Heteroscedasticity-consistent Standard Errors - White's Heteroscedasticity-consistent Estimator

White's Heteroscedasticity-consistent Estimator

If the regression errors are independent, but have distinct variances σi2, then which can be estimated with . This provides White's (1980) estimator, often referred to as HCE (heteroskedasticity-consistent estimator):

v_{HCE} = (X'X)^{-1} X'\operatorname{diag}(\hat u_1^2, \ldots, \hat u_n^2)X(X'X)^{-1}

The estimator can be derived in terms of the generalized method of moments (GMM).

Alternative estimators have been proposed in MacKinnon & White (1985) that correct for unequal variances of regression residuals due to different leverage. Unlike the asymptotic White's estimator, their estimators are unbiased when the data are homoscedastic.

Read more about this topic:  Heteroscedasticity-consistent Standard Errors

Famous quotes containing the word white:

    ““Hear me,” he said to the white commander. “I am tired. My heart is sick and sad. Our chiefs are dead; the little children are freezing. My people have no blankets, no food. From where the sun stands, I will fight no more forever.””
    —For the State of Montana, U.S. public relief program (1935-1943)