An Illustration on the Quantile-Based Calculation of the Standard Error of Equating in Kernel Equating
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Date
2021
Journal Title
Journal ISSN
Volume Title
Publisher
Springer Cham
Abstract
Liou 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.
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Keywords
Standard error of equating, Delta method, Bahadur representation of sample quantiles