About: Estimation of covariance matrices

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In statistics, sometimes the covariance matrix of a multivariate random variable is not known but has to be estimated. Estimation of covariance matrices then deals with the question of how to approximate the actual covariance matrix on the basis of a sample from the multivariate distribution. Simple cases, where observations are complete, can be dealt with by using the sample covariance matrix. The sample covariance matrix (SCM) is an unbiased and efficient estimator of the covariance matrix if the space of covariance matrices is viewed as an extrinsic convex cone in Rp×p; however, measured using the intrinsic geometry of positive-definite matrices, the SCM is a biased and inefficient estimator. In addition, if the random variable has a normal distribution, the sample covariance matrix has

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rdfs:label	Estimation of covariance matrices (en)
rdfs:comment	In statistics, sometimes the covariance matrix of a multivariate random variable is not known but has to be estimated. Estimation of covariance matrices then deals with the question of how to approximate the actual covariance matrix on the basis of a sample from the multivariate distribution. Simple cases, where observations are complete, can be dealt with by using the sample covariance matrix. The sample covariance matrix (SCM) is an unbiased and efficient estimator of the covariance matrix if the space of covariance matrices is viewed as an extrinsic convex cone in Rp×p; however, measured using the intrinsic geometry of positive-definite matrices, the SCM is a biased and inefficient estimator. In addition, if the random variable has a normal distribution, the sample covariance matrix has (en)
dcterms:subject	Statistical deviation and dispersion Estimation methods
Wikipage page ID	974723 (xsd:integer)
Wikipage revision ID	1111500204 (xsd:integer)
Link from a Wikipage to another Wikipage	Sample mean and covariance Sample mean and sample covariance Scalar (mathematics) Trace (matrix) Determinant Statistical deviation and dispersion Joint probability distribution Bessel's correction Bias of an estimator Variance Vector field Vector space James–Stein estimator Python programming language Complex number Covariance Cross-covariance Matrix exponential Estimation theory Estimator Outlier Multivariate normal distribution Multivariate random variable Convex combination Convex cone Cross-validation (statistics) Likelihood function Linear algebra MATLAB Single-index model Singular matrix Statistics Identity matrix Symmetric space Tangent space Wishart distribution Expected value Factor analysis Normal distribution Diagonal matrix Pearson product-moment correlation coefficient Principal component analysis Dependent variable Probability density function First order condition Random variable Regression analysis Riemannian manifold Invertible matrix Covariance matrix Sample mean Estimation methods Efficiency (statistics) Missing data Differential geometry Digamma function Positive-definite matrix Positive-semidefinite matrix Spectral theorem Independent variable Estimator bias Matrix calculus Maximum likelihood Sample (statistics) Exponential map (Lie theory) Robust statistics Propagation of uncertainty Scatter matrix Heteroscedasticity Maximum likelihood estimate R programming language Observed value Riemannian curvature Sample covariance matrix Variance components Statistical independence Bayesian method Biased estimator Missing at random Missing values Matrix logarithm Random vector Wide-sense stationary Precision matrix Unbiased estimator dbr:Intrinsic_bias
Link from a Wikipage to an external page	http://scikit-learn.org/stable/modules/covariance.html
sameAs	Estimation of covariance matrices Estimation of covariance matrices Estimation of covariance matrices Estimation of covariance matrices
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