Abstract : The research reported falls under the headings: (a) order statistics; (b) competing risks; (c) nonparametric statistics, and (d) cyclic designs. (a) Concomitants of order statistics were introduced and studied as a class, and applications in selection and double sampling provided. The robustness of various estimators of location and scale in the presence of outliers was examined and the necessary tables prepared. Characterizations of distributions by properties of order statistics were given. A text on order statistics is being revised. (b) A parametric approach to the theory of competing risks was developed and a monograph a competing risks prepared. Applications to reliability under multiple causes of failure are included. (c) A number of problems were resolved in nonparametric estimation and in the asymptotic theory of linear rank statistics, U-statistics, and quantiles. (d) Following earlier work by the author a monograph on cyclic designs was co-authored. This is in a form ready for use, with worked examples provided. (Author)