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Heteroskedasticity-consistent standard errors that differ from classical standard errors may indicate model misspecification. Substituting heteroskedasticity-consistent standard errors does not resolve this misspecification, which may lead to bias in the coefficients. In most situations, the problem should be found and fixed. [5]
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The statistical errors, on the other hand, are independent, and their sum within the random sample is almost surely not zero. One can standardize statistical errors (especially of a normal distribution) in a z-score (or "standard score"), and standardize residuals in a t-statistic, or more generally studentized residuals.
Thus, regression analysis using heteroscedastic data will still provide an unbiased estimate for the relationship between the predictor variable and the outcome, but standard errors and therefore inferences obtained from data analysis are suspect. Biased standard errors lead to biased inference, so results of hypothesis tests are possibly wrong.
A great advantage of bootstrap is its simplicity. It is a straightforward way to derive estimates of standard errors and confidence intervals for complex estimators of the distribution, such as percentile points, proportions, Odds ratio, and correlation coefficients.
Huber-White standard errors assume is diagonal but that the diagonal value varies, while other types of standard errors (e.g. Newey–West, Moulton SEs, Conley spatial SEs) make other restrictions on the form of this matrix to reduce the number of parameters that the practitioner needs to estimate.
Any non-linear differentiable function, (,), of two variables, and , can be expanded as + +. If we take the variance on both sides and use the formula [11] for the variance of a linear combination of variables (+) = + + (,), then we obtain | | + | | +, where is the standard deviation of the function , is the standard deviation of , is the standard deviation of and = is the ...
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