Dependence and the dimensionality reduction principle

DOI10.1007/BF02530545zbMath1056.62054OpenAlexW2067823266MaRDI QIDQ1768126

Yannis G. Yatracos

Publication date: 14 March 2005

Published in: Annals of the Institute of Statistical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02530545

zbMATH Keywords

minimum distance estimationrates of convergenceKolmogorov's entropyprojection pursuitdimensionality reduction\(\varphi\)-mixingadditive and multiplicative regression models

Mathematics Subject Classification ID

Nonparametric regression and quantile regression (62G08) Asymptotic properties of nonparametric inference (62G20)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nonparametric function estimation for time series by local average estimators
• Nonparametric estimates of regression quantiles and their local Bahadur representation
• A regression type problem
• Rates of convergence of minimum distance estimators and Kolmogorov's entropy
• Projection pursuit
• The dimensionality reduction principle for generalized additive models
• Asymptotic methods in statistical decision theory
• Additive regression and other nonparametric models
• A lower bound on the error in nonparametric regression type problems
• On the estimation of the derivatives of a function with the derivatives of an estimate
• Estimation of a projection-pursuit type regression model
• Global nonparametric estimation of conditional quantile functions and their derivatives
• \(L_ 1\)-optimal estimates for a regression type function in \(R^ d\)
• Asymptotics in statistics: some basic concepts
• Nonparametric function estimation involving time series
• Minimum Hellinger distance estimates for parametric models
• The use of polynomial splines and their tensor products in multivariate function estimation. (With discussion)
• Rates of convergence of estimates, Kolmogorov's entropy and the dimensionality reduction principle in regression
• Minimum distance regression-type estimates with rates under weak dependence
• Pathologies of some minimum distance estimators
• The ``automatic robustness of minimum distance functionals
• Optimal global rates of convergence for nonparametric regression
• Convergence of estimates under dimensionality restrictions
• The Minimum Distance Method
• Moment inequalities for mixing sequences of random variables
• Robust estimation via minimum distance methods
• Probability Inequalities for Sums of Bounded Random Variables