estderr

Estderr refers to the estimated standard error, a statistic that quantifies the precision or uncertainty of an estimator based on observed data. The standard error is the standard deviation of the estimator’s sampling distribution, and the term “estimated” emphasizes that the value is derived from the sample rather than known a priori.

In practice, estderr is derived from an estimated variance. For a parameter estimate, it is often the square root of an estimated variance, using a model’s variance-covariance structure or a residual variance measure. For example, the estimated standard error of a sample mean is s / sqrt(n), where s is the sample standard deviation and n is the sample size. In regression analysis, the estderr of a coefficient is typically sqrt(MSE × (X'X)^{-1}_{jj}), where MSE is the mean square error from the model and (X'X)^{-1}_{jj} is a diagonal element of the inverse of the design matrix, reflecting how data influence that coefficient.

Estderr can also be obtained through resampling methods such as bootstrap or jackknife, especially when analytic formulas are unavailable or when robust standard errors are desired. Robust standard errors, or heteroskedasticity-consistent estderr, adjust for certain model misspecifications.

Usage and interpretation: estderr is used to form confidence intervals and conduct hypothesis tests. A confidence interval may be constructed as estimate ± (critical value) × estderr. The reliability of estderr depends on model assumptions, sample size, and the method used to estimate the variance; violations can affect accuracy.