Sequential elimination: Fast sorts for unbiased quantile estimation

Sequential Elimination (S.E.) is a simple approach, based on standard algorithms, to the sorting of large dimensional arrays for the estimation of quantiles of unknown distributions. Sorting on sub-arrays and eliminating elements outside properly constructed intervals, S.E. is faster than available alternatives and produces unbiased, consistent and efficient estimates. S.E. is used to tabulate critical values for ADF and conditional EG from 10 10 simulations for the testing of unit-roots and no-cointegration, respectively. The new critical values are applied to the testing of the presence of rational bubbles in the U.S. stock market.