On Order Statistics and Some Applications of Combinatorial Methods in Statistics.
PURDUE UNIV LAFAYETTE IND DEPT OF STATISTICS
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The objective of the present report is to present some of the basic results in the theory of order statistics, describe the trend of the work done in certain areas by referring to the landmark papers and indicate some of the recent results. After a brief description of the basic theory Section 2 and the results concerning moments and inequalities Section 3, some important asymptotic results of Gnedenko, Smirnov, Renyi, Berman and Kiefer have been discussed in Section 4. The next two sections deal with some applications of combinatorial methods in the theory of order statistics and fluctation theory. These results are mainly conerned with the applications of the ballot lemma and its generalizations and the use of the equivalence principle. Section 7 gives an outline of some problems in estimation and hypothesis testing. The last section discusses the role of order statistics in the subset selection problems and the algebraic structure involved in identification problems. Author
- Statistics and Probability