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- Title
Piecewise Monotonic Data Approximation: Spline Representation and Linear Model - Basic Statistics.
- Authors
Vassiliou, E. E.; Demetriou, I. C.
- Abstract
We derive basic statistics for the least squares piecewise monotonic approximation to noisy data. It is known that this approximation is the solution of a combinatorial problem, which is decomposed quite efficiently into separate monotonic approximation problems. Each monotonic section consists of disjoint intervals of adjacent equal components. We provide a B-spline representation of the solution and state the associated linear regression model. It is shown that the dispersion matrix of the model estimated coefficients is a positive definite diagonal matrix. Hence, confidence intervals and tests for the coefficients of the linear model are derived immediately and stably. A numerical example illustrates some technical aspects of an optimal fit, and demonstrates the estimation capability of the linear model. Our results suggest some subjects for future work.
- Subjects
LEAST squares; REGRESSION analysis; STATISTICS; CONFIDENCE intervals; SPLINE theory
- Publication
IAENG International Journal of Applied Mathematics, 2022, Vol 52, Issue 1, p238
- ISSN
1992-9978
- Publication type
Article