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Periodic Splinets

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Název: Periodic Splinets
Autoři: Nassar, Hiba, Podgórski, Krzysztof
Přispěvatelé: Lund University, Lund University School of Economics and Management, LUSEM, Department of Statistics, Lunds universitet, Ekonomihögskolan, Statistiska institutionen, Originator
Zdroj: Communications in Statistics: Simulation and Computation. :1-16
Témata: Natural Sciences, Mathematical Sciences, Probability Theory and Statistics, Naturvetenskap, Matematik, Sannolikhetsteori och statistik
Popis: Periodic splines represent a specific category of splines, defined across a series of knots on a circle, making them particularly suitable for addressing interpolation challenges associated with closed curves and representing functions defined on a circle. Although the term ‘periodic’ suggests temporal context, the periodic splines can represent any data that have a circle as their domain. This paper introduces a method for implementing objects that represent such splines and outlines the derivation of an efficient orthogonal basis. The newly proposed orthonormalized basis, referred to as a periodic splinet, builds upon concepts and tools previously introduced for interval-based splines. Employing this methodology, periodic splines and splinets have been integrated into an updated version of the R package, Splinets 1.5.0. Additionally, the computational tools developed in this study have been applied to the functional analysis of a prototypical example of circular functional data, namely wind direction and speeds.
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  Data: Periodic splines represent a specific category of splines, defined across a series of knots on a circle, making them particularly suitable for addressing interpolation challenges associated with closed curves and representing functions defined on a circle. Although the term ‘periodic’ suggests temporal context, the periodic splines can represent any data that have a circle as their domain. This paper introduces a method for implementing objects that represent such splines and outlines the derivation of an efficient orthogonal basis. The newly proposed orthonormalized basis, referred to as a periodic splinet, builds upon concepts and tools previously introduced for interval-based splines. Employing this methodology, periodic splines and splinets have been integrated into an updated version of the R package, Splinets 1.5.0. Additionally, the computational tools developed in this study have been applied to the functional analysis of a prototypical example of circular functional data, namely wind direction and speeds.
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