HC4 is a more recent approach that can be superior to HC3. HC3 tends to produce superior results than HC2. HC2 reduces the bias due to points of high leverage. the diagonal elements of the OLS hat matrix, as described in Multiple Regression using Matrices and Multiple Regression Outliers and Influencers), n = samples size and k = number of independent variables. Here, the h i are the leverage values (i.e. Each estimate is again the square root of the elements of the diagonal of the covariance matrix as described above, except that we use a different version of S. We next define four other measures, which are equivalent for large samples, but which can be less biased for smaller samples. These estimates are BLUE ( best linear unbiased estimate), but only for large samples. Heteroskedasticity just means non-constant variance. We call these standard errors heteroskedasticity-consistent (HC) standard errors. Where the elements of S are the squared residuals from the OLS method. The Huber-White robust standard errors are equal to the square root of the elements on the diagional of the covariance matrix. While if the homogeneity of variances assumption is not met then Thus, to calculate the standard error for the regression coefficients when the homogeneity of variance assumption is violated, we need to calculate cov( B) as described above based on the residuals for the usual ordinary least squares calculation.
We should multiply S by n/( n−k−1) but for large n the difference is unimportant. E = 0 and E = 0, means that S is the diagonal matrix whose diagonal elements are. Where S is the covariance matrix of the residuals, which under the assumption that the residuals have mean 0 and are not autocorrelated, i.e. In the Huber-White’s Robust Standard Errors approach, the OLS method is used to calculate the regression coefficients, but the covariance matrix of the coefficient matrix is calculated by Worse yet the standard errors will be biased and inconsistent. In this case, these estimates won’t be the best linear estimates since the variances of these estimates won’t necessarily be the smallest. Even when the homogeneity of variance assumption is violated the ordinary least squares (OLS) method calculates unbiased, consistent estimates of the population regression coefficients.
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