WhiteStandardfehler

WhiteStandardfehler, in statistics also known as White's robust standard errors, refers to a class of heteroskedasticity-robust estimators of the covariance matrix of regression coefficients. They provide standard errors and test statistics that remain valid under heteroskedasticity, without assuming constant variance of the error term.

The method was introduced by Halbert White in 1980 in Econometrica to allow consistent estimation of the covariance matrix when errors are heteroskedastic. It is commonly used in linear regression and is implemented in many econometrics packages under names such as robust or HC0–HC4.

Computation: In ordinary least squares with design matrix X and residuals e, the robust covariance estimator is Cov_hat(β) = (X'X)^{-1} [ sum_i e_i^2 x_i x_i' ] (X'X)^{-1}, which can be written in a sandwich form with Ω_hat = diag(e_i^2). More general variants (HC1, HC2, HC3) adjust for degrees of freedom or leverage. The square roots of the diagonal elements give WhiteStandardfehler for the regression coefficients.

Usage and limitations: WhiteStandardfehler are preferred when heteroskedasticity is suspected or detected and help to obtain valid hypothesis tests. They do not, however, solve issues caused by autocorrelation or model misspecification; in small samples they may be biased, and finite-sample corrections or alternative estimators (e.g., Newey-West for autocorrelated data) may be necessary.