Optimal inference with a multidimensional multiscale statistic

DOI10.1214/21-EJS1914zbMath1493.62037arXiv1806.02194MaRDI QIDQ2074288

Pratyay Datta, Bodhisattva Sen

Publication date: 9 February 2022

Published in: Electronic Journal of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1806.02194

zbMATH Keywords

kernel estimationBrownian sheetHölder classes of functionsasymptotic minimax testingmultivariate continuous white noise modelsignal detection on hyperrectangles

Mathematics Subject Classification ID

Nonparametric regression and quantile regression (62G08) Minimax procedures in statistical decision theory (62C20) Nonparametric inference and fuzziness (62G86)

Uses Software

• HSMUCE

Cites Work

• Exact asymptotics for the scan statistic and fast alternatives
• Multiscale methods for shape constraints in deconvolution: confidence statements for qualitative features
• A martingale approach to scan statistics
• A continuous Gaussian approximation to a nonparametric regression in two dimensions
• Estimation for the distribution of two-dimensional discrete scan statistics
• Optimal detection of multi-sample aligned sparse signals
• Adaptive goodness-of-fit tests based on signed ranks
• Multiscale inference about a density
• Asymptotic equivalence for nonparametric regression with multivariate and random design
• Exact convergence rate for the maximum of standardized Gaussian increments
• Detection of spatial clustering with average likelihood ratio test statistics
• Renormalization exponents and optimal pointwise rates of convergence
• An extension of stochastic integrals in the plane
• Asymptotically minimax hypothesis testing for nonparametric alternatives. I
• Asymptotically minimax hypothesis testing for nonparametric alternatives. II
• Asymptotically minimax hypothesis testing for nonparametric alternatives. III
• Asymptotic equivalence of nonparametric regression and white noise
• Tail probabilities for the null distribution of scanning statistics
• Asymptotically exact nonparametric hypothesis testing in sup-norm and at a fixed point
• Multiscale inference for multivariate deconvolution
• Sharp minimax adaptation over Sobolev ellipsoids in nonparametric testing
• Multiscale inference for a multivariate density with applications to X-ray astronomy
• Multiple window and cluster size scan procedures
• Multiscale testing of qualitative hypotheses
• Nonparametric goodness-of-fit testing under Gaussian models
• Rates of strong uniform consistency for multivariate kernel density estimators. (Vitesse de convergence uniforme presque sûre pour des estimateurs à noyaux de densités multivariées)
• Maxima of partial sums indexed by geometrical structures
• Using the generalized likelihood ratio statistic for sequential detection of a change-point
• Weak convergence and empirical processes. With applications to statistics
• Estimation and detection of functions from anisotropic Sobolev classes
• Multiscale scanning in inverse problems
• Multidimensional multiscale scanning in exponential families: limit theory and statistical consequences
• Optimal and fast detection of spatial clusters with scan statistics
• Detection of an anomalous cluster in a network
• Detection of a sparse submatrix of a high-dimensional noisy matrix
• Minimax goodness-of-fit testing in multivariate nonparametric regression
• Properties of higher criticism under strong dependence
• Optimal detection of a jump in the intensity of a Poisson process or in a density with likelihood ratio statistics
• Variable Window Scan Statistics for Normal Data
• Near-Optimal Detection of Geometric Objects by Fast Multiscale Methods
• Multiple Window Discrete Scan Statistics
• A spatial scan statistic
• An Adaptive, Rate-Optimal Test of a Parametric Mean-Regression Model Against a Nonparametric Alternative
• Multiparameter Processes
• Detection with the scan and the average likelihood ratio
• Heterogeneous Change Point Inference
• Functions of bounded variation, signed measures, and a general Koksma–Hlawka inequality
• Multiscale Change Point Inference

This page was built for publication: Optimal inference with a multidimensional multiscale statistic