New variants of heteroscedasticity consistent covariance matrix estimator for linear regression model in presence of unknown heteroscedasticity and high leverage points

When heteroscedasticity is present, the ordinary least squares (OLS) covariance matrix estimator becomes inconsistent and biased, leading to unreliable inferences about regression coefficients. To address this issue, the literature advocates the use of the tests based on heteroscedasticity consistent covariance matrix estimators (HCCMEs), particularly HC3-based tests, for small sample sizes. However, HC3-based inferences can become overly liberal in the presence of high-leverage points. To overcome these limitations, HC4 and HC5 estimators have been proposed, as they effectively address heteroscedasticity while accounting for high-leverage points. Traditional HCCMEs rely on OLS leverage, which is often less effective in identifying extreme high-influence points due to the swamping effect. To address this limitation and enhance the performance of HCCMEs, we introduce two new variants, HC3h and HC4h, that incorporate potential leverage. Unlike OLS leverage, potential leverage is computed after deleting individual cases, thereby increasing sensitivity to extreme high-leverage points and mitigating the swamping effect. This adjustment improves the robustness of the estimators in the presence of influential observations. Our simulation study evaluates the robustness of standard errors using the null rejection rate as a performance metric. Additionally, we present two illustrative examples using real-world data to assess the finite-sample behavior of these new estimators compared to existing ones.