 Heteroskedasticity-consistent standard errors

Heteroskedasticity-consistent standard errors use an estimated regression covariance that remains consistent when error variances vary across observations. For ordinary least squares, the basic sandwich estimate is $(X^{T}X{)}^{-1}{X}^T\mathrm{diag}({\hat{\epsilon }}_i^2)X(X^{T}X{)}^{-1}$. The resulting standard errors are square roots of its diagonal entries. This is a regression application of a sandwich covariance matrix.

Heteroskedasticity-consistent standard errors (HCSE) are a type of standard error estimate used in regression analysis when the assumption of homoskedasticity (constant variance of the error terms) is violated. In other words, heteroskedasticity refers to a situation where the variability of the errors varies across levels of an independent variable, which can lead to unreliable standard errors if not addressed.