Two-sample rank tests with truncated populations

LetX ₁,…,X _m andY ₁,…,Y _n be two independent samples from continuous distributionsF andG respectively. Using a Hoeffding (1951) type theorem, we obtain the distributions of the vector S=(S ₍₁₎,…,S _(n)), whereS _(j)=# (X _i ’s≤Y _(j)) andY _(j) is thej-th order statistic ofY sample, under three truncation models: (a)G is a left truncation ofF orG is a right truncation ofF, (b)F is a right truncation ofH andG is a left truncation ofH, whereH is some continuous distribution function, (c)G is a two tail truncation ofF. Exploiting the relation between S and the vectorR of the ranks of the order statistics of theY-sample in the pooled sample, we can obtain exact distributions of many rank tests. We use these to compare powers of the Hajek test (Hajek 1967), the Sidak Vondracek test (1957) and the Mann-Whitney-Wilcoxon test. We derive some order relations between the values of the probagility-functions under each model. Hence find that the tests based onS ₍₁₎ andS _(n) are the UMP rank tests for the alternative (a). We also find LMP rank tests under the alternatives (b) and (c).     

Estimation in sampling on two successive occasions

For estimating the mean of a finite population on the second of two successive occasions from a simple random sample, the authors [1] have proposedelsewhere an estimate which utilizes the data obtained from the sample on the first occasion as ancillary information. In this paper, it is shown that this estimate is more efficient than the one similar to that of P athak and R ao [2] in all situations where the well known ratio estimate in simple random sampling is no less efficient than the usual regression estimate or the R ao -H artley -C ochran estimate in sampling with varying probabilities and without replacement.     

Tournament incentives and match outcomes in women's professional tennis

Our research examines the effect of prize money differentials in women's professional tennis tournaments on the probability that the favoured player wins the match. This study adds to the existing literature on tournament theory through its focus on Rosen's (1986) elimination-style, match play tournament model. We estimate a standard probit model using a unique data set containing detailed information on prize money, player-specific characteristics, and match play outcomes for all tournaments played during the 2004 tour sponsored by the Women's Tennis Association (WTA). Our results support predictions by Rosen's tournament model. Larger prize money differentials have a positive, statistically significant effect on the favoured player's probability of winning the match. In addition, the number of stages remaining has a significant, negative effect on winning, consistent with tournament theory predictions associated with the number of contestants in a tournament.