Smoothing noisy data using dynamic programming and generalized cross-validation.
Smoothing and differentiation of noisy data using spline functions requires the selection of an unknown smoothing parameter. The method of generalized cross-validation provides an excellent estimate of the smoothing parameter from the data itself even when the amount of noise associated with the data is unknown. In the present model only a single smoothing parameter must be obtained, but in a more general context the number may be larger. In an earlier work, smoothing of the data was accomplished by solving a minimization problem using the technique of dynamic programming. This paper shows how the computations required by generalized cross-validation can be performed as a simple extension of the dynamic programming formulas. The results of numerical experiments are also included.
Dohrmann
C R
CR
Department of Mechanical Engineering, Ohio State University, Columbus 43210.
Busby
H R
HR
Trujillo
D M
DM
D000465:Algorithms; D000704:Analysis of Variance; D001696:Biomechanical Phenomena; D003627:Data Interpretation, Statistical; D008962:Models, Theoretical; D009716:Numerical Analysis, Computer-Assisted