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AN ASYMPTOTIC ERROR BOUND FOR TESTING MULTIPLE QUANTUM HYPOTHESES
ASYMPTOTIC ERROR BOUND TESTING MULTIPLE QUANTUM HYPOTHESES
2015/8/25
We consider the problem of detecting the true quantum state among r possible ones, based of measurements performed on n copies of a finitedimensional quantum system. A special case is the problem of d...
Asymptotically Optimal Discrimination between Pure Quantum States
multiple quantum state discrimination generalized quantum Chernoff distance quantum hypothesis testing error exponents
2015/8/25
We consider the decision problem between a finite numberof states of a finite quantum system, when an arbitrarily large number of copies of the system is available for measurements. We provide an uppe...
Exponential error rates in multiple state discrimination on a quantum spin chain
Exponential error rates multiple state discrimination quantum spin chain
2015/8/25
We consider decision problems on finite sets of hypotheses represented by pairwise different shift-invariant states on a quantum spin chain. The decision in favor of one of the hypotheses is based on ...
Asymptotic Equivalence of Spectral Density Estimation and Gaussian White Noise
Stationary Gaussian process spectral density Sobolev classes Le Cam distance asymptotic equivalence Whittle likelihood log-periodogram regression nonparametric Gaussian scale model signal in Gaussian white noise
2015/8/25
We consider the statistical experiment given by a sample y(1), . . . , y(n) of a stationary Gaussian process with an unknown smooth spectral density f. Asymptotic equivalence, in the sense of Le Cam’s...
ASYMPTOTIC EQUIVALENCE OF SPECTRAL DENSITY ESTIMATION AND GAUSSIAN WHITE NOISE
ASYMPTOTIC EQUIVALENCE SPECTRAL DENSITY ESTIMATION GAUSSIAN WHITE NOISE
2015/8/25
We consider the statistical experiment given by a sample y(1), . . . , y(n) of a stationary Gaussian process with an unknown smooth spectral density f . Asymptotic equivalence, in the sense of Le Cam’...
THE CHERNOFF LOWER BOUND FOR SYMMETRIC QUANTUM HYPOTHESIS TESTING
CHERNOFF LOWER BOUND SYMMETRIC QUANTUM HYPOTHESIS TESTING
2015/8/25
We consider symmetric hypothesis testing in quantum statistics, where the hypotheses are density operators on a finite-dimensional complex Hilbert space, representing states of a finite quantum system...
A functional Hungarian construction for the sequential empirical process
functional Hungarian construction sequential empirical process
2015/8/25
We establish a KMT coupling for the sequential empirical process and the KieferMüller process. The processesare indexed by functions f from a Hölder class H, but the supremum over f ∈ H is taken ...
Equivalence Asymptotique des Experiences Statistiques
Equivalence Asymptotique Experiences Statistiques
2015/8/25
The idea of approximating a sequence of statistical experiments by a gaussian family goes back to Wald (1943), but has been fully developed by Lucien Le Cam, who introduced the term "local asymptotic ...
A FUNCTIONAL HUNGARIAN CONSTRUCTION FOR SUMS OF INDEPENDENT RANDOM VARIABLES
Komlos-Major–Tusnády inequality Partial sum process Non-identically distributed variables Function classes Asymptotic equivalence of statistical experiments
2015/8/25
We develop a Hungarian construction for the partial sum process of independent non-identically distributed random variables. The process is indexed by functions f from a class H, but the supremum over...
ASYMPTOTIC EQUIVALENCE FOR NONPARAMETRIC REGRESSION
ASYMPTOTIC EQUIVALENCE NONPARAMETRIC REGRESSION
2015/8/25
We consider a nonparametric model En, generated by independent observations Xi, i = 1, ..., n, with densities p(x, θi), i = 1, ..., n, the parameters of which θi = f(i/n) ∈ Θ are driven by the values ...
ASYMPTOTIC EQUIVALENCE OF ESTIMATING A POISSON INTENSITY AND A POSITIVE DIFFUSION DRIFT
ASYMPTOTIC EQUIVALENCE ESTIMATING A POISSON INTENSITY POSITIVE DIFFUSION DRIFT
2015/8/25
We consider a diffusion model of small variance type with positive drift density varying in a nonparametric set. We investigate Gaussian and Poisson approximations to this model in the sense of asympt...
Asymptotic Error Rates in Quantum Hypothesis Testing
Asymptotic Error Rates Quantum Hypothesis Testing
2015/8/25
We consider the problem of discriminating between two different states of a finite quantum system in the setting of large numbers of copies, and find a closed form expression for the asymptotic expone...
Maximum likelihood estimation of a nonparametric signal in white noise by optimal control
Nonparametric signal in white noise Maximum likelihood Smoothness classes Extremal problems Optimal control Iterative solution
2015/8/25
We study extremal problems related to nonparametric maximum likelihood estimation (MLE) of a signal in white noise.The aim is to reduce these to standard problems of optimal control which can be solve...
Minimax Risk: Pinsker Bound
COMMUNICATION THEORY, STATISTICAL DENSITY ESTIMATION FISHER INFORMATION KERNEL ESTIMATORS LINEAR ESTIMATORS, BAYES LOCAL ASYMPTOTIC NORMALITY METHOD OF SIEVES MINIMAX ESTIMATION NOISE (SIGNAL PROCESSING IN THE PRESENCE OF ) PREDICTION AND FILTERING LINEAR SIEVES, METHOD OF SPECTRAL ANALYSIS SHRINKAGE ESTIMATORS SMOOTHNESS PRIORS SOBOLEV SPACES SPLINE FUNCTIONS STATIONARY PROCESSES STEIN EFFECT
2015/8/25
We give an account of the Pinsker bound describing the exact asymptotics of the minimax risk in a class of nonparametric smoothing problems. The parameter spaces are Sobolev classes or ellipsoids, and...
The Asymptotic Minimax Constant for Sup-Norm Loss in Nonparametric Density Estimation
Density estimation exact constant optimal recovery uniform norm risk white noise
2015/8/25
We develop the exact constant of the risk asymptotics in the uniform norm for density estimation. This constant has first been found for nonparametric regression and for signal estimation in Gaussian ...