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Results 1 - 10
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623
From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images
, 2007
"... A full-rank matrix A ∈ IR n×m with n < m generates an underdetermined system of linear equations Ax = b having infinitely many solutions. Suppose we seek the sparsest solution, i.e., the one with the fewest nonzero entries: can it ever be unique? If so, when? As optimization of sparsity is combin ..."
Abstract
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Cited by 427 (36 self)
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is combinatorial in nature, are there efficient methods for finding the sparsest solution? These questions have been answered positively and constructively in recent years, exposing a wide variety of surprising phenomena; in particular, the existence of easily-verifiable conditions under which optimally
Strong invariance principles for dependent random variables
- ANNALS PROBA
, 2007
"... We establish strong invariance principles for sums of stationary and ergodic processes with nearly optimal bounds. Applications to linear and some nonlinear processes are discussed. Strong laws of large numbers and laws of the iterated logarithm are also obtained under easily verifiable conditions. ..."
Abstract
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Cited by 65 (9 self)
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We establish strong invariance principles for sums of stationary and ergodic processes with nearly optimal bounds. Applications to linear and some nonlinear processes are discussed. Strong laws of large numbers and laws of the iterated logarithm are also obtained under easily verifiable conditions.
Stochastic Equicontinuity in Nonlinear Time Series Models
, 2013
"... In this paper I provide simple and easily verifiable conditions under which a strong form of stochastic equicontinuity holds in a wide variety of modern time series models. In contrast to most results currently available in the literature, my methods avoid mixing conditions. I discuss several applic ..."
Abstract
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Cited by 2 (0 self)
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In this paper I provide simple and easily verifiable conditions under which a strong form of stochastic equicontinuity holds in a wide variety of modern time series models. In contrast to most results currently available in the literature, my methods avoid mixing conditions. I discuss several
Nonlocal Boundary Value Problem for Strongly Singular Higher-Order Linear Functional-Differential Equations
"... For strongly singular higher-order differential equations with deviating arguments, under nonlocal boundary conditions, Agarwal-Kiguradze type theorems are established, which guarantee the presence of the Fredholm property for the problems considered. We also provide easily verifiable conditions tha ..."
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For strongly singular higher-order differential equations with deviating arguments, under nonlocal boundary conditions, Agarwal-Kiguradze type theorems are established, which guarantee the presence of the Fredholm property for the problems considered. We also provide easily verifiable conditions
On Strong Convergence for Sums of Dependent Random Variables
, 2004
"... We present a strong convergence theory for sums of stationary and ergodic processes. Laws of large numbers and iterated logarithm are established under simple and easily verifiable conditions. The results refine previous ones by providing an explicit rate of a natural martingale approximation. An ..."
Abstract
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Cited by 1 (1 self)
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We present a strong convergence theory for sums of stationary and ergodic processes. Laws of large numbers and iterated logarithm are established under simple and easily verifiable conditions. The results refine previous ones by providing an explicit rate of a natural martingale approximation
OPERATORS WITH COMPATIBLE RANGES IN AN ALGEBRA GENERATED BY TWO ORTHOGONAL PROJECTIONS
, 2018
"... Abstract. The criterion is obtained for operators A from the algebra generated by two orthogonal projections P, Q to have a compatible range, i.e., coincide with A * on the orthogonal complement to the sum of the kernels of A and A * . In the particular case of A being a polynomial in P, Q, some ea ..."
Computing Variance for Interval Data is NP-Hard
, 2002
"... When we have only interval ranges [x i ; x i ] of sample values x 1 ; : : : ; xn , what is the interval [V ; V ] of possible values for the variance V of these values? We prove that the problem of computing the upper bound V is NP-hard. We provide a feasible (quadratic time) algorithm for computi ..."
Abstract
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Cited by 67 (49 self)
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for computing the lower bound V on the variance of interval data. We also provide a feasible algorithm that computes V under reasonable easily verifiable conditions.
A necessary and sufficient condition for consensus over random networks
- IEEE Transactions on Automatic Control
, 2008
"... Abstract — In this paper we consider the consensus problem for stochastic switched linear dynamical systems. For discretetime and continuous-time stochastic switched linear systems, we present necessary and sufficient conditions under which such systems reach a consensus almost surely. In the discre ..."
Abstract
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Cited by 89 (6 self)
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arguments. These easily verifiable conditions depend on the spectrum of the average weight matrix and the average Laplacian matrix for the discrete-time and continuous-time cases, respectively. I.
Degenerate U- and V-statistics under weak dependence: Asymptotic theory and bootstrap consistency
"... We devise a general result on the consistency of model-based bootstrap methods for U-and V-statistics under easily verifiable conditions. For that purpose we derive the limit distribution of degree-2 degenerate U- and V-statistics for weakly dependent R^d-valued random variables first. To this end, ..."
Abstract
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Cited by 5 (1 self)
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We devise a general result on the consistency of model-based bootstrap methods for U-and V-statistics under easily verifiable conditions. For that purpose we derive the limit distribution of degree-2 degenerate U- and V-statistics for weakly dependent R^d-valued random variables first. To this end
A-Posteriori Identifiability of the Maxwell Slip Model of Hysteresis ⋆
"... Abstract: The a–posteriori identifiability of the Maxwell Slip model of hysteresis is addressed. The necessary and sufficient conditions that guarantee that the available data are informative enough are provided. An Output Error type estimator is subsequently postulated and its consistency is establ ..."
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is established. It is specifically shown that the estimates converge in probability to their actual counterparts under easily verifiable conditions on the Maxwell Slip model structure, the excitation, and mild assumptions on the additive measurement noise. The analytical results are verified through Monte Carlo
Results 1 - 10
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623
