In this talk, Prof. Puri will introduce a broad class of statistics which includes as special cases, the unsigned simple linear rank statistic, signed rank statistic, linear combination of functions of order statistics, linear functions of the concomitants of order statistics and rank combinatorial statistic, among possibly others. For this class, (i) asymptotic normality is established, (ii) the rates of convergence to normality are derived, and (iii) large deviation probabilities are investigated. The results obtained supersede all the results obtained thus far in this direction.