Geometrizing rates of convergence. II

DOI10.1214/aos/1176348114zbMath0754.62028OpenAlexW2070086983MaRDI QIDQ1175379

Richard C. Liu, David L. Donoho

Publication date: 25 June 1992

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aos/1176348114

zbMATH Keywords

Hellinger distancemodulus of continuitymode estimationdensity estimationmonotone likelihood ratioloss functionsrobust nonparametric regressionminimax testscomposite, infinite dimensional hypothesesestimating rate of tail decayestimation of distribution functionalshardest simple two-point testing subproblemnonlinear cases

Mathematics Subject Classification ID

Density estimation (62G07) Nonparametric hypothesis testing (62G10) Asymptotic properties of nonparametric inference (62G20) Nonparametric robustness (62G35)

Related Items

A conversation with Larry Brown, Efficient estimation of functionals of the spectral density of stationary Gaussian fields, An efficient nonparametric estimator for models with nonlinear dependence, Minimax estimation of linear functionals over nonconvex parameter spaces., Obtaining minimax lower bounds: a review, Optimal rate of convergence of monotone empirical Bayes tests for normal means, Nonparametric estimation by convex programming, Minimax estimation of norms of a probability density. I: Lower bounds, Estimation of the global mode of a density: minimaxity, adaptation, and computational complexity, Minimax and adaptive inference in nonparametric function estimation, Optimal rates of convergence for estimating the null density and proportion of nonnull effects in large-scale multiple testing, Identifiability and rates of estimation for scale parameters in location mixture models, Minimax kernels for density estimation with biased data, Scalable Hyperparameter Selection for Latent Dirichlet Allocation, Estimation of Entropy and Mutual Information, Optimal convergence rates for density estimation from grouped data, SEMIPARAMETRIC IDENTIFICATION AND FISHER INFORMATION, On the estimation of a support curve of indeterminate sharpness, Asymptotic optimality in stochastic optimization, Optimal adaptive estimation of a quadratic functional, A two-stage rank test using density estimation, A note on the inverse estimation of band-limited signals, Superefficiency in nonparametric function estimation, Donsker-type theorems for nonparametric maximum likelihood estimators, Nonparametric estimation of multivariate convex-transformed densities, Concentration rate and consistency of the posterior distribution for selected priors under monotonicity constraints, Adaptive confidence bands, Deconvolution from panel data with unknown error distribution, Optimal covariance matrix estimation for high-dimensional noise in high-frequency data, The right complexity measure in locally private estimation: it is not the Fisher information, On robustness and local differential privacy, Methodology for nonparametric bias reduction in kernel regression estimation, Estimating linear and quadratic forms via indirect observations, Adaptive estimation of linear functionals by model selection, Optimal rate of empirical Bayes tests for lower truncation parameters., Geometrizing rates of convergence under local differential privacy constraints, Lower bounds to the accuracy of inference on heavy tails, On semiparametric statistical inferences in the moderate deviation zone, On deconvolution of distribution functions, On local uniformity for estimators and confidence limits, Nonparametric estimation of a class of smooth functions, Hypothesis testing by convex optimization, MAXIMAL UNIFORM CONVERGENCE RATES IN PARAMETRIC ESTIMATION PROBLEMS, Optimal third root asymptotic bounds in the statistical estimation of thresholds, Variance estimation in nonparametric regression via the difference sequence method, A general lower bound of minimax risk for absolute‐error loss, Is Temporal Difference Learning Optimal? An Instance-Dependent Analysis, Multiscale inference for a multivariate density with applications to X-ray astronomy, Model selection for Gaussian regression with random design, An adaptation theory for nonparametric confidence intervals, Testing composite hypotheses, Hermite polynomials and optimal estimation of a nonsmooth functional, Adaptive estimation of linear functionals under different performance measures, Estimating structured high-dimensional covariance and precision matrices: optimal rates and adaptive estimation, Efficient estimation of smooth functionals in Gaussian shift models, Estimating the intensity of a random measure by histogram type estimators, Optimal rates of convergence for sparse covariance matrix estimation, Log-density estimation in linear inverse problems, Selecting local models in multiple regression by maximizing power, Stein 1956: Efficient nonparametric testing and estimation, Estimation of smooth functionals in normal models: bias reduction and asymptotic efficiency, Convergence rates for kernel regression in infinite-dimensional spaces, Minimax quadratic estimation of a quadratic functional, Augmented minimax linear estimation, Information-theoretic determination of minimax rates of convergence, Inference for the mode of a log-concave density, Minimax kernels for nonparametric curve estimation, The nonexistence of confidence sets for discontinuous functionals., Estimation of smooth functionals in high-dimensional models: bootstrap chains and Gaussian approximation, Adaptive estimation of a quadratic functional by model selection., Least squares estimators of the mode of a unimodal regression function, Lucien Le Cam 1924--2000., The statistical work of Lucien Le Cam., Unnamed Item, Rates of convergence of empirical Bayes tests for a normal mean