Next, "Although this does result in an unbiased estimator of tau_i, it is clearly useless for all practical purposes. A more sanguine way of putting this would be that the estimator, despite being unbiased, likely has very high variance" (WGB) compared to "But this estimator can have very high variance" (Spiess).

Next, "As an alternative estimator of tau_i, consider [Equation (12)]" (WGB) compared to "We can modify this estimator by regression adjustments y-hat to obtain [Equation (1)]" (Spiess). The equations are again the same, with the adjustment called m-hat in WGB and y-hat in Spiess.I hate that I have repeat it, but again this is standard notation, at least in the statistics literature dealing with TE and talking about regression adjusted treatment effects.

Next, "if m-hat is independent of the i-th participant's treatment assignment - then tau_i-hat is an unbiased estimator of tau" (WGB) compared to "As long as y_i-hat only uses information from x_i and z_-i and not the outcome y_i or treatment assignment d_i, tau_i-hat will still be unbiased" (Spiess).

Next, "The advantage of this estimator is that it will have a low variance as long as m-hat ~= m" (WGB) compared to "Which regression adjustment minimizes variance? Optimally the investigator would set y-hat to (1-p)y_i(1)+py_i(0)" (Spiess). Equation (6) in WGB tells us that m is the same as the object that Spiess is setting y-hat to.What is wrong with you? The notation is standard in the literature. If you don't understand the new theorems the papers prove, then GTFO. Don't come here complaining without understanding the results. If you have proof that his theorems were copied, point it out here and call him out. But this forum enables baseless libel like yours.

This