We will denote as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\widehat {{\mathrm{Var}}}$$\end{document}Var^ and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\widehat {{\mathrm{Cov}}}$$\end{document}Cov^ the operators that compute the sample variance and covariance, i.e.,: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\widehat {{\mathrm{Var}}}(Y) = \hat \sigma _Y^2 = \mathop {\sum}\nolimits_{i = 1,n} {\left( {Y_i - \bar Y} \right)^2/(n - 1)} $$\end{document}Var^(Y)=σ^Y2= ∑i=1,nYi-Ȳ2∕(n-1) with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\bar Y = \mathop {\sum}\nolimits_{i = 1,n} {Y_i/n} $$\end{document}Ȳ= ∑i=1,nYi∕n. Let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hat \sigma _l^2 = \widehat {{\mathrm{Var}}}(X_l)$$\end{document}σ^l2=Var^(Xl), \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hat \sigma _g^2 = \widehat {{\mathrm{Var}}}\left( {T_g} \right)$$\end{document}σ^g2=Var^Tg and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{\Gamma }}_g = ({\bf{X}} - {\bar{\bf X}})\prime ({\bf{X}} - {\bar{\bf X}})/n$$\end{document}Γg=(X-X¯)′(X-X¯)∕n, where X′ is the p × n matrix of SNP data and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\bar{\mathbf X}}$$\end{document}X¯ is a n × p matrix where column l has the column mean of Xl (p being the number of SNPs in the model for gene g, typically p ≪ n).
