Unbiased Estimators of Ability Parameters, of their Variance, and of their Parallel-Forms Reliability

Given known item parameters, unbiased estimators are derived i) for an examinee's ability parameter θ and for his proportion-correct true score ς, ii) for the variances of θ and ς across examinees in the group tested, and iii) for the parallel-forms reliability of the maximum likelihood estimator \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} $$\hat \theta$$ .