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The paper discusses research which has been completed in the areas of chi-square testing, weak convergence of empirical distribution functions of random variables subject to perturbation and scale factors, selection procedures in two-way lay outs, some aspects of nonparametric inference, Bahadur efficiencies of some tests for uniformity on the circle, rank tests for some linear hypotheses in paired comparison designs, and nonparametric procedures. The work in progress includes nonparametric procedures for exchangeable processes and other classes of stochastic processes, for incomplete block designs, circular data, and multiple regression.