Analysis of the forward search using some new results for martingales and empirical processes

DOI10.3150/14-BEJ689zbMath1388.62206arXiv1602.00886MaRDI QIDQ265297

Søren Glud Johansen, Bent Nielsen

Publication date: 1 April 2016

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1602.00886

zbMATH Keywords

forward searchfixed point resultiterated exponential martingale inequalityquantile processweighted and marked empirical process

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Estimation in multivariate analysis (62H12) Linear regression; mixed models (62J05) Robustness and adaptive procedures (parametric inference) (62F35)

Related Items

Asymptotic Analysis of Iterated 1-Step Huber-Skip M-Estimators with Varying Cut-Offs ⋮ Robust methods for heteroskedastic regression ⋮ The forward search interactive outlier detection in cointegrated VAR analysis ⋮ Robust Bayesian regression with the forward search: theory and data analysis ⋮ Introducing Prior Information into the Forward Search for Regression ⋮ How to Marry Robustness and Applied Statistics ⋮ Testing for coefficient distortion due to outliers with an application to the economic impacts of climate change ⋮ BOUNDEDNESS OF M-ESTIMATORS FOR LINEAR REGRESSION IN TIME SERIES ⋮ Wild adaptive trimming for robust estimation and cluster analysis ⋮ Asymptotic Theory of Outlier Detection Algorithms for Linear Time Series Regression Models ⋮ Rejoinder: Asymptotic Theory of Outlier Detection Algorithms for Linear Time Series Regression Models ⋮ The power of monitoring: how to make the most of a contaminated multivariate sample ⋮ Corrigendum to: ``Analysis of the forward search using some new results for martingales and empirical processes ⋮ Heteroscedasticity testing after outlier removal

Uses Software

• R
• ForwardSearch

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Fast calibrations of the forward search for testing multiple outliers in regression
• Exponential inequalities for self-normalized martingales with applications
• Weak convergence of empirical and quantile processes in sup-norm metrics via KMT-constructions
• Weak convergence of randomly weighted dependent residual empiricals with applications to autoregression
• Robust diagnostic regression analysis
• A journey in single steps: robust one-step \(M\)-estimation in linear regression
• On residual empirical processes of stochastic regression models with applications to time series
• Strong consistency and robustness of the forward search estimator of multivariate location and scatter
• Detecting atypical observations in financial data: the forward search for elliptical copulas
• The forward search: theory and data analysis
• Rejoinder: The forward search: theory and data analysis
• Finding an Unknown Number of Multivariate Outliers
• The empirical process of autoregressive residuals
• Least Median of Squares Regression
• Trimmed Least Squares Estimation in the Linear Model
• Influence Functions of Iteratively Reweighted Least Squares Estimators
• On One-Step GM Estimates and Stability of Inferences in Linear Regression
• One-Step Huber Estimates in the Linear Model
• An Asymptotic Expansion for the Tail Area of the t-Distribution
• An Easy Method for Obtaining Percentage Points of Order Statistics
• Fast Very Robust Methods for the Detection of Multiple Outliers
• Inconsistency of Resampling Algorithms for High-Breakdown Regression Estimators and a New Algorithm
• EXPLOITING INFINITE VARIANCE THROUGH DUMMY VARIABLES IN NONSTATIONARY AUTOREGRESSIONS
• A Note on Quantiles in Large Samples
• On Bahadur's Representation of Sample Quantiles
• Some Inequalities on Mill's Ratio and Related Functions
• A Study of R. A. Fisher's $z$ Distribution and the Related F Distribution
• Discussion: The forward search: theory and data analysis