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

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.

Our upper bounds mainly generalize those in the work

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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

SUMMARY. We show that in density estimation for continuous time processes minimax rates are the same as in the i.i.d. case. 1.

, 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

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

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.