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CONVERGENCE OF KERNEL FUNCTIONS FOR CUBIC SMOOTHING SPLINES ON NON‐EQUISPACED GRIDS
Author(s) -
Hoog F.R.,
Anderssen R.S.
Publication year - 1988
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1988.tb00466.x
Subject(s) - smoothing spline , smoothing , monotone cubic interpolation , grid , kernel (algebra) , convergence (economics) , mathematics , spline (mechanical) , cubic hermite spline , thin plate spline , spline interpolation , polyharmonic spline , mathematical optimization , geometry , combinatorics , bicubic interpolation , statistics , physics , economic growth , economics , bilinear interpolation , thermodynamics
summary Numerical experimentation with data, which is quite noisy and on a highly non‐even grid, shows that cubic smoothing splines give a visually pleasing fit to the data, even when the interpolating spline oscillates wildly. In part, Silverman (1984) has explained this fact by showing that the cubic smoothing spline converges, to a certain kernel approximation as the number of data points is increased. In this paper, we examine the convergence of the kernel functions which generate the cubic smoothing spline fit to data, under weaker conditions on the non‐even grid than imposed by Silverman.