Topic
Covariance function
About: Covariance function is a research topic. Over the lifetime, 6364 publications have been published within this topic receiving 223460 citations.
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Book•
14 Sep 1984
TL;DR: In this article, the distribution of the Mean Vector and the Covariance Matrix and the Generalized T2-Statistic is analyzed. But the distribution is not shown to be independent of sets of Variates.
Abstract: Preface to the Third Edition.Preface to the Second Edition.Preface to the First Edition.1. Introduction.2. The Multivariate Normal Distribution.3. Estimation of the Mean Vector and the Covariance Matrix.4. The Distributions and Uses of Sample Correlation Coefficients.5. The Generalized T2-Statistic.6. Classification of Observations.7. The Distribution of the Sample Covariance Matrix and the Sample Generalized Variance.8. Testing the General Linear Hypothesis: Multivariate Analysis of Variance9. Testing Independence of Sets of Variates.10. Testing Hypotheses of Equality of Covariance Matrices and Equality of Mean Vectors and Covariance Matrices.11. Principal Components.12. Cononical Correlations and Cononical Variables.13. The Distributions of Characteristic Roots and Vectors.14. Factor Analysis.15. Pattern of Dependence Graphical Models.Appendix A: Matrix Theory.Appendix B: Tables.References.Index.
9,693 citations
Posted Content•
TL;DR: In this article, a simple method of calculating a heteroskedasticity and autocorrelation consistent covariance matrix that is positive semi-definite by construction is described.
Abstract: This paper describes a simple method of calculating a heteroskedasticity and autocorrelation consistent covariance matrix that is positive semi-definite by construction. It also establishes consistency of the estimated covariance matrix under fairly general conditions.
5,822 citations
TL;DR: Using a coordinate descent procedure for the lasso, a simple algorithm is developed that solves a 1000-node problem in at most a minute and is 30-4000 times faster than competing methods.
Abstract: We consider the problem of estimating sparse graphs by a lasso penalty applied to the inverse covariance matrix. Using a coordinate descent procedure for the lasso, we develop a simple algorithm--the graphical lasso--that is remarkably fast: It solves a 1000-node problem ( approximately 500,000 parameters) in at most a minute and is 30-4000 times faster than competing methods. It also provides a conceptual link between the exact problem and the approximation suggested by Meinshausen and Buhlmann (2006). We illustrate the method on some cell-signaling data from proteomics.
5,577 citations
TL;DR: The authors presented conditions under which a simple extension of common nonparametric covariance matrix estimation techniques yields standard error estimates that are robust to very general forms of spatial and temporal dependence as the time dimension becomes large.
Abstract: Many panel data sets encountered in macroeconomics, international economics, regional science, and finance are characterized by cross-sectional or “spatial” dependence. Standard techniques that fail to account for this dependence will result in inconsistently estimated standard errors. In this paper we present conditions under which a simple extension of common nonparametric covariance matrix estimation techniques yields standard error estimates that are robust to very general forms of spatial and temporal dependence as the time dimension becomes large. We illustrate the relevance of this approach using Monte Carlo simulations and a number of empirical examples.
3,763 citations
TL;DR: This paper introduces an estimator that is both well-conditioned and more accurate than the sample covariance matrix asymptotically, that is distribution-free and has a simple explicit formula that is easy to compute and interpret.
2,497 citations