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Nonlinear Estimators and Tail Bounds for Dimension Reduction in l1 Using Cauchy Random Projections
dimension reduction l1 norm Johnson-Lindenstrauss (JL) lemma Cauchy random projections
2015/8/21
For1 dimension reduction in the l1 norm, the method of Cauchy random projections multiplies the original data matrix A ∈ Rn×D with a random matrix R ∈ RD×k (k D) whose entries are i.i.d. samples of ...
Bandits with heavy tail
Bandits heavy tail
2012/11/22
The stochastic multi-armed bandit problem is well understood when the reward distributions are sub-Gaussian. In this paper we examine the bandit problem under the weaker assumption that the distributi...
Tail estimates for norms of sums of log-concave random vectors
log-concave random vectors concentration inequalities deviation inequalities random matrices
2011/9/15
Abstract: We establish new tail estimates for order statistics and for the Euclidean norms of projections of an isotropic log-concave random vector. More generally, we prove tail estimates for the nor...
Tail Asymptotic of Sum and Product of Random Variables with Applications in the Theory of Extremes of Conditionally Gaussian Processes
tail asymptotic Laplace method self-similar processes Gaussian processes locally stationary processes
2011/9/15
Abstract: We consider two independent random variables with the given tail asymptotic (e.g. power or exponential). We find tail asymptotic for their sum and product. This is done by some cumbersome bu...
Bounding Standard Gaussian Tail Probabilities
Bounding Standard Gaussian Tail Probabilities
2011/1/20
We review various inequalities for Mills' ratio (1 )= , where and denote the standard Gaussian density and distribution function, respectively. Elementary considerations involving nit...
Approximate tail probabilities of the maximum of a chi-square field on multi-dimensional lattice points and their applications to detection of loci interactions
Approximate tail probabilities a chi-square field multi-dimensional lattice points
2011/1/4
Define a chi-square random field on a multi-dimensional lattice points index set with a direct-product covariance structure, and consider the distribution of the maximum of this random field. We provi...
Let $\{X_t, t \geq 1\}$ be a sequence of identically distributed and pairwise asymptotically independent random variables with regularly varying tails and $\{ \Theta_t, t\geq1 \}$ be a sequence of pos...
Sub-Gaussian tail bounds for the width and height of conditioned Galton--Watson trees
Sub-Gaussian tail conditioned Galton--Watson trees
2010/11/23
We study the height and width of a Galton--Watson tree with offspring distribution B satisfying E(B)=1, 0 < Var(B) < infinity, conditioned on having exactly n nodes. Under this conditioning, we deriv...
We give an asymptotic expression for the tail of the maximum of Brownian motion minus a parabola. This confirms a conjecture about the exponential term in the tail behavior, due to Svante Janson.
Tail behavior of stationary solutions of random difference equations: the case of regular matrices
Markov renewal theory implicit renewal theory Harris recurrence
2010/12/1
Given a sequence (Mn,Qn)n≥1 of i.i.d. random variables with generic copy (M,Q)such that M is a regular d × d matrix and Q takes values in Rd, we consider the random difference equation (RDE) Rn = MnRn...
The Ratio Between the Tail of a Series and its Approximating Integral
Series Tail Ratio Monotonic Zeta function
2008/6/26
The Ratio Between the Tail of a Series and its Approximating Integral.
On comparison of the tail index of heavy tail distributions using Pitman's measure of closeness
Stable distributions Pitman’s measure of closeness
2010/9/15
The objective of this paper is to compare estimators which are a function of sample averages (a modification of Fan’s estimators) based on different sample sizes for all symmetric stable distributions...
ALMOST SURE CONVERGENCE OF THE STABLE TAIL EMPIRICAL DEPENDENCE FUNCTION IN MULTIVARIATE EXTREME STATISTICS
Multivariate extreme value s
2007/12/11
In this paper we prove the almost sure convergence of the stable tail empirical dependence function for multivariate extreme values.