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- Title
Numerical algorithms for spline interpolation on space of probability density functions.
- Authors
Adouani, Ines; Samir, Chafik
- Abstract
This paper addresses the problem of spline interpolations on P , the space of probability density functions when only a few observations p i ∈ P are available. Given a finite set of n + 1 distinct time instants t i and corresponding data points p i ∈ P , we consider the general problem of estimating a spline as a special regularized function γ on P with γ (t i) = p i . In particular, we focus on estimating missing data using smooth temporal splines to overcome the discrete nature of observations. In addition to generalizing splines on P with minimal squared-norm of the acceleration, we give numerical schemes for solving C 1 and C 2 splines from data points p i ∈ P . The two solutions are then shown to be computationally efficient, geometrically simpler, extensible, and can be transposed to other spaces and applications.
- Subjects
SPLINES; INTERPOLATION spaces; PROBABILITY density function; INTERPOLATION algorithms; STATISTICAL smoothing; MISSING data (Statistics); SPLINE theory
- Publication
Computational & Applied Mathematics, 2023, Vol 42, Issue 3, p1
- ISSN
0101-8205
- Publication type
Article
- DOI
10.1007/s40314-023-02262-5