The properties of the heteroscedasticity non-consistent variances and heteroscedasticity consistent variances are reviewed. Unlike the related existing results, the following cases are discussed separately: (i) the cases where the explanatory variables are strictly exogenous; and (ii) the cases where the explanatory variables may or may not be strictly exogenous. The latter cases allow weakly dependent explanatory variables such as those generating from an autoregressive process. New results on the original robust variance (denoted by $H{C}_0$) and its variants (denoted by $H{C}_1,$ $H{C}_2,$ $H{C}_3,$ $H{C}_4$ and $H{C}_j$) are derived. In particular, the followings are shown: (i) the ordering of the original robust variance and its variants; (ii) the asymptotic equivalence among different variants of robust variance; and (iii) under quadratic form of heteroscedasticity (with mesokurtic/leptokurtic normalized error) or GARCH(1,1)-error, non-robust variance rejects more often than robust variance. Simulation studies suggest $H{C}_4$ by and large does not over-rejects or mildly under-rejects.

审查了异方差非一致性方差和异方差一致性方差的性质。与现有的相关结果不同，以下情况将单独讨论：（i）解释变量严格外生的情况；（ii）解释变量可能是严格外生的，也可能不是严格外生的。后一种情况允许使用弱相关的解释变量，例如从自回归过程中产生的那些变量。原始鲁棒方差的新结果（表示为$H{C}_0$）及其变体（表示为 $H{C}_{\mathrm{1个}}，$ $H{C}_{\mathrm{2个}}，$ $H{C}_3，$ $H{C}_4$ 和 $H{C}_{Ĵ}$）派生。具体来说，显示以下内容：（i）原始鲁棒方差及其变体的排序；（ii）鲁棒方差的不同变体之间的渐近等价；（iii）在二次方差的异方差性中（具有中速/轻度归一化误差）或GARCH（1,1）-误差，非稳健方差比稳健方差更容易被拒绝。模拟研究表明$H{C}_4$ 总的来说，不会过度拒绝或轻度拒绝。