Mathematics
http://hdl.handle.net/2022/13431
Mon, 21 May 2018 19:03:58 GMT2018-05-21T19:03:58ZStatistical inference based on incomplete blocks designs
http://hdl.handle.net/2022/22107
Statistical inference based on incomplete blocks designs
Puri, Madan L.; Shane, Harold D.
In an earlier paper (Shane and Puri, 1969), the authors developed a class of asymptotically nonparametric tests for a bivariate paired comparison model. This paper unifies and complements the results of the previous paper by deriving a class of genuinely distribution free tests for the same problem but under the more general framework of $p(\ge2)$-variate situations. This is done by exploiting the theory of permutation distribution under sign invariant transformations to a class of rank order statistics. Asymptotic properties of these permutation rank order tests are studied and certain stochastic equivalence relationship with a similar class of multisample extensions of the $p$-variate one sample rank order tests proposed by Sen and Puri (1967) are derived. The asymptotic power properties of these tests are also studied.
Publisher's, offprint version
Thu, 01 Jan 1970 00:00:00 GMThttp://hdl.handle.net/2022/221071970-01-01T00:00:00ZOn the Asymptotic Normality of One Sample Rank Order Test Statistics
http://hdl.handle.net/2022/22096
On the Asymptotic Normality of One Sample Rank Order Test Statistics
Puri, Madan L.; Sen, P. K.
The asymptotic normality of a class of one sample rank order test statistics is established. This class includes among other test statistics the well-known normal scores test of symmetry developed by Fraser [2] and the Wilcoxon paired comparison test [8].
Publisher's, offprint version
Wed, 01 Jan 1969 00:00:00 GMThttp://hdl.handle.net/2022/220961969-01-01T00:00:00ZCentering of Signed Rank Statistics with a Continuous Score-Generating Function
http://hdl.handle.net/2022/22095
Centering of Signed Rank Statistics with a Continuous Score-Generating Function
Puri, Madan L.; Ralescu, Stefan S.
For a continuous score generating function, Hájek [2] established the asymptotic normality of a simple linear rank statistic $S_N $ with natural parameters $({\bf E}S_N ,{\operatorname{Var}}S_N )$ as well as $({\bf E}S_N ,\sigma _N^2 )$, where $\sigma _N^2 $ is some constant. The permissibility of replacing ${\bf E}S_N $ by a simpler constant $\mu _N $ was shown by Hoeffding [4] under conditions slightly stronger than Hájek’s. Following Hájek’s methods, Hušková [5] derived the asymptotic normality of a simple signed rank statistic $S_N^ + $ with parameters $({\bf E}S_N^ + ,{\operatorname{Var}}S_N^ + )$ as well as $({\bf E}S_N^2 ,\sigma _N^2 )$ and left open the problem of the replacement of ${\bf E}S_N^ + $ by some simpler constant. In this note we close this problem of the replacement of ${\bf E}S_N^ + $ by a simpler constant $\mu _N^ + $. The solution is a follow-up of Hoeffding [4]. We also provide a slight generalization with regard to the choice of scores.
Publisher's, offprint version
Tue, 01 Jan 1985 00:00:00 GMThttp://hdl.handle.net/2022/220951985-01-01T00:00:00ZThe Order of Normal Approximation for Signed Linear Rank Statistics
http://hdl.handle.net/2022/22094
The Order of Normal Approximation for Signed Linear Rank Statistics
Puri, Madan L.; Wu, Tiee-Jian
The rate of convergence of the cdf (cumulative distribution function) of the signed linear rank statistics to the normal one is investigated. Under suitable assumptions, it is shown that the convergence rate is of order $O(N^{-1/2+\delta})$ for any $\delta > 0$.
Publisher's, offprint version
Thu, 01 Jan 1987 00:00:00 GMThttp://hdl.handle.net/2022/220941987-01-01T00:00:00Z