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On the restricted convergence of the intermediate and central terms of order statistics
Order statistics intermediate value distributions weak convergence
2009/9/21
As the distribulivn function (dd) of the suitably normalized
general intermediate (or central) term of order statistics converges
on an interval [c, dl to an arbitrary nondecreasing function,
the c...
Almost sure convergence of the distributional limit theorem for order statistics
Almost sure convergence distributional limit theorem order statistics
2009/9/21
Let X,, n 2 1, be a sequence of independent and identically
distributed rmdom variables and X,,, < X,,, < . . . < X,, denote
the order statistics of Xi,.. ., X,. For any sequenoe 01 integers
{k,) w...
A NOTE ON THE ALMOST SURE CONVERGENCE OF CENTRAL ORDER STATISTICS
Central order statistics almost sure limit theorem summation methods
2009/9/18
We prove almost sure versions of distributional limit
theorems for central order statistics. We develop a new method which
not only gives a simplified proof of existing results in the literature, bu...
CONVERGENCE RATES IN THE LAW OF LARGE NUMBERS FOR ARRAYS
Arrays of rowwise independent random variables complete convergence
2009/9/18
In this paper we present new suficient conditions for
complete convergence for $urns of arrays of rowwise independent random
variables. These conditions appear to be necessary and sufficient
in the...
CONVERGENCE RATE IN CLT FOR VECTOR-VALUED RANDOM FIELDS WITH SELF-N63RMALIZATIQ)N
Random fields dependence conditions CLT random matrix normalization convergence rate
2009/9/18
Statistical version of the central limit theorem (CLT)
with random matrix normalization is established for random fields
with valuea in a space Rk (k 3 1). Dependence structure of the field
under c...
ON THE RANDOM FUNCTIONAL CENTRAL LIMIT THEOREMS WITH ALMOST SURE CONVERGENCE
Almost sure central limit theorem functional random-sum central limit theorem lbgarithmic averages
2009/9/18
In this paper we present functional random-sum central
limit theorems with almost sure convergence for independent nonidentically
distributed random variables. We consider the case where
the summat...
FINITE DIFFERENCE EQUATIONS AND CONVERGENCE RATES IN THE CENTRAL LIMIT THEOREM
Finite difference equations central limit theorem convergence rate interpolation theory
2009/9/18
We apply the theory of finite difference equations to
the central limit theorem, using interpolation of Banach spaces and
Fourier multipliers. Let S,T be a normalized sum of i.i.d. random vectors,
...
CONVERGENCE IN VARIATION OF THE JOINT LAWS OF MULTIPLE STABLE STOCHASTIC INTEGRALS
Convergence in variation multiple stochastic integrals stable process LePage representation
2009/9/18
In this note, we are interested in the regularity in the sense
of total variation of the joint laws of multiple stable stochastic integrals.
Namely, we show that the convergence
L
Id1 ...
One more approach to the convergence of the empirical process to the Brownian bridge
Empirical process Donsker Theorem Brownian bridge
2009/9/16
A theorem of Donsker asserts that the empirical process converges in distribution to the Brownian bridge. The aim of this paper is to provide a new and simple proof of this fact.
Sup-norm convergence rate and sign concentration property of Lasso and Dantzig estimators
Linear model Lasso Dantzig Sparsity Model selection Sign consistency
2009/9/16
We derive the l∞ convergence rate simultaneously for Lasso and Dantzig estimators in a high-dimensional linear regression model under a mutual coherence assumption on the Gram matrix of the design and...
Almost sure convergence of extreme order statistics
almost sure convergence order statistics
2009/9/16
Let $M_{n}^{(k)}$ denote the $k$th largest maximum of a sample $(X_{1},X_{2}, \ldots, X_{n})$ from parent $X$ with continuous distribution. Assume there exist normalizing constants $a_{n}>0$, $b_{n}in...
A strong uniform convergence rate of a kernel conditional quantile estimator under random left-truncation and dependent data
Kernel estimator quantile function rate of convergence strong mixing strong uniform consistency truncated data
2009/9/16
In this paper we study some asymptotic properties of the kernel conditional quantile estimator with randomly left-truncated data which exhibit some kind of dependence. We extend the result obtained by...
Fixing Convergence of Gaussian Belief Propagation
Fixing Convergence Gaussian Belief Propagation
2010/3/17
Gaussian belief propagation (GaBP) is an iterative
message-passing algorithm for inference in Gaussian graphical
models. It is known that when GaBP converges it converges to the
correct MAP estimat...
Convergence to the viscous porous medium equation and propagation of chaos
Nonlinear stochastic differential equations Viscous porous medium equation Interacting particle systems
2009/6/12
Convergence to the viscous porous medium equation and propagation of chaos.
Convergence of the Tóth lattice filling curve to the Tóth-Werner plane filling curve
convergence Tóth lattice filling curve Tóth-Werner plane
2009/6/12
Convergence of the Tóth lattice filling curve to the Tóth-Werner plane filling curve.