-validated smoothing spline. Journal of the Royal Statistical Society, Series B 45 (1):133–50. doi:10.1111/j.2517-6161.1983.tb01239.x.
   Google Scholar
• Watson, G. S. 1964. Smooth regression analysis. Sankhya, Series A 26:359–72.
   Google Scholar
• Wuytack, L. 1979. Padé approximation and its applications. Lectures notes in mathematics, Vol. 765. Berlin: Springer.
   Google Scholar
• Zhang, D., and E. Cherkaev. 2009. Reconstruction of spectral function from effective permittivity of a composite material using rational function approximations. Journal of Computational Physics 228 (15):5390–409. doi:10.1016/j.jcp.2009.04.014.
   Web of Science ®Google Scholar
• Zhang, D., and E. Cherkaev. 2008. Pade approximations for identification of air bubble volume from temperature or frequency dependent permittivity of a two-component mixture. Inverse Problems in Science and Engineering 16 (4):425–45. doi:10.1080/17415970701529213.
   Web of Science ®Google Scholar
• Zhang, D., M. P. Lamoureux, G. F. Margrave, and E. Cherkaev. 2011. Rational approximation for estimation of quality Q factor and phase velocity in linear, viscoelastic, isotropic media. Computational Geosciences 15:117–33.. doi:10.1007/s10596-010-9201-7.
   Web of Science ®Google Scholar