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Fitting Matérn smoothness parameters using automatic differentiation

Statistics and Computing, 2023
The Matérn covariance function is ubiquitous in the application of Gaussian processes to spatial statistics and beyond. Perhaps the most important reason for this is that the smoothness parameter $ν$ gives complete control over the mean-square differentiability of the process, which has significant implications for the behavior of estimated quantities ...
Geoga, Christopher J.   +3 more
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Electrical parameters of smooth muscle cells

American Journal of Physiology-Legacy Content, 1963
Spikes in circular intestinal muscle fibers show volume-conductor shapes and conduct faster in low resistance medium than in air. Longitudinal space constant is 1.0 mm (20 cell lengths if 50% overlap); transverse space constant is 0.27 mm or 50 cell widths.
T, NAGAI, C L, PROSSER
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Speech coding parameter smoothing method

The Journal of the Acoustical Society of America, 1998
A decoding method and apparatus for speech coding systems which takes into account the fact that the human auditory system is sensitive to changes in signal characteristics. For example, a sustained distortion of the spectral characteristic of reconstructed speech is usually less perceptible than an objectively smaller distortion which changes as a ...
Willem Bastiaan Kleijn   +1 more
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Smoothed eigenspace-based parameter estimation

Automatica, 1994
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Krim, H., Proakis, J. G.
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Smoothing parameter selection for smooth distribution functions

Journal of Statistical Planning and Inference, 1993
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Choosing the Smoothing Parameter

2001
We have now come to just about the most important aspect of nonparametric density estimation: choosing the smoothing parameter in kernel estimation that will give near-optimal results for large classes of densities.
P. P. B. Eggermont, V. N. LaRiccia
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Algorithms for Optimal Smoothing Parameter

2001
As before, let the linear continuous operators A : X → Z, T : X → Y be defined in the Hilbert spaces, z be an element of the space Z. Present as in Chapter 1 the variational principle for the interpolating spline σ ∈ X in the following way $$\sigma = \arg \mathop {\min }\limits_{u \in X,{A_u} = z} ||{T_u}||Y$$ (12.1) and for the smoothing ...
Anatoly Yu. Bezhaev   +1 more
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Parameter Estimation Using Least-Squares Polynomial Smoothing

IEEE Transactions on Systems, Man, and Cybernetics, 1973
This paper considers several aspects of parameter estimation using least-squares polynomial smoothing of noisy observations. These aspects are 1) the choice of estimation times, 2) the simultaneous or independent use of data, and 3) the use of a polynomial of improper degree to fit the observations.
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Smoothing parameter selection in hazard estimation

Statistics & Probability Letters, 1991
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sarda, P., Vieu, P.
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The smoothing parameter, confidence interval and robustness for smoothing splines

Journal of Nonparametric Statistics, 2005
Diagnostic measure for nonparametric regression using splines is given. The measure which incorporates important information provided by the smoothing parameter has the potential of identifying ‘unusual’ observations. These influential observations can substantially influence the global behavior of the fitted curve.
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