Asymptotic properties of complete smoothing splines and applications
In this paper the authors develop a generalized cross validation (GCV) method for estimating a good value for the smoothing parameter in using complete splines for fitting noisy data. By analyzing the eigenvalues of an appropriate energy matrix, we are able to show that, assuming each measurement is subject to independent identically distributed random errors with mean zero, the method is asymptotically optimal. In particular, we show that in the limit as the number of data points becomes large, the ratio of the expected value of the error using our estimated parameter to that obtained using the optimal parameter approaches one. In addition, we discuss the numerical computation of the smoothing parameter. In this connection, the authors present a new algorithm for efficiently computing the central bands (and thus the trace) of the inverse of a banded matrix. This algorithm may be of interest in its own right.
- Research Organization:
- Center for Approximation Theory, Dept. of Mathematics, Texas A and M Univ., College Station, TX 77843
- OSTI ID:
- 5398253
- Journal Information:
- SIAM J. Sci. Stat. Comput.; (United States), Journal Name: SIAM J. Sci. Stat. Comput.; (United States) Vol. 9:1; ISSN SIJCD
- Country of Publication:
- United States
- Language:
- English
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