HC3 is the finite-sample variant of the heteroskedasticity-consistent covariance estimator proposed by MacKinnon and White (1985). It weights each squared OLS residual by the inverse squared leverage, $\widehat{V}_{HC3}=(X^\top X)^{-1}\left(\sum_i \frac{\hat e_i^2}{(1-h_{ii})^2}\, x_i x_i^\top\right)(X^\top X)^{-1}$, where $h_{ii}$ is the i-th diagonal of the hat matrix $H=X(X^\top X)^{-1}X^\top$. The leverage correction approximates a jackknife variance and inflates the contribution of high-leverage points, yielding better Type I error control than HC0/HC1 in small samples. Long and Ervin (2000) recommend HC3 as the default when $N<250$.