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Strong law of large numbers for supercritical superprocesses under second moment condition
superprocess scaling limit theorem Hunt process spec- tral gap h-transform martingale measure
2016/1/26
Strong law of large numbers for supercritical superprocesses under second moment condition.
Preconditioning to Comply with the Irrepresentable Condition
Preconditioning Lasso Sign consistency
2016/1/20
Preconditioning is a technique from numerical linear algebra that can accelerate algorithms to solve systems of equations. In this pa-per, we demonstrate how preconditioning can circumvent a stringent...
Subspaces that Minimize the Condition Number of a Matrix
Subspaces Minimize Condition Number Matrix
2015/7/9
We define the condition number of a nonsingular matrix on a subspace, and consider the problem of finding a subspace of given dimension that minimizes the condition number of a given matrix. We give a...
A Primal Condition for Approachability with Partial Monitoring
Primal Condition Approachability with Partial Monitoring
2013/6/17
In approachability with full monitoring there are two types of conditions that are known to be equivalent for convex sets: a primal and a dual condition. The primal one is of the form: a set C is appr...
Model Selection for High-Dimensional Regression under the Generalized Irrepresentability Condition
Model Selection High-Dimensional Regression Generalized Irrepresentability Condition
2013/6/13
In the high-dimensional regression model a response variable is linearly related to $p$ covariates, but the sample size $n$ is smaller than $p$. We assume that only a small subset of covariates is `ac...
Preconditioning to comply with the Irrepresentable Condition
Preconditioning Lasso Sign consistency
2012/9/18
Preconditioning is a technique from numerical linear algebra that can accelerate algorithms to solve systems of equations. In this pa-per, we demonstrate how preconditioning can circumvent a stringent...
Condition Numbers of Indefinite Rank 2 Ghost Wishart Matrices
Condition Numbers Indefinite Rank 2 Ghost Wishart Matrices
2012/9/19
We define an indefinite Wishart matrix as a matrix of the formA=WTWΣ, where Σis an indefinite diagonal matrix andWis a matrix of independent standard normals. We focus on the case whereWis L×2which ha...
The linearity condition and adaptive estimation in single-index regressions
linearity condition adaptive estimation single-index regressions
2010/3/9
We show that under a linearity condition on the distribution of the predictors,
the coefficient vector in a single-index regression can be estimated with
the same efficiency as in the case when the ...
Size-biased branching population measures and the multi-type x\logx condition
general branching process immigration size-biased measure xlogx condition
2010/3/9
We investigate the x log x condition for a general (Crump–Mode–Jagers) multi-type branching
process with a general type space by constructing a size-biased population measure that relates
to the ord...
On a random version of the Anscombe condition and its applications
a random version the Anscombe condition applications
2009/9/23
The paper proves theorems of [6] which are given
here in a more general form. Moreover, some applications of the
introduced version of the Anscornbe condition are discussed.
LOCAL LARGE DEVIATION THEOREM FOR SUMS OF LLD. RANDOM VECTORS WHEN THE CRAMER CONDITION HOLDS IN THE WHOLE SPACE
Abel theorem conjugate density Laplace method slow variation
2009/9/21
A class of multidimensiond distributions is considered.
This class contains all the elliptically contoured distributions having
sup-exponential weight function. Each representative of the class dete...
Risk Bounds for Classification Trees under a Margin Condition
Classification CART Pruning Margin Risk Bounds
2010/3/18
Risk bounds for Classification and Regression Trees (CART, Breiman et. al. 1984)
classifiers are obtained under a margin condition in the binary supervised classification
framework. These risk bound...
A Necessary and Sufficient Condition for the Lambda-Coalescent to Come Down from Infinity
coalescent Kochen-StoneLemma
2009/5/4
Let $Pi_{infty}$ be the standard $Lambda$-coalescent of Pitman, which is defined so that $Pi_{infty}(0)$ is the partition of the positive integers into singletons, and, if $Pi_n$ denotes the restricti...
A Condition for Weak Disorder for Directed Polymers in Random Environment
Directed polymer in random environment weak disorder size-biasing
2009/4/28
We give a sufficient criterion for the weak disorder regime of directed polymers in random environment, which extends a well-known second moment criterion. We use a stochastic representation of the si...
Strong Law of Large Numbers Under a General Moment Condition
quasi-stationary sequence strong law of large numbers maximum inequality
2009/4/27
We use our maximum inequality for p-th order random variables (p>1) to prove a strong law of large numbers (SLLN) for sequences of p-th order random variables. In particular, in the case p=2 our resu...