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559
Semiparametric minimax rates
- Electronic Journal of Statistics
, 2009
"... Abstract: We consider the minimax rate of testing (or estimation) of nonlinear functionals defined on semiparametric models. Existing methods appear not capable of determining a lower bound on the minimax rate of testing (or estimation) for certain functionals of interest. In particular, if the sem ..."
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Cited by 1 (0 self)
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Abstract: We consider the minimax rate of testing (or estimation) of nonlinear functionals defined on semiparametric models. Existing methods appear not capable of determining a lower bound on the minimax rate of testing (or estimation) for certain functionals of interest. In particular
Information-Theoretic Determination of Minimax Rates of Convergence
- Ann. Stat
, 1997
"... In this paper, we present some general results determining minimax bounds on statistical risk for density estimation based on certain information-theoretic considerations. These bounds depend only on metric entropy conditions and are used to identify the minimax rates of convergence. ..."
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Cited by 151 (24 self)
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In this paper, we present some general results determining minimax bounds on statistical risk for density estimation based on certain information-theoretic considerations. These bounds depend only on metric entropy conditions and are used to identify the minimax rates of convergence.
Permutation estimation and minimax rates of identifiability
, 2013
"... The problem of matching two sets of features appears in various tasks of computer vision and can be often formalized as a problem of permutation estimation. We address this problem from a statistical point of view and provide a theoretical analysis of the accuracy of several natural estimators. To t ..."
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Cited by 1 (1 self)
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. To this end, the notion of the minimax rate of identifiability is introduced and its expression is obtained as a function of the sample size, noise level and dimensionality. We consider the cases of homoscedastic and heteroscedastic noise and carry out, in each case, upper bounds on the identifiability
MINIMAX RATES OF DENSITY ESTIMATORS FOR CONTINUOUS TIME PROCESSES
"... SUMMARY. We show that in density estimation for continuous time processes minimax rates are the same as in the i.i.d. case. 1. ..."
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Cited by 6 (3 self)
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SUMMARY. We show that in density estimation for continuous time processes minimax rates are the same as in the i.i.d. case. 1.
Local Privacy and Statistical Minimax Rates
"... Abstract—Working under local differential privacy—a model of privacy in which data remains private even from the statistician or learner—we study the tradeoff between privacy guarantees and the utility of the resulting statistical estimators. We prove bounds on information-theoretic quantities, incl ..."
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, including mutual information and Kullback-Leibler divergence, that influence estimation rates as a function of the amount of privacy preserved. When combined with minimax techniques such as Le Cam’s and Fano’s methods, these inequalities allow for a precise characterization of statistical rates under local
NEW MINIMAX RATES FOR INVERSE PROBLEMS
"... Abstract: We consider inverse problems where one wishes to recover an unknown function from the observation of a transformation of it by a linear operator, cor-rupted by an additive white noise perturbation. We assume that the operator admits a singular value decomposition where the eigenvalues deca ..."
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decay in a polynomial way, and where Jacobi polynomials appear as eigenfunctions. This includes, as an application, the well known Wicksell’s problem. We determine the asymptotic rate of the minimax risk for this model in a wide framework, considering (Lp)1<p<∞ losses, and Besov-like regularity
Information Theoretic Determination of Minimax Rates of Convergence
- Annals of Statistics
, 1995
"... In this paper, we present some general results determining minimax bounds on statistical risk for density estimation based on certain information-theoretic considerations. These bounds depend only on metric entropy conditions and are used to identify the minimax rates of convergence. ..."
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Cited by 9 (2 self)
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In this paper, we present some general results determining minimax bounds on statistical risk for density estimation based on certain information-theoretic considerations. These bounds depend only on metric entropy conditions and are used to identify the minimax rates of convergence.
Results 1 - 10
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559