Quantile kernel regression is a flexible way to estimate the percentile of a scholar's quality stratified by a measurable characteristic, without imposing inappropriate assumption about functional form or population distribution. Quantile kernel regression is here applied to identifying the one-in-a-hundred economist per age cohort according to the Hirsch index.
The author:"The Hirsch index (Hirsch, 2005) is an often-used measure of life-time achievement. The Hirsch index is the highest number h for which holds that an author has h publications that are cited h times or more. The Hirsch index cannot fall over time and tends to increase. Any ranking based on the Hirsch index thus favours those with a longer career. This is fine for many purposes, but not if the aim is to identify excellent individuals in a cohort, e.g., for hiring scholars (Ellison, 2010). The Hirsch rate (Burrell, 2006 and Liang, 2006) – the Hirsch index over the number of active years – corrects for career length. However, the Hirsch rates assume a linear relationship between Hirsch index and active years. This may be problematic when comparing job candidates of different ages if the relationship is (locally) non-linear. This paper therefore proposes quantile kernel regression (Sheather & Marron, 1990) as a method to find exceptional researchers. Kernel regression does not impose linearity or any other functional form. Quantile regression focuses the analysis on exceptional, rather than average, scholars. The proposed method is applied to a sample of 32,000 economists. For illustration, I am looking for the one-in-a-hundred economists in each age group."....."In this paper, I propose quantile kernel regression as a way of identifying excellent scholars by cohort. Like the crown indicator, the proposed method finds people who stand out – but percentiles have a natural interpretation whereas z-scores do not (unless the distribution is Normal). Like the Hirsch rate, the proposed method distinguished between people of different age – but kernel regression does not impose linearity. I illustrate the proposed method with a large sample of economists. The results appear reasonable, but need to be tested still against data from other disciplines, against alternative assumptions on kernel regression, against alternative non-parametric methods, and against parametric methods for quantile regression. This is deferred to future research."
Figure: Fig. 5. The 99%ile as estimated by the kernel density and as approximated by the Crown index (displayed on left axis) and the number of standard deviations (‘sigma’) between the mean and the 99%ile (displayed on the right axis).
Journal of Informetrics
Volume 7, Issue 4, October 2013, Pages 803–810