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These are also known as heteroskedasticity-robust standard errors (or simply robust standard errors), Eicker–Huber–White standard errors (also Huber–White standard errors or White standard errors), [1] to recognize the contributions of Friedhelm Eicker, [2] Peter J. Huber, [3] and Halbert White.
White test is a statistical test that establishes whether the variance of the errors in a regression model is constant: that is for homoskedasticity. This test, and an estimator for heteroscedasticity-consistent standard errors , were proposed by Halbert White in 1980. [ 1 ]
Correction factor versus sample size n.. When the random variable is normally distributed, a minor correction exists to eliminate the bias.To derive the correction, note that for normally distributed X, Cochran's theorem implies that () / has a chi square distribution with degrees of freedom and thus its square root, / has a chi distribution with degrees of freedom.
The effect of Yates's correction is to prevent overestimation of statistical significance for small data. This formula is chiefly used when at least one cell of the table has an expected count smaller than 5. = = The following is Yates's corrected version of Pearson's chi-squared statistics:
In Julia, the CovarianceMatrices.jl package [11] supports several types of heteroskedasticity and autocorrelation consistent covariance matrix estimation including Newey–West, White, and Arellano. In R , the packages sandwich [ 6 ] and plm [ 12 ] include a function for the Newey–West estimator.
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.
A Reed–Solomon code (like any MDS code) is able to correct twice as many erasures as errors, and any combination of errors and erasures can be corrected as long as the relation 2E + S ≤ n − k is satisfied, where is the number of errors and is the number of erasures in the block.
Although the 30 samples were all simulated under the null, one of the resulting p-values is small enough to produce a false rejection at the typical level 0.05 in the absence of correction. Multiple comparisons arise when a statistical analysis involves multiple simultaneous statistical tests, each of which has a potential to produce a "discovery".
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