A guided random walk through some high dimensional problems

DOI10.1007/s13171-010-0017-2zbMath1209.62163OpenAlexW2075080801MaRDI QIDQ2431011

Jayanta K. Ghosh, Junyong Park

Publication date: 8 April 2011

Published in: Sankhyā. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13171-010-0017-2

Mathematics Subject Classification ID

Bayesian inference (62F15) Applications of graph theory (05C90) Random matrices (algebraic aspects) (15B52) Empirical decision procedures; empirical Bayes procedures (62C12) Paired and multiple comparisons; multiple testing (62J15)

Related Items

Estimation of empirical null using a mixture of normals and its use in local false discovery rate, Good, great, or lucky? Screening for firms with sustained superior performance using heavy-tailed priors, Higher criticism for large-scale inference, especially for rare and weak effects

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Estimating the proportion of false null hypotheses among a large number of independently tested hypotheses
• Bayes and empirical-Bayes multiplicity adjustment in the variable-selection problem
• Consistency of a recursive estimate of mixing distributions
• Microarrays, empirical Bayes and the two-groups model
• Regularization through variable selection and conditional MLE with application to classification in high dimensions
• A CLT for regularized sample covariance matrices
• Covariance regularization by thresholding
• High-dimensional classification using features annealed independence rules
• Multivariate analysis and Jacobi ensembles: largest eigenvalue, Tracy-Widom limits and rates of convergence
• Flexible covariance estimation in graphical Gaussian models
• Independent rule in classification of multivariate binary data
• Fixed-domain asymptotic properties of tapered maximum likelihood estimators
• Some thoughts on empirical Bayes estimation
• Compound decision theory and empirical Bayes methods
• The positive false discovery rate: A Bayesian interpretation and the \(q\)-value
• Some theory for Fisher's linear discriminant function, `naive Bayes', and some alternatives when there are many more variables than observations
• General empirical Bayes wavelet methods and exactly adaptive minimax estimation
• The control of the false discovery rate in multiple testing under dependency.
• Some results on false discovery rate in stepwise multiple testing procedures.
• Higher criticism for detecting sparse heterogeneous mixtures.
• A stochastic process approach to false discovery control.
• Needles and straw in haystacks: Empirical Bayes estimates of possibly sparse sequences
• Estimation of sums of random variables: examples and information bounds
• An exploration of aspects of Bayesian multiple testing
• Persistence of plug-in rule in classification of high dimensional multivariate binary data
• General maximum likelihood empirical Bayes estimation of normal means
• Nonparametric empirical Bayes and compound decision approaches to estimation of a high-dimensional vector of normal means
• Estimation and confidence sets for sparse normal mixtures
• Adapting to unknown sparsity by controlling the false discovery rate
• Variable Selection in High-Dimensional Multivariate Binary Data with Application to the Analysis of Microbial Community DNA Fingerprints
• Adapting to Unknown Smoothness via Wavelet Shrinkage
• Oracle and Adaptive Compound Decision Rules for False Discovery Rate Control
• Prediction and estimation for the compound Poisson distribution
• Ideal spatial adaptation by wavelet shrinkage
• Strong Control, Conservative Point Estimation and Simultaneous Conservative Consistency of False Discovery Rates: A Unified Approach
• A Direct Approach to False Discovery Rates
• An improved Bonferroni procedure for multiple tests of significance
• Parametric Empirical Bayes Inference: Theory and Applications
• Stein's Estimation Rule and Its Competitors--An Empirical Bayes Approach
• Empirical Bayes Estimates for Large-Scale Prediction Problems
• The Empirical Bayes Approach to Statistical Decision Problems
• Empirical Bayes on vector observations: An extension of Stein's method