Functional Data Analysis using Splines and Orthogonal Spline Bases
Construction of a Splinets object
Derivatives of splines
Calculating the definite integral of a spline.
Evaluating splines at given arguments.
Correcting support sets and reshaping the matrix of derivatives at the...
Combining two Splinets objects
Gramian matrix, norms, and inner products of splines
Indefinite integrals of splines
Diagnostics of splines
Diagnostics of splines and their generic correction
Linear transformation of splines.
Adding graphs of splines to a plot
Plotting splines
Projecting into spline spaces
Refining splines through adding knots
Random splines
Organizing indices in a spline basis in the net form
B-splines, periodic B-splines and their orthogonalization
The class to represent a collection of splines
Subsampling from a set of splines
Switching between representations of the matrices of derivatives
Splines are efficiently represented through their Taylor expansion at the knots. The representation accounts for the support sets and is thus suitable for sparse functional data. Two cases of boundary conditions are considered: zero-boundary or periodic-boundary for all derivatives except the last. The periodical splines are represented graphically using polar coordinates. The B-splines and orthogonal bases of splines that reside on small total support are implemented. The orthogonal bases are referred to as 'splinets' and are utilized for functional data analysis. Random spline generator is implemented as well as all fundamental algebraic and calculus operations on splines. The optimal, in the least square sense, functional fit by 'splinets' to data consisting of sampled values of functions as well as splines build over another set of knots is obtained and used for functional data analysis. The S4-version of the object oriented R is used. <doi:10.48550/arXiv.2102.00733>, <doi:10.1016/j.cam.2022.114444>, <doi:10.48550/arXiv.2302.07552>.
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