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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...
Parametric Stein operators and variance bounds
Chernoff inequality Cramer-Rao inequality parameter of interest Stein charac-terization Stein’s method
2013/6/17
Stein operators are differential operators which arise within the so-called Stein's method for stochastic approximation. We propose a new mechanism for constructing such operators for arbitrary (conti...
Global risk bounds and adaptation in univariate convex regression
Global risk bounds adaptation univariate convex regression
2013/6/13
We consider the problem of nonparametric estimation of a convex regression function $\phi_0$. We study global risk bounds and adaptation properties of the least squares estimator (LSE) of $\phi_0$. Un...
Discrepancy bounds for uniformly ergodic Markov chain quasi-Monte Carlo
Information visualization Formal Concept Analysis Galois sub-hierarchy
2013/4/27
In [Chen, D., Owen, Ann. Stat., 39, 673--701, 2011] Markov chain Monte Carlo (MCMC) was studied under the assumption that the driver sequence is a deterministic sequence rather than independent U(0,1)...
Uniform error bounds for a continuous approximation of non-negative random variables
gamma distribution Laplace transform phase-type distribution
2010/10/19
In this work, we deal with approximations for distribution functions of non-negative random variables. More specifically, we construct continuous approximants using an acceleration technique over a w...