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In Stata, the command newey produces Newey–West standard errors for coefficients estimated by OLS regression. [13] In MATLAB, the command hac in the Econometrics toolbox produces the Newey–West estimator (among others). [14] In Python, the statsmodels [15] module includes functions for the covariance matrix using Newey–West.
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 ...
Precisely which covariance matrix is of concern is a matter of context. Alternative estimators have been proposed in MacKinnon & White (1985) that correct for unequal variances of regression residuals due to different leverage. [11] Unlike the asymptotic White's estimator, their estimators are unbiased when the data are homoscedastic.
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 R p×p; however, measured using the intrinsic geometry of positive ...
=, where is a lower triangular matrix obtained by a Cholesky decomposition of such that = ′, where is the covariance matrix of the errors Φ i = J A i J ′ , {\displaystyle \Phi _{i}=JA^{i}J',} where J = [ I k 0 … 0 ] , {\displaystyle J={\begin{bmatrix}\mathbf {I} _{k}&0&\dots &0\end{bmatrix}},} so that J {\displaystyle J} is a k ...
The covariance matrix of the parameters can be estimated as ... Stata: "var" EViews: "VAR" ... Variance decomposition;
The covariance matrix (also called second central moment or variance-covariance matrix) of an random vector is an matrix whose (i,j) th element is the covariance between the i th and the j th random variables.
where n is the number of observations and Σ is a (symmetric positive semi-definite) covariance matrix. Suppose we want to estimate the variance of a scalar-valued function h of the estimator B. Keeping only the first two terms of the Taylor series, and using vector notation for the gradient, we can estimate h(B) as