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- Estimation_of_covariance_matrices abstract "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 normal distribution, the sample covariance matrix has Wishart distribution and a slightly differently scaled version of it is the maximum likelihood estimate. Cases involving missing data require deeper considerations. Another issue is the robustness to outliers: "Sample covariance matrices are extremely sensitive to outliers".Statistical analyses of multivariate data often involve exploratory studies of the way in which the variables change in relation to one another and this may be followed up by explicit statistical models involving the covariance matrix of the variables. Thus the estimation of covariance matrices directly from observational data plays two roles: to provide initial estimates that can be used to study the inter-relationships; to provide sample estimates that can be used for model checking.Estimates of covariance matrices are required at the initial stages of principal component analysis and factor analysis, and are also involved in versions of regression analysis that treat the dependent variables in a data-set, jointly with the independent variable as the outcome of a random sample.".
- Estimation_of_covariance_matrices wikiPageExternalLink index.html.
- Estimation_of_covariance_matrices wikiPageExternalLink covariance.html.
- Estimation_of_covariance_matrices wikiPageID "974723".
- Estimation_of_covariance_matrices wikiPageRevisionID "591231972".
- Estimation_of_covariance_matrices hasPhotoCollection Estimation_of_covariance_matrices.
- Estimation_of_covariance_matrices subject Category:Estimation_for_specific_parameters.
- Estimation_of_covariance_matrices subject Category:Statistical_deviation_and_dispersion.
- Estimation_of_covariance_matrices 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.".
- Estimation_of_covariance_matrices label "Estimation of covariance matrices".
- Estimation_of_covariance_matrices sameAs m.03vtnk.
- Estimation_of_covariance_matrices sameAs Q5401390.
- Estimation_of_covariance_matrices sameAs Q5401390.
- Estimation_of_covariance_matrices wasDerivedFrom Estimation_of_covariance_matrices?oldid=591231972.
- Estimation_of_covariance_matrices isPrimaryTopicOf Estimation_of_covariance_matrices.