Asymptotics for high dimensional regression \(M\)-estimates: fixed design results
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Publication:1626624
DOI10.1007/s00440-017-0824-7zbMath1406.62084arXiv1612.06358OpenAlexW2737845155MaRDI QIDQ1626624
Lihua Lei, Noureddine El Karoui, Peter J. Bickel
Publication date: 21 November 2018
Published in: Probability Theory and Related Fields (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1612.06358
robust regressionhigh-dimensional statisticsM-estimationleave-one-out analysissecond order Poincaré inequality
Asymptotic distribution theory in statistics (62E20) Nonparametric robustness (62G35) Linear inference, regression (62J99) Analysis of variance and covariance (ANOVA) (62J10)
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Cites Work
- High dimensional robust M-estimation: asymptotic variance via approximate message passing
- A central limit theorem applicable to robust regression estimators
- High-dimensionality effects in the Markowitz problem and other quadratic programs with linear constraints: risk underestimation
- Limit of the smallest eigenvalue of a large dimensional sample covariance matrix
- Hanson-Wright inequality and sub-Gaussian concentration
- High-dimensional variable selection
- Fluctuations of eigenvalues and second order Poincaré inequalities
- Spectral analysis of large dimensional random matrices
- Concentration of measure and spectra of random matrices: applications to correlation matrices, elliptical distributions and beyond
- Asymptotic behavior of M-estimators of p regression parameters when \(p^ 2/n\) is large. I. Consistency
- On the central limit theorem in \(R^ p\) when p\(\rightarrow \infty\)
- The smallest eigenvalue of a large dimensional Wishart matrix
- Asymptotic behavior of M estimators of p regression parameters when \(p^ 2/n\) is large. II: Normal approximation
- A distribution-free M-estimator of multivariate scatter
- Asymptotics with increasing dimension for robust regression with applications to the bootstrap
- A limit theorem for the norm of random matrices
- Some asymptotic theory for the bootstrap
- A note on an inequality involving the normal distribution
- The strong limits of random matrix spectra for sample matrices of independent elements
- Asymptotic behavior of M-estimators for the linear model
- Robust regression: Asymptotics, conjectures and Monte Carlo
- On the distribution of the largest eigenvalue in principal components analysis
- Inadmissibility of maximum likelihood estimators in some multiple regression problems with three or more independent variables
- Smallest singular value of random matrices and geometry of random polytopes
- On the subspaces of \(L^p\) \((p > 2)\) spanned by sequences of independent random variables
- Fourier analysis of distribution functions. A mathematical study of the Laplace-Gaussian law
- On robust regression with high-dimensional predictors
- Non-asymptotic theory of random matrices: extreme singular values
- Smallest singular value of a random rectangular matrix
- Asymptotic Statistics
- Some estimates of norms of random matrices
- Statistical Tools for Finance and Insurance
- Robust Estimation of a Location Parameter
- DISTRIBUTION OF EIGENVALUES FOR SOME SETS OF RANDOM MATRICES
- A Bound on Tail Probabilities for Quadratic Forms in Independent Random Variables
- A Note on Asymptotic Joint Normality
- The 1972 Wald Lecture Robust Statistics: A Review
- Probability
- Robust Statistics
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