Search Results - "Johnstone, Iain"

PCA in High Dimensions: An Orientation by Johnstone, Iain M., Paul, Debashis

“…When the data are high dimensional, widely used multivariate statistical methods such as principal component analysis can behave in unexpected ways. In…”
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OPTIMAL SHRINKAGE OF EIGENVALUES IN THE SPIKED COVARIANCE MODEL by Donoho, David, Gavish, Matan, Johnstone, Iain

“…We show that in a common high-dimensional covariance model, the choice of loss function has a profound effect on optimal estimation. In an asymptotic framework…”
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TESTING IN HIGH-DIMENSIONAL SPIKED MODELS by Johnstone, Iain M., Onatski, Alexei

“…We consider the five classes of multivariate statistical problems identified by James (Ann. Math. Stat. 35 (1964) 475–501), which together cover much of…”
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Multivariate Analysis and Jacobi Ensembles: Largest Eigenvalue, Tracy-Widom Limits and Rates of Convergence by Johnstone, Iain M.

“…Let A and B be independent, central Wishart matrices in p variables with common covariance and having m and n degrees of freedom, respectively. The…”
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Statistical challenges of high-dimensional data by Johnstone, Iain M., Titterington, D. Michael

“…Modern applications of statistical theory and methods can involve extremely large datasets, often with huge numbers of measurements on each of a comparatively…”
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On minimax optimality of sparse Bayes predictive density estimates by Mukherjee, Gourab, Johnstone, Iain M.

“…We study predictive density estimation under Kullback–Leibler loss in ℓ0-sparse Gaussian sequence models. We propose proper Bayes predictive density estimates…”
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MINIMAX BOUNDS FOR SPARSE PCA WITH NOISY HIGH-DIMENSIONAL DATA by Birnbaum, Aharon, Johnstone, Iain M., Nadler, Boaz, Paul, Debashis

“…We study the problem of estimating the leading eigenvectors of a high-dimensional population covariance matrix based on independent Gaussian observations. We…”
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On Consistency and Sparsity for Principal Components Analysis in High Dimensions by Johnstone, Iain M., Lu, Arthur Yu

“…Principal components analysis (PCA) is a classic method for the reduction of dimensionality of data in the form of n observations (or cases) of a vector with p…”
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Larry Brown's Work on Admissibility by Johnstone, Iain M.

“…Many papers in the early part of Brown's career focused on the admissibility or otherwise of estimators of a vector parameter. He established that…”
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Tracy–Widom at each edge of real covariance and MANOVA estimators by Fan, Zhou, Johnstone, Iain M.

“…We study the sample covariance matrix for real-valued data with general population covariance, as well as MANOVA-type covariance estimators in variance…”
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EIGENVALUE DISTRIBUTIONS OF VARIANCE COMPONENTS ESTIMATORS IN HIGH-DIMENSIONAL RANDOM EFFECTS MODELS by Fan, Zhou, Johnstone, Iain M.

“…We study the spectra of MANOVA estimators for variance component covariance matrices in multivariate random effects models. When the dimensionality of the…”
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Optimal shrinkage of eigenvalues in the spiked covariance model by Donoho, David, Gavish, Matan, Johnstone, Iain

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ASYMPTOTICS OF EIGENSTRUCTURE OF SAMPLE CORRELATION MATRICES FOR HIGH-DIMENSIONAL SPIKED MODELS by Morales-Jimenez, David, Johnstone, Iain M., McKay, Matthew R., Yang, Jeha

“…Sample correlation matrices are widely used, but for high-dimensional data little is known about their spectral properties beyond “null models”, which assume…”
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On the Distribution of the Largest Eigenvalue in Principal Components Analysis by Johnstone, Iain M.

“…Let x(1)denote the square of the largest singular value of an n × p matrix X, all of whose entries are independent standard Gaussian variates. Equivalently,…”
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Spin Glass to Paramagnetic Transition and Triple Point in Spherical SK Model by Johnstone, Iain M., Klochkov, Yegor, Onatski, Alexei, Pavlyshyn, Damian

“…This paper studies spin glass to paramagnetic transition in the Spherical Sherrington–Kirkpatrick model with ferromagnetic Curie-Weiss interaction with…”
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Accurate Prediction of Phase Transitions in Compressed Sensing via a Connection to Minimax Denoising by Donoho, D. L., Johnstone, I., Montanari, A.

“…Compressed sensing posits that, within limits, one can undersample a sparse signal and yet reconstruct it accurately. Knowing the precise limits to such…”
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Adapting to unknown sparsity by controlling the false discovery rate by Abramovich, Felix, Benjamini, Yoav, Donoho, David L., Johnstone, Iain M.

“…We attempt to recover an n-dimensional vector observed in white noise, where n is large and the vector is known to be sparse, but the degree of sparsity is…”
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Normalization, testing, and false discovery rate estimation for RNA-sequencing data by Li, Jun, Witten, Daniela M, Johnstone, Iain M, Tibshirani, Robert

“…We discuss the identification of genes that are associated with an outcome in RNA sequencing and other sequence-based comparative genomic experiments…”
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Needles and Straw in Haystacks: Empirical Bayes Estimates of Possibly Sparse Sequences by Johnstone, Iain M., Silverman, Bernard W.

“…An empirical Bayes approach to the estimation of possibly sparse sequences observed in Gaussian white noise is set out and investigated. The prior considered…”
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Tail sums of Wishart and Gaussian eigenvalues beyond the bulk edge by Johnstone, Iain M.

“…Summary Consider the classical Gaussian unitary ensemble of size N and the real white Wishart ensemble with N variables and n degrees of freedom. In the limits…”
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