HuberSpline: Huber (1974) Minimal Fisher (location) information spline via...
In REBayes: Empirical Bayes Estimation and Inference
HuberSpline R Documentation
Huber (1974) Minimal Fisher (location) information spline via conic optimization
Description
\min \sum \frac{(f_{i+1}-f_i )^2}{( f_{i+1}+f_i )/2} = \sum \frac{u_i^2}{v_i/2} \approx I(F)
Usage
HuberSpline(x, p, grid, kappa = 0)
Arguments
x
quantiles to be interpolated
p
probabilities associated with x
grid
grid values for fitted object
kappa
width of Kolmogorov neighborhood
Details
\Leftrightarrow \quad \min \sum w_i \; \mbox{s.t.} \; u_i^2 \leq 2 v_i w_i
subject to interpolation of constraints F(x_j) = p_j, \; j=1,...,n.
When \kappa > 0, I(F) is minimized within a Kolmogorov neighborhood
of the constraint points, rather than interpolating them.
The generalization to Kolmogorov neighborhoods is due to Donoho
and Reeves (2013).
N.B. When the grid is not equispaced, one would have to include grid spacings.
Value
An object of class density with solution f*
Author(s)
R. Koenker and J. Gu
References
P. J. Huber. (1974) "Fisher Information and Spline Interpolation."
Ann. Statist. 2 (5) 1029 - 1033,
D. L. Donoho and G. Reeves, (2013) Achieving Bayes MMSE Performance in the Sparse Signal
Gaussian White Noise Model when the Noise Level is Unknown, Proc. IEEE Symposium Istanbul, Turkey.
REBayes documentation built on Dec. 3, 2025, 5:06 p.m.
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| HuberSpline | R Documentation |
Huber (1974) Minimal Fisher (location) information spline via conic optimization
Description
\min \sum \frac{(f_{i+1}-f_i )^2}{( f_{i+1}+f_i )/2} = \sum \frac{u_i^2}{v_i/2} \approx I(F)
Usage
HuberSpline(x, p, grid, kappa = 0)
Arguments
x |
quantiles to be interpolated |
p |
probabilities associated with x |
grid |
grid values for fitted object |
kappa |
width of Kolmogorov neighborhood |
Details
\Leftrightarrow \quad \min \sum w_i \; \mbox{s.t.} \; u_i^2 \leq 2 v_i w_i
subject to interpolation of constraints F(x_j) = p_j, \; j=1,...,n.
When \kappa > 0, I(F) is minimized within a Kolmogorov neighborhood
of the constraint points, rather than interpolating them.
The generalization to Kolmogorov neighborhoods is due to Donoho
and Reeves (2013).
N.B. When the grid is not equispaced, one would have to include grid spacings.
Value
An object of class density with solution f*
Author(s)
R. Koenker and J. Gu
References
P. J. Huber. (1974) "Fisher Information and Spline Interpolation." Ann. Statist. 2 (5) 1029 - 1033,
D. L. Donoho and G. Reeves, (2013) Achieving Bayes MMSE Performance in the Sparse Signal Gaussian White Noise Model when the Noise Level is Unknown, Proc. IEEE Symposium Istanbul, Turkey.
R Package Documentation
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Note that we can't provide technical support on individual packages. You should contact the package authors for that.
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