The use of spearman's footrule in testing for trend when the data are incomplete

Spearman's footrule under progressive censoring

“…Spearman's footrule or its variants, such as the Kendall tau coefficient or Spearman's rank correlation, is often used for testing randomness against a trend alternative; we refer to Alvo and Charbonneau (1997) for a recent account. Typically, in such a case, one uses the statistic D n;k ðrÞ for a specified value of k ð nÞ, and this is known as the incomplete ranking.…”

“…For a treatise on the analysis of partially ranked data with plausible applications we refer to Critchlow (1985). For further work along this line, we may refer to Alvo and Charbonneau (1997) where the Spearman footrule is used in testing for trend when the data are incomplete; other pertinent references are cited there. Because of the affinity of the Spearman footrule to the classical Spearman rank correlation and the Kendall tau measure, their study extends to all these measures as well.…”

“…We consider here a statistic which extends the Spearman footrule to progressively censored schemes, and thereby includes the Alvo and Charbonneau (1997) incomplete ranking model as a special case.…”