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When uniform weak convergence fails: empirical processes for dependence functions via epi- and hypographs
bootstrap copula epigraph hypograph stable tail dependence function minimum distance estimation weak convergence
2013/6/14
For copulas whose partial derivatives are not continuous everywhere on the interior of the unit cube, the empirical copula process does not converge weakly with respect to the supremum distance. This ...
Adaptive estimation in nonparametric regression with one-sided errors
adaptive convergence rates non-regular regression frontier estimation bandwidth selection Lepski's method minimax optimality Pickands estimator
2013/6/14
We consider the model of non-regular nonparametric regression where smoothness constraints are imposed on the regression function and the regression errors are assumed to decay with some sharpness lev...
Multiple testing of local maxima for detection of peaks in ChIP-Seq data
False discovery rate kernel smoothing matched filter Poisson sequence topological inference
2013/6/14
A topological multiple testing approach to peak detection is proposed for the problem of detecting transcription factor binding sites in ChIP-Seq data. After kernel smoothing of the tag counts over th...
Estimating Average Causal Effects Under Interference Between Units
Estimating Average Causal Effects Interference Between Units
2013/6/14
This paper presents a randomization-based framework for estimating causal effects under interference between units. We develop the case of estimating average unit-level causal effects from a randomize...
A general approach of least squares estimation and optimal filtering
Least squares Optimal filtering Matched filter Noise Optimization Power Spectrum Density
2013/6/17
The least squares method allows fitting parameters of a mathematical model from experimental data. This article proposes a general approach of this method. After introducing the method and giving a fo...
On some interrelations of generalized $q$-entropies and a generalized Fisher information, including a Cramér-Rao inequality
Cramér-Rao inequality generalizedq-entropy generalized Gaussians de Bruijn identity
2013/6/17
In this communication, we describe some interrelations between generalized $q$-entropies and a generalized version of Fisher information. In information theory, the de Bruijn identity links the Fisher...
Some results on a $χ$-divergence, an~extended~Fisher information and~generalized~Cramer-Rao inequalities
Some results $χ$-divergence an~extended~Fisher information generalized~Cramer-Rao inequalities
2013/6/17
We propose a modified $\chi^{\beta}$-divergence, give some of its properties, and show that this leads to the definition of a generalized Fisher information. We give generalized Cram\'er-Rao inequalit...
Local Privacy and Minimax Bounds: Sharp Rates for Probability Estimation
Local Privacy Minimax Bounds Sharp Rates Probability Estimation
2013/6/14
We provide a detailed study of the estimation of probability distributions---discrete and continuous---in a stringent setting in which data is kept private even from the statistician. We give sharp mi...
Limit theorems for kernel density estimators under dependent samples
Kernel density estimator consistency convergence rate mixing rate
2013/6/14
In this paper, we construct a moment inequality for mixing dependent random variables, it is of independent interest. As applications, the consistency of the kernel density estimation is investigated....
Statistical Significance of Clustering using Soft Thresholding
Covariance Estimation High Dimension Invariance Principles Unsupervised Learning
2013/6/14
Clustering methods have led to a number of important discoveries in bioinformatics and beyond. A major challenge in their use is determining which clusters represent important underlying structure, as...
Parallel Gaussian Process Regression with Low-Rank Covariance Matrix Approximations
Parallel Gaussian Process Regression Low-Rank Covariance Matrix Approximations
2013/6/14
Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due ...
The Optimal Hard Threshold for Singular Values is 4/sqrt(3)
Optimal Hard Threshold Singular Values 4/sqrt(3)
2013/6/14
We consider recovery of low-rank matrices from noisy data by hard thresholding of singular values, where singular values below a prescribed threshold \lambda are set to 0. We study the asymptotic MSE ...
Adapting the Stochastic Block Model to Edge-Weighted Networks
Adapting Stochastic Block Model Edge-Weighted Networks
2013/6/14
We generalize the stochastic block model to the important case in which edges are annotated with weights drawn from an exponential family distribution. This generalization introduces several technical...
Adaptive confidence intervals for regression functions under shape constraints
Adaptation confidence interval convex function coverage probability expected length minimax estimation modulus of continuity monotone func-tion nonparametric regression shape constraint white noise model
2013/6/14
Adaptive confidence intervals for regression functions are constructed under shape constraints of monotonicity and convexity. A natural benchmark is established for the minimum expected length of conf...
A simple proof for the multivariate Chebyshev inequality
Chebyshev (Tchebychev) inequality Mahalanobis distance Principal compo-nents Ellipsoid
2013/6/14
In this paper a simple proof of the Chebyshev's inequality for random vectors obtained by Chen (arXiv:0707.0805v2, 2011) is obtained. This inequality gives a lower bound for the percentage of the popu...