Adaptive estimation of a quadratic functional by model selection.

From MaRDI portal
Publication:1848826

DOI10.1214/aos/1015957395zbMath1105.62328OpenAlexW1560153690MaRDI QIDQ1848826

Yanyan Li

Publication date: 14 November 2002

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

Full work available at URL: https://doi.org/10.1214/aos/1015957395




Related Items

Greedy Algorithm Almost Dominates in Smoothed Contextual BanditsRandom sections of ellipsoids and the power of random informationPhaselift is robust to a constant fraction of arbitrary errorsRestricted isometry property of principal component pursuit with reduced linear measurementsParticle dual averaging: optimization of mean field neural network with global convergence rate analysis*On the proliferation of support vectors in high dimensions*Goodness-of-fit tests for high-dimensional Gaussian linear modelsModel Selection With Lasso-Zero: Adding Straw to the Haystack to Better Find NeedlesUnnamed ItemUnnamed ItemPerformance of Johnson--Lindenstrauss Transform for $k$-Means and $k$-Medians ClusteringStructural inference from reduced forms with many instrumentsUnnamed ItemExact matrix completion via convex optimizationConvergence rate of Bayesian supervised tensor modeling with multiway shrinkage priorsRegularized estimation in sparse high-dimensional multivariate regression, with application to a DNA methylation studyOn randomized trace estimates for indefinite matrices with an application to determinantsGroup sparse recovery via group square-root elastic net and the iterative multivariate thresholding-based algorithmData assimilation using time-delay nudging in the presence of Gaussian noiseDeep unsupervised feature selection by discarding nuisance and correlated featuresAn Improved Analysis and Unified Perspective on Deterministic and Randomized Low-Rank Matrix ApproximationDebiasing convex regularized estimators and interval estimation in linear modelsAdaptive denoising of signals with local shift-invariant structureThe Lasso with structured design and entropy of (absolute) convex hullsShould we estimate a product of density functions by a product of estimators?Unnamed ItemUnnamed ItemUnnamed ItemOn approximations of the PSD cone by a polynomial number of smaller-sized PSD conesEstimation of high-dimensional change-points under a group sparsity structureSupport union recovery in high-dimensional multivariate regressionAdapting to unknown noise level in sparse deconvolutionDetecting the large entries of a sparse covariance matrix in sub-quadratic timeNear-optimal estimation of simultaneously sparse and low-rank matrices from nested linear measurementsTowards classical hardness of module-LWE: the linear rank caseSemiparametric estimation of the high-dimensional elliptical distributionThe smoothed complexity of Frank-Wolfe methods via conditioning of random matrices and polytopesLikelihood Ratio Tests for a Large Directed Acyclic GraphEigenvector delocalization for non‐Hermitian random matrices and applicationsSingular value perturbation and deep network optimizationSparse quadratic classification rules via linear dimension reductionSparse PCA: optimal rates and adaptive estimationAggregation of affine estimatorsApproximating Spectral Clustering via Sampling: A ReviewRobust Estimators in High-Dimensions Without the Computational IntractabilityTargeted Random Projection for Prediction From High-Dimensional FeaturesThe Lanczos Algorithm Under Few Iterations: Concentration and Location of the OutputNorm and Trace Estimation with Random Rank-one VectorsEigenvectors of Orthogonally Decomposable FunctionsAdaptive quadratic functional estimation of a weighted density by model selectionUnnamed ItemUnnamed ItemFast rate of convergence in high-dimensional linear discriminant analysisOn tight bounds for the LassoClassification Error of the Thresholded Independence RuleModel selection for estimating the non zero components of a Gaussian vectorAdaptive estimation of a quadratic functional of a density by model selectionAdaptive tests of qualitative hypothesesAdaptive nonparametric confidence setsUnnamed ItemUnnamed ItemA new large deviation inequality for U-statistics of order 2Variance-stabilization-based compressive inversion under Poisson or Poisson–Gaussian noise with analytical boundsOptimal Adaptation for Early Stopping in Statistical Inverse ProblemsParseval inequalities and lower bounds for variance-based sensitivity indicesRecursive estimators of integrated squared density derivativesA selective review of group selection in high-dimensional modelsRandomized maximum-contrast selection: subagging for large-scale regressionPrincipal component analysis in the local differential privacy modelAdaptive tests for periodic signal detection with applications to laser vibrometryThe bias of isotonic regressionEffect of Depth and Width on Local Minima in Deep LearningAdaptive Global Testing for Functional Linear ModelsParallelization of a Common Changepoint Detection MethodJohnson-Lindenstrauss lemma for circulant matrices**Tight lower bound of sparse covariance matrix estimation in the local differential privacy modelRate optimal estimation of quadratic functionals in inverse problems with partially unknown operator and application to testing problemsOptimal Estimation of Genetic Relatedness in High-Dimensional Linear ModelsNonparametric screening under conditional strictly convex loss for ultrahigh dimensional sparse dataSpectral Methods for Passive Imaging: Nonasymptotic Performance and RobustnessNonparametric confidence intervals for the integral of a function of an unknown densitySharp Oracle Inequalities for Square Root RegularizationMultidimensional linear functional estimation in sparse Gaussian models and robust estimation of the meanOn the asymptotic variance of the debiased LassoOn Approximating Matrix Norms in Data StreamsProbability Bounds for Polynomial Functions in Random VariablesUnnamed ItemUnnamed ItemFluid heterogeneity detection based on the asymptotic distribution of the time-averaged mean squared displacement in single particle tracking experimentsLocalizing differentially evolving covariance structures via scan statisticsMean-square estimation of nonlinear functionals via Kalman filteringROP: matrix recovery via rank-one projectionsUnnamed ItemUnnamed ItemRobust Width: A Characterization of Uniformly Stable and Robust Compressed SensingNew analysis of manifold embeddings and signal recovery from compressive measurementsCurve registration by nonparametric goodness-of-fit testingRealigning random statesDo semidefinite relaxations solve sparse PCA up to the information limit?Optimal multiple change-point detection for high-dimensional dataOn accuracy of Gaussian approximation in Bayesian semiparametric problemsPath regularity of the Brownian motion and the Brownian sheetA Variable Density Sampling Scheme for Compressive Fourier Transform InterferometryProvable sample-efficient sparse phase retrieval initialized by truncated power methodInteractive versus noninteractive locally differentially private estimation: two elbows for the quadratic functionalSimple adaptive estimation of quadratic functionals in nonparametric IV modelsDimension-free bounds for sums of dependent matrices and operators with heavy-tailed distributionsEarly stopping for statistical inverse problems via truncated SVD estimationOn principal components regression, random projections, and column subsamplingHigh-dimensional analysis of semidefinite relaxations for sparse principal componentsOn estimation of the diagonal elements of a sparse precision matrixAn improved global risk bound in concave regressionOn the optimization landscape of tensor decompositionsMultidimensional two-component Gaussian mixtures detectionAsymptotic normality of quadratic estimatorsEstimating linear functionals of a sparse family of Poisson meansStochastic Airy semigroup through tridiagonal matricesGrouped variable importance with random forests and application to multiple functional data analysisOptimal adaptive estimation of a quadratic functionalOptimal functional supervised classification with separation conditionSimple bounds for recovering low-complexity modelsProbably certifiably correct \(k\)-means clusteringOn change-point estimation under Sobolev sparsityOptimal detection of sparse principal components in high dimensionQuality gain analysis of the weighted recombination evolution strategy on general convex quadratic functionsOptimal variable selection in multi-group sparse discriminant analysisLearning a factor model via regularized PCAAdaptive tests of linear hypotheses by model selectionGaussian measures on the of space of Riemannian metricsRandom design analysis of ridge regressionMultivariate Hadamard self-similarity: testing fractal connectivityBayesian shrinkage towards sharp minimaxityAdaptive covariance matrix estimation through block thresholdingScalable interpretable learning for multi-response error-in-variables regressionPrediction error after model searchWitnessed \(k\)-distanceA variant of the Johnson-Lindenstrauss lemma for circulant matricesTwo are better than one: fundamental parameters of frame coherenceMinimax goodness-of-fit testing in ill-posed inverse problems with partially unknown operatorsEstimating linear and quadratic forms via indirect observationsDetecting curved edges in noisy images in sublinear timeNon asymptotic minimax rates of testing in signal detection with heterogeneous variancesLaplace deconvolution with noisy observationsBayesian fusion estimation via \(t\) shrinkageAdaptive estimation of linear functionals by model selectionSimultaneous estimation of the mean and the variance in heteroscedastic Gaussian regressionSmoothed residual stopping for statistical inverse problems via truncated SVD estimationOn the total variation regularized estimator over a class of tree graphsMinimax optimal procedures for testing the structure of multidimensional functionsHanson-Wright inequality in Hilbert spaces with application to \(K\)-means clustering for non-Euclidean dataAdaptive risk bounds in unimodal regressionOnline estimation of integrated squared density derivativesRisk of estimators for Sobol' sensitivity indices based on metamodelsFinite-sample analysis of \(M\)-estimators using self-concordanceConcave group methods for variable selection and estimation in high-dimensional varying coefficient modelsThe spectral norm of random inner-product kernel matricesThe road to deterministic matrices with the restricted isometry propertySuper-resolution from noisy dataGreedy subspace pursuit for joint sparse recoveryDiscrete uncertainty principles and sparse signal processingLocally adaptive estimation of evolutionary wavelet spectraIsotonic regression meets LassoMaximum pairwise Bayes factors for covariance structure testingA tight degree 4 sum-of-squares lower bound for the Sherrington-Kirkpatrick HamiltonianAdaptive minimax testing for circular convolutionEuclidean distance between Haar orthogonal and Gaussian matricesOptimal bounds for aggregation of affine estimatorsAdaptive estimation of high-dimensional signal-to-noise ratiosOptimal estimation of variance in nonparametric regression with random designMinimax estimation of the integral of a power of a densityData-driven neighborhood selection of a Gaussian fieldDeviation optimal learning using greedy \(Q\)-aggregationA global homogeneity test for high-dimensional linear regressionGreedy variance estimation for the LASSOHigh-dimensional Gaussian model selection on a Gaussian designVariable selection for partially linear models via Bayesian subset modeling with diffusing priorNoise level estimation in high-dimensional linear modelsTesting for high-dimensional network parameters in auto-regressive modelsNon-parametric adaptive estimation of order 1 Sobol indices in stochastic models, with an application to epidemiologyA simple adaptive estimator of the integrated square of a densityNonparametric estimation for i.i.d. Gaussian continuous time moving average modelsEigenvectors of random matrices: A surveyTuning-Free Heterogeneity Pursuit in Massive NetworksEstimating the intensity of a random measure by histogram type estimatorsLearning non-parametric basis independent models from point queries via low-rank methodsTight conditions for consistency of variable selection in the context of high dimensionalityStein 1956: Efficient nonparametric testing and estimationSecond-order Stein: SURE for SURE and other applications in high-dimensional inferenceOptimality of spectral clustering in the Gaussian mixture modelPrediction bounds for higher order total variation regularized least squaresOn the regularization effect of stochastic gradient descent applied to least-squaresEmpirical Bayesian test of the smoothnessGaussian model selection with an unknown varianceAsymptotic analysis for extreme eigenvalues of principal minors of random matricesThe all-or-nothing phenomenon in sparse linear regressionAsymptotic equivalence and adaptive estimation for robust nonparametric regressionConsistency of a range of penalised cost approaches for detecting multiple changepointsTwo-stage algorithm for estimation of nonlinear functions of state vector in linear Gaussian continuous dynamical systemsMarginals of a spherical spin Glass model with correlated disorderOn the robustness of minimum norm interpolators and regularized empirical risk minimizersStabilize deep ResNet with a sharp scaling factor \(\tau\)AdaBoost and robust one-bit compressed sensingOptimal detection of the feature matching map in presence of noise and outliersRandomly initialized EM algorithm for two-component Gaussian mixture achieves near optimality in \(O(\sqrt{n})\) iterationsFunctional convergence of sequential \(U\)-processes with size-dependent kernelsOn two continuum armed bandit problems in high dimensionsNonquadratic estimators of a quadratic functional



Cites Work