ustat_var.ustat_samp_covar.ustat_samp_covar_fast

ustat_var.ustat_samp_covar.ustat_samp_covar_fast(Atmp, Btmp, Ctmp, Dtmp, w=None)

Estimates the sampling covariance between the estimate of \(\operatorname{Cov}(a^A, a^B)\) and the estimates of \(\operatorname{Cov}(a^C, a^D)\). Calling ustat_samp_covar_fast(A,B,C,D) is equivalent to, but often faster than, calling ustat_samp_covar(A,B,C,D). Fundamentally, this function calls vcv_samp_covar_XXXX(), vcv_samp_covar_XXXY(), vcv_samp_covar_XXYY(), and vcv_samp_covar_XYXY().

By setting \(A=B=C=D\), for example, one will simply get the sampling variance of a variance estimate.

Parameters:

• Atmp (array) – J-by-\(\operatorname{max}(T_j)\) array containing data/residuals for outcome A

• Btmp (array) – J-by-\(\operatorname{max}(T_j)\) array containing data/residuals for outcome D

• Ctmp (array) – J-by-\(\operatorname{max}(T_j)\) array containing data/residuals for outcome C

• Dtmp (array) – J-by-\(\operatorname{max}(T_j)\) array containing data/residuals for outcome D

• w (array) – Row-wise/teacher-level weights (optional). If included, must have the same number of elements as rows of A, B, C, and D, and must be 1-dimensional (e.g. one weight per teacher/row).

Returns:

a float representing the sampling covariance \(Cov(Cov(a^A, a^B), Cov(a^C, a^D))\)

Return type:

float