Determining the dimension of iterative Hessian transformation

DOI10.1214/009053604000000661zbMath1069.62033arXivmath/0508598OpenAlexW3097997553MaRDI QIDQ2388334

Bing Li, R. Dennis Cook

Publication date: 12 September 2005

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

Full work available at URL: https://arxiv.org/abs/math/0508598

zbMATH Keywords

eigenvaluesdimension reductionconditional meanasymptotic testorder determination

Mathematics Subject Classification ID

Multivariate distribution of statistics (62H10) Nonparametric regression and quantile regression (62G08) Asymptotic distribution theory in statistics (62E20) Asymptotic properties of nonparametric inference (62G20) Nonparametric statistical resampling methods (62G09)

Related Items

Conditional variance estimator for sufficient dimension reduction, On dimension folding of matrix- or array-valued statistical objects, Quantile-slicing estimation for dimension reduction in regression, Model-free envelope dimension selection, On a new hybrid estimator for the central mean space, Metric Learning via Cross-Validation, Predictive power of principal components for single-index model and sufficient dimension reduction, Functional envelope for model-free sufficient dimension reduction, Inference for the Dimension of a Regression Relationship Using Pseudo-Covariates, Estimation of inverse mean: an orthogonal series approach, Sufficient dimension reduction based on an ensemble of minimum average variance estimators, Partial dynamic dimension reduction for conditional mean in regression, Successive direction extraction for estimating the central subspace in a multiple-index regres\-sion, On surrogate dimension reduction for measurement error regression: An invariance law, A sparse eigen-decomposition estimation in semiparametric regression, A Shrinkage Estimation of Central Subspace in Sufficient Dimension Reduction, Estimating multi-index models with response-conditional least squares, Fusing sufficient dimension reduction with neural networks

Uses Software

• ARC

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On almost linearity of low dimensional projections from high dimensional data
• A characterization of spherical distributions
• The asymptotic distribution of singular values with applications to canonical correlations and correspondence analysis
• Dimension reduction for the conditional mean in regressions with categorical predictors
• Regression analysis under link violation
• Dimension reduction for conditional mean in regression
• Asymptotics of graphical projection pursuit
• Estimating the Structural Dimension of Regressions Via Parametric Inverse Regression
• A note On outlier sensitivity of Sliced Inverse Regression
• Estimating Optimal Transformations for Multiple Regression and Correlation
• Principal Hessian Directions Revisited
• Sliced Inverse Regression for Dimension Reduction
• On Principal Hessian Directions for Data Visualization and Dimension Reduction: Another Application of Stein's Lemma
• Determining the Dimensionality in Sliced Inverse Regression
• Reweighting to Achieve Elliptically Contoured Covariates in Regression
• Identifying Regression Outliers and Mixtures Graphically
• Dimension Reduction for the Conditionalkth Moment in Regression
• Tail areas of linear combinations of chi-squares and non-central chi-squares
• Comment