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  2. Covariance matrix - Wikipedia

    en.wikipedia.org/wiki/Covariance_matrix

    Throughout this article, boldfaced unsubscripted and are used to refer to random vectors, and Roman subscripted and are used to refer to scalar random variables.. If the entries in the column vector = (,, …,) are random variables, each with finite variance and expected value, then the covariance matrix is the matrix whose (,) entry is the covariance [1]: 177 ...

  3. Estimation of covariance matrices - Wikipedia

    en.wikipedia.org/wiki/Estimation_of_covariance...

    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 R p×p; however, measured using the intrinsic geometry of positive-definite matrices, the SCM is a biased and inefficient estimator. [1]

  4. Newey–West estimator - Wikipedia

    en.wikipedia.org/wiki/Newey–West_estimator

    In Julia, the CovarianceMatrices.jl package [11] supports several types of heteroskedasticity and autocorrelation consistent covariance matrix estimation including Newey–West, White, and Arellano. In R , the packages sandwich [ 6 ] and plm [ 12 ] include a function for the Newey–West estimator.

  5. Fisher information - Wikipedia

    en.wikipedia.org/wiki/Fisher_information

    The Fisher information matrix is used to calculate the covariance matrices associated with maximum-likelihood estimates. It can also be used in the formulation of test statistics, such as the Wald test. In Bayesian statistics, the Fisher information plays a role in the derivation of non-informative prior distributions according to Jeffreys ...

  6. Reduced chi-squared statistic - Wikipedia

    en.wikipedia.org/wiki/Reduced_chi-squared_statistic

    In weighted least squares, the definition is often written in matrix notation as =, where r is the vector of residuals, and W is the weight matrix, the inverse of the input (diagonal) covariance matrix of observations.

  7. Pearson correlation coefficient - Wikipedia

    en.wikipedia.org/wiki/Pearson_correlation...

    Pearson's correlation coefficient is the covariance of the two variables divided by the product of their standard deviations. The form of the definition involves a "product moment", that is, the mean (the first moment about the origin) of the product of the mean-adjusted random variables; hence the modifier product-moment in the name.

  8. Cross-covariance matrix - Wikipedia

    en.wikipedia.org/wiki/Cross-covariance_matrix

    In probability theory and statistics, a cross-covariance matrix is a matrix whose element in the i, j position is the covariance between the i-th element of a random vector and j-th element of another random vector. When the two random vectors are the same, the cross-covariance matrix is referred to as covariance matrix.

  9. Partial correlation - Wikipedia

    en.wikipedia.org/wiki/Partial_correlation

    Computing this requires , the inverse of the covariance matrix which runs in () time (using the sample covariance matrix to obtain a sample partial correlation). Note that only a single matrix inversion is required to give all the partial correlations between pairs of variables in V {\displaystyle \mathbf {V} } .