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Semiparametric minimax rates

by James Robins , Eric Tchetgen Tchetgen , Lingling Li , Aad Van Der Vaart , James Robins , Eric Tchetgen Tchetgen , Lingling Li , Aad Van Der Vaart - 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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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

by Yuhong Yang, Andrew Barron - 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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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.

Minimax Rates for Homology Inference

by Sivaraman Balakrishnan Aless, Ro Rinaldo Don Sheehy, Aarti Singh, Larry Wasserman, Of Niyogi, Weinberger (henceforth Nsw
"... Our upper bounds mainly generalize those in the work ..."
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Our upper bounds mainly generalize those in the work

Minimax rates of estimation

by Garvesh Raskutti, Martin J. Wainwright, Bin Yu , 2009
"... ar ..."
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Minimax rate of convergence and the performance

by Shahar Mendelson , 2013
"... ar ..."
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Permutation estimation and minimax rates of identifiability

by Olivier Collier, Arnak Dalalyan , 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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. 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

by Denis Bosq
"... 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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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

by Martin J. Wainwright
"... 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

by Thomas Willer
"... 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

by Andrew Barron, Yuhong Yang - 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. ..."
Abstract - Cited by 9 (2 self) - Add to MetaCart
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 of 559