Heteroskedastikrobusten

Heteroskedastikrobusten is a term used to describe a set of statistical methods and inference procedures that remain valid when the variance of the regression error terms is not constant across observations. The focus is on making reliable conclusions about model coefficients despite heteroskedasticity.

In ordinary least squares (OLS) regression, coefficient estimates are unbiased and consistent under mild conditions, but the standard errors can be biased when error variance varies. This leads to unreliable hypothesis tests and confidence intervals. Heteroskedastikrobusten methods adjust the estimated covariance matrix of the coefficients to provide robust inference in the presence of non-constant error variance.

Common approaches are heteroskedasticity-robust covariance matrix estimators, also known as robust standard errors (for example White’s or Huberman–White variants, HC0–HC3). These yield t-tests and confidence intervals that remain valid under fairly general forms of heteroskedasticity in large samples. For clustered data, cluster-robust standard errors extend these ideas to account for within-cluster correlation. In time series with autocorrelation, HAC (heteroskedasticity and autocorrelation consistent) estimators such as Newey–West are used. When a specific structure of the variance is known, generalized least squares (GLS) or feasible GLS (FGLS) can improve efficiency over OLS.

Limitations include finite-sample biases and potential inefficiency if the variance structure is misspecified. Robust methods address inference but do not necessarily correct underlying model misspecification. Diagnostic tests for heteroskedasticity, such as the Breusch–Pagan or White tests, are often employed in conjunction with these techniques.

See also: heteroskedasticity, robust standard errors, White’s test, Breusch–Pagan test, sandwich estimator, GLS, HAC.