An Illustration on the Quantile-Based Calculation of the Standard Error of Equating in Kernel Equating

Abstract

AbstractLiou and Cheng (J Educ Behav Stat 20(3):259–286, 1995) discussed large-sample approximations for the standard error of equating (SEE) using the results of Bahadur (Ann Math Stat 37(3):577–580, 1966) and Ghosh (Ann Math Stat 42(6):1957–1961, 1971) on the asymptotic representation of sample quantiles. In this paper we revisit the Bahadur representation of sample quantiles, describe its use for the calculation of the SEE of Kernel equating, and present a comparison with the more traditionally used Delta method.KeywordsStandard error of equatingDelta methodBahadur representation of sample quantiles