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Bounds for the Sum of Dependent Risks and Worst Value-at-Risk with Monotone Marginal Densities
Complete mixability Monotone density Sum of dependent risks Value-at- Risk
2016/1/25
In quantitative risk management, it is important and challenging to find sharp bounds for the distribution of the sum of dependent risks with given marginal distributions, but an unspecified dependenc...
Likelihood Bounds for Constrained Estimation with Uncertainty
Likelihood Bounds Constrained Estimation Uncertainty
2015/7/10
This paper addresses the problem of finding bounds on the optimal maximum a posteriori (or maximum likelihood) estimate in a linear model under the presence of model uncertainty. We introduce the nove...
Generalized Chebyshev Bounds via Semidefinite Programming
semidefi nite programming convex optimization duality theory Chebyshev inequalities
2015/7/10
A sharp lower bound on the probability of a set defined by quadratic inequalities, given the first two moments of the distribution, can be efficiently computed using convex optimization. This result g...
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...
Regret Bounds for Reinforcement Learning with Policy Advice
Regret Bounds Reinforcement LearningPolicy Advice
2013/6/13
In some reinforcement learning problems an agent may be provided with a set of input policies, perhaps learned from prior experience or provided by advisors. We present a reinforcement learning with p...
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)...
Bounds on the Maximum Bayes Error Given Moments
the Maximum Bayes Error class-conditional Curto Fialkow’s solutions
2011/6/17
We show how to compute lower bounds for the maximum possible Bayes error if the class-conditional distributions
must satisfy moment constraints. Our approach makes use of Curto and Fialkow’s solution...
Sharper lower bounds on the performance of the empirical risk minimization algorithm
empirical risk minimization learning theory lower bound multidimensional central limit theorem uniform central limit theorem
2011/3/24
We present an argument based on the multidimensional and the uniform central limit theorems, proving that, under some geometrical assumptions between the target function $T$ and the learning class $F$...
Quantitative bounds for Markov chain convergence: Wasserstein and total variation distances
convergence rate coupling Gibbs sampler iterated random functions local
2011/3/24
We present a framework for obtaining explicit bounds on the rate of convergence to equilibrium of a Markov chain on a general state space, with respect to both total variation and Wasserstein distance...
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...
Intrinsic Bounds and False Discovery Rate Control in Multiple Testing Problems
Multiple testing False Discovery Rate Benjamini Hochberg’s procedure power criticality proportion of true null hypotheses
2010/3/11
When testing a large number of independent hypotheses, three different questions are of
interest: are some hypotheses true alternatives? How many of them? Which of them?
These questions give rise to...
Lower bounds for volatility estimation in microstructure noise models
Brownian motion Variance estimation Kullback-Leibler divergence Minimaxrate Microstructure noise
2010/3/10
In this paper we derive lower bounds in minimax sense for estimation of the instantaneous
volatility if the diffusion type part cannot be observed directly but under
some additional Gaussian noise. ...
Lower bounds for the minimax risk using $f$-divergences and applications
Minimax lower bounds f-divergences Fano’sinequality Pinsker’s inequality Reconstruction from supportfunctions
2010/3/10
A new lower bound involving f-divergences between
the underlying probability measures is proved for the minimax
risk in estimation problems. The proof just uses the convexity
of the function f and ...