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On l2 Error Bounds of the Elastic Net when p>>n
Lasso naive Elastic Net Elastic Net model selection consistency estimation consistency
2016/1/20
We study the estimation property of the Elastic Net in high-dimensional settings where the number of parameters p is comparable to or larger than the sample size n. In such a situation one often assum...
Evaluation of Signal in Space Error Bounds to Support Aviation Integrity
Evaluation of Signal in Space Error Bounds to Support Aviation Integrity
2015/6/25
The modernization of GPS and the addition of new GNSS constellations bring forth a multitude of new signals with new capabilities. One of the intended purposes of some of these new signals is the prov...
Evaluation of Signal in Space Error Bounds to Support Aviation Integrity
Evaluation Signal Space Error Bounds Support Aviation Integrity
2015/6/25
In order to make use of signals over which they have no control, aviation authorities must have a clear understanding of the commitments and capabilities of these new signals. This paper proposes equa...
Guaranteed Error Bounds for Model Reduction of Linear Time-Varying Systems
Time-Varying Systems Model Reduction
2015/6/19
New techniques are presented for the model reduction of linear time-varying and linear periodically-varying systems, including the formulation and proof of guaranteed upper bounds for the error. The c...
Error Bounds for Balanced Model Reduction of Linear Time-Varying Systems
Time-Varying Systems Model Reduction
2015/6/19
Error-bounds are developed for balanced truncation of linear time-varying systems, leading to an extension of the `twice the sum of the tail' formulae, well-known in the time-invariant case. The appro...
Optimal error bounds for two-grid schemes applied to the Navier-Stokes equations
two-grid schemes the Navier-Stokes equations
2010/11/18
We consider two-grid mixed-finite element schemes for the spatial discretization of the incompressible Navier-Stokes equations. A standard mixed-finite element method is applied over the coarse grid ...
Uniform error bounds for a continuous approximation of non-negative random variables
gamma distribution Laplace transform phase-type distribution
2010/10/19
In this work, we deal with approximations for distribution functions of non-negative random variables. More specifically, we construct continuous approximants using an acceleration technique over a w...
Error bounds for small jumps of Lévy processes and financial applications
Approximation of small jumps L´ evy processes Skorokhod embedding
2010/10/21
The pricing of exotic options in exponential L\'evy models amounts to the computation of expectations of functionals of the whole path of a L\'evy process. In many situations, Monte-Carlo methods are ...
Error bounds for small jumps of Lévy processes and financial applications
Approximation of small jumps L´ evy processes Skorokhod embedding
2010/12/16
The pricing of exotic options in exponential L´evy models amounts to the computation of expectations of functionals of the whole path of a L´evy process. In many situations, Monte-Carlo me...
Error bounds on the non-normal approximation of Hermite power variations of fractional Brownian motion
Hermite power variation fractional Brownian motion
2009/3/20
Let q≥2 be a positive integer, B be a fractional Brownian motion with Hurst index H∈(0,1), Z be an Hermite random variable of index q, and Hq denote the q-th Hermite polynomial. For any n≥1, set Vn=∑0...
Inequalities Between the Quadrature Operators and Error Bounds of Quadrature Rules
Approximate integration Quadrature rules Convex functions of higher order
2008/7/1
The order structure of the set of six operators connected with quadrature rules is established in the class of 3-convex functions. Convex combinations of these operators are studied and their error bo...
On Error Bounds for Gauss-Legendre and Lobatto Quadrature Rules
Convex functions of higher orders Approximate integration Quadrature rules
2008/6/27
The error bounds for Gauss-Legendre and Lobatto quadratures are proved for
four times differentiable functions (instead of six times differentiable functions as in the classical results). Auxiliaril...
Sharp Error Bounds for Some Quadrature Formulae and Applications
Sharp error bounds Quadrature formulae Numerical integration
2008/6/26
In the article ''N. Ujevic, A generalization of the pre-Grüss inequality and applications to some quadrature formulae, J. Inequal. Pure Appl. Math., 3(2), Art. 13, 2002'' error bounds for some quadrat...
Sharp Error Bounds for the Trapezoidal Rule and Simpson's Rule
Numerical integration Trapezoidal rule Simpson's rule
2008/6/26
Sharp Error Bounds for the Trapezoidal Rule and Simpson's Rule.
On Quadrature Rules, Inequalities and Error Bounds
Approximate integration Quadrature rules Convex functions of higher order
2010/1/22
The order structure of the set of six operators connected with quadrature rules is established in the class of 5-convex functions. An error bound of the Lobatto quadrature rule with five knots is g...