On the equivalence of two stochastic approaches to spline smoothing

1986 ◽  
Vol 23 (A) ◽  
pp. 391-405 ◽  
Author(s):  
Craig F. Ansley ◽  
Robert Kohn
Keyword(s):  
Stochastic Process ◽  
Hilbert Space ◽  
Minimization Problem ◽  
Stochastic Models ◽  
Conditional Expectation ◽  
Smoothing Spline ◽  
Computational Algorithms ◽  
Spline Smoothing ◽  
Optimal Smoothing ◽  
Space Formulation

Wahba (1978) and Weinert et al. (1980), using different models, show that an optimal smoothing spline can be thought of as the conditional expectation of a stochastic process observed with noise. This observation leads to efficient computational algorithms. By going back to the Hilbert space formulation of the spline minimization problem, we provide a framework for linking the two different stochastic models. The last part of the paper reviews some new efficient algorithms for spline smoothing.

On the equivalence of two stochastic approaches to spline smoothing

1986 ◽  
Vol 23 (A) ◽  
pp. 391-405 ◽  
Author(s):  
Craig F. Ansley ◽  
Robert Kohn
Keyword(s):  
Stochastic Process ◽  
Hilbert Space ◽  
Minimization Problem ◽  
Stochastic Models ◽  
Conditional Expectation ◽  
Smoothing Spline ◽  
Computational Algorithms ◽  
Spline Smoothing ◽  
Optimal Smoothing ◽  
Space Formulation

Wahba (1978) and Weinert et al. (1980), using different models, show that an optimal smoothing spline can be thought of as the conditional expectation of a stochastic process observed with noise. This observation leads to efficient computational algorithms. By going back to the Hilbert space formulation of the spline minimization problem, we provide a framework for linking the two different stochastic models. The last part of the paper reviews some new efficient algorithms for spline smoothing.

scholarly journals On intensities of modulated Cox measures

1998 ◽  
Vol 11 (3) ◽  
pp. 411-423 ◽  
Author(s):  
Jewgeni H. Dshalalow
Keyword(s):  
Stochastic Process ◽  
Stochastic Models ◽  
Queueing Systems ◽  
Random Measure ◽  
Random Measures ◽  
Explicit Formulas ◽  
State Dependent

In this paper we introduce and study functionals of the intensities of random measures modulated by a stochastic process ξ, which occur in applications to stochastic models and telecommunications. Modulation of a random measure by ξ is specified for marked Cox measures. Particular cases of modulation by ξ as semi-Markov and semiregenerative processes enabled us to obtain explicit formulas for the named intensities. Examples in queueing (systems with state dependent parameters, Little's and Campbell's formulas) demonstrate the use of the results.

Optimal Smoothing Spline with Constraints on Its Derivatives

2014 ◽  
Vol 7 (2) ◽  
pp. 104-111 ◽  
Author(s):  
Hiroyuki KANO ◽  
Hiroyuki FUJIOKA ◽  
Clyde F. MARTIN
Keyword(s):  
Smoothing Spline ◽  
Optimal Smoothing

scholarly journals A functional Hodrick–Prescott filter

2017 ◽  
Vol 25 (2) ◽  
Author(s):  
Boualem Djehiche ◽  
Hiba Nassar
Keyword(s):  
Hilbert Space ◽  
Linear Operator ◽  
Functional Data ◽  
Separable Hilbert Space ◽  
Underlying Distribution ◽  
Smoothing Operator ◽  
Infinite Dimensional ◽  
Optimal Smoothing ◽  
Functional Version

AbstractWe propose a functional version of the Hodrick–Prescott filter for functional data which take values in an infinite-dimensional separable Hilbert space. We further characterize the associated optimal smoothing operator when the associated linear operator is compact and the underlying distribution of the data is Gaussian.

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