Concentration and goodness-of-fit in higher dimensions: (Asymptotically) distribution-free methods

DOI10.1214/aos/1017938922zbMath0961.62041OpenAlexW2000060358MaRDI QIDQ1568266

Wolfgang Polonik

Publication date: 30 January 2001

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

Full work available at URL: https://doi.org/10.1214/aos/1017938922

zbMATH Keywords

diagnostic plotsminimum volume setsempirical process theorygeneralized quantile transformationKolmogoroff-Smirnov test

Mathematics Subject Classification ID

Nonparametric hypothesis testing (62G10) Asymptotic properties of nonparametric inference (62G20) Order statistics; empirical distribution functions (62G30) Graphical methods in statistics (62A09)

Related Items

Densities, spectral densities and modality., Finite population corrections for the Kolmogorov–Smirnov tests, Testing for multivariate volatility functions using minimum volume sets and inverse regression, Asymptotically Distribution-Free Goodness-of-Fit Testing: A Unifying View, Generalized probability--probability plots, Level sets and minimum volume sets of probability density functions., On the asymptotics of trimmed best \(k\)-nets, Goodness-of-fit tests for copulas, Complexity-penalized estimation of minimum volume sets for dependent data, Mass volume curves and anomaly ranking, Bivariate density estimation using BV regularisation, Quantile functions for multivariate analysis: approaches and applications, Local extremes, runs, strings and multiresolution. (With discussion), Generalized quantile processes based on multivariate depth functions, with applications in nonparametric multivariate analysis.

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Martingale Approach in the Theory of Goodness-of-Fit Tests
• Goodness of fit problem and scanning innovation martingales
• Asymptotic behaviour of S-estimates of multivariate location parameters and dispersion matrices
• An innovation approach to goodness-of-fit tests in \(R^ m\)
• A test for goodness-of-fit based on an empirical probability measure
• Sums of functions of nearest neighbor distances, moment bounds, limit theorems and a goodness of fit test
• Uniform convergence of the empirical distribution function over convex sets
• Minimum volume sets and generalized quantile processes
• Granulometric smoothing
• The silhouette, concentration functions and ML-density estimation under order restrictions.
• Measuring mass concentrations and estimating density contour clusters -- An excess mass approach
• Weak convergence and empirical processes. With applications to statistics
• Metric entropy of some classes of sets with differentiable boundaries
• Convergence of stochastic processes