Determining the number of components in a factor model from limited noisy data

By Shira Kritchman, Boaz Nadler. 2008

234 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability, Signal Processing

View Paper: https://www.semanticscholar.org/paper/8760441cf09a891eeae345f5a2e797ba351973ae

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Statistics and Probability

In Signal Processing

Citations in the corpus

Asymptotic power of sphericity tests for high-dimensional data (2013, background): “…of recent studies in various applied fields including population and medical genetics [Patterson, Price and Reich (2006)], econometrics [Onatski (2009, 2010)], wireless communication [Bianchi et al. (2011)], chemometrics [Kritchman and Nadler (2008)] and signal processing [Perry and Wolfe (2010)].”
Selecting the number of principal components: estimation of the true rank of a noisy matrix (2014, methodology): “In the context of inference based on the distribution of eigenvalues, Muirhead (1982), Theorem 9.6.2 on page 409, and, more recently, Kritchman and Nadler (2008) have proposed methods for testing essentially the same hypothesis as in this paper.”
Regression on manifolds: Estimation of the exterior derivative (2011, methodology): “PCR cannot be easily extended to have lasso-type regularization.”
Random matrix theory in statistics: A review (2014, methodology): “In addition, Tracy–Widom law for the largest eigenvalue has been extensively used for signal detection (Bianchi et al., 2011; Kritchman and Nadler, 2008; Nadler et al., 2008; Onatski, 2009).”
Non-Parametric Detection of the Number of Signals: Hypothesis Testing and Random Matrix Theory (2009, methodology): “Under the assumption of signals, a simple estimator of the noise level is via maximum likelihood [34] (20) As discussed below, this estimator has a negative bias, which may lead to overestimation of the number of signals, specifically for small sample sizes [23].”
Bi-cross-validation for factor analysis (2015, methodology): “Kritchman and Nadler [33] developed an algorithm based on a sequence of hypothesis tests which are connected with the Roy’s classical largest root test [54] to check for sphericity of a covariance matrix.”