{smcl} {* 26oct2005}{...} {cmd:help somersd_mata} {hline} {title:Title} {p 4 4 2} {bf:somersd_mata -- Mata functions used by somersd} {title:Contents} {col 5} {bf:Online} {col 5}{bf:help entry{col 22}Function{col 40}Purpose} {col 5}{hline} {col 5}{bf:{help mf_blncdtree:blncdtree()}}{...} {col 24}{cmd:blncdtree()}{...} {col 44}create balanced binary search tree {col 24}{cmd:_blncdtree()}{...} {col 44}create balanced binary search subtree {col 24}{cmd:tidottree()}{...} {col 44}concordance-discordance difference totals {col 24}{cmd:tidot()}{...} {col 44}concordance-discordance difference totals {col 44}(inefficiently) {col 5}{bf:{help mf_u2jackpseud:_u2jackpseud()}}{...} {col 24}{cmd:_u2jackpseud()}{...} {col 44}jackknife pseudovalues for degree-2 U statistics {col 24}{cmd:_v2jackpseud()}{...} {col 44}jackknife pseudovalues for degree-2 V statistics {col 5}{bf:{help mf_somdtransf:_somdtransf()}}{...} {col 24}{cmd:_somdtransf()}{...} {col 44}transformations used by {help somersd} {col 5}{bf:{help mf_bcsf_bracketing:_bcsf_bracketing()}}{...} {col 24}{cmd:_bcsf_bracketing()}{...} {col 44}bracketing a value of a monotonic bounded step function {col 24}{cmd:_bcsf_bisect()}{...} {col 44}bracket convergence by bisection method {col 24}{cmd:_bcsf_regula()}{...} {col 44}bracket convergence by regula falsi method {col 24}{cmd:_bcsf_ridders()}{...} {col 44}bracket convergence by Ridders' method {col 5}{hline} {title:Description} {p 4 4 2} The functions above are used by {helpb somersd} to calculate jackknife pseudovalues for sample means, Hoeffding U statistics and Von Mises V statistics, and by {helpb censlope} to carry out bracket convergence in the iterative estimation of percentile slopes. The pseudovalues are based on concordance-discordance difference totals, which can be calculated efficiently using balanced binary search trees. The program {helpb somersd} uses these pseudovalues to calculate infinitesimal jackknife confidence intervals for Somers' D or for Kendall's tau-a. {title:Author} {p 4 4 2} Roger Newson, Imperial College London, UK.{break} Email: {browse "mailto:r.newson@imperial.ac.uk":r.newson@imperial.ac.uk} {title:Also see} {p 4 13 2} Online: {helpb mata}, {break} {helpb somersd}, if installed {p_end}