From Eq. (4), the variance of the bias-adjusted estimate is approximately\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${var\left( {\hat \beta _{GY}^\prime } \right) + var\left( {\hat b\hat \beta _{GX}} \right) = \sigma _{GY}^2 + \hat b^2\sigma _{GX}^2 + \hat \beta _{GX}^2var\left( {\hat b} \right) + \sigma _{GX}^2var\left( {\hat b} \right)}$$\end{document}varβ^GY′+varb^β^GX=σGY2+b^2σGX2+β^GX2varb^+σGX2varb^Although there is no theory that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hat \beta _{GY}$$\end{document}β^GY is normally distributed, a normal approximation works well in practice. Further details are provided in the Methods.
