caa a22 4500 475762576 CHVBK 20180406123555.0 cr unu---uuuuu 170329e20001201xx s 000 0 eng 10.1023/A:1026519531699 doi (NATIONALLICENCE)springer-10.1023/A:1026519531699 Optimal allocation procedure in ranked set sampling for unimodal and multi-modal distributions [Elektronische Daten] [O¨mer O¨ztu¨rk, Douglas Wolfe] This paper presents a ranked set sample allocation procedure that is optimal for a number of nonparametric test procedures. We define a function that measures the amount of information provided by each observation given the actual joint ranking of all the units in a set. The optimal ranked set sample allocates order statistics by maximizing this information function. This paper shows that the optimal allocation of order statistics in a ranked set sample is determined by the location of the mode(s) of the underlying distribution. For unimodal, symmetric distributions, optimal allocation always quantifies the middle observation(s). If the underlying distribution with cdf F is a multi-modal distribution with modes $$R, \ldots ,R_k $$ , then the optimal allocation procedure quantifies observations at $$mF(R_1 ), \ldots ,mF(R_1 )$$ in a set of size m. We provide similar results for unimodal, asymmetric distributions. We also propose a new sign test which considers the relative positions of the quantified observations from the same cycle in a ranked set sample. The proposed sign test provides improvement in the Pitman efficiency over the ranked set sample sign test of Hettmansperger (1995). It is shown that the information optimal allocation procedure induced by Pitman efficiency is equivalent to the optimal allocation procedure induced by the information criteria. We show that the finite sample distribution of the proposed test based on this optimal design is binomial. Kluwer Academic Publishers, 2000 design nationallicence unequal allocation nationallicence pitman efficiency nationallicence nonparametric testing nationallicence mode nationallicence information nationallicence O¨ztu¨rk O¨mer Department of Statistics, Ohio State University, 1465 Mt. Vernon Ave., 43302-5695, Marion, OH aut Wolfe Douglas Department of Statistics, Ohio State University, 1958 Neil Ave., 43210, Columbus, OH aut Environmental and Ecological Statistics Kluwer Academic Publishers 7/4(2000-12-01), 343-356 1352-8505 7:4<343 2000 7 10651 https://doi.org/10.1023/A:1026519531699 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1026519531699 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- O¨ztu¨rk O¨mer Department of Statistics, Ohio State University, 1465 Mt. Vernon Ave., 43302-5695, Marion, OH aut NATIONALLICENCE 700 1- Wolfe Douglas Department of Statistics, Ohio State University, 1958 Neil Ave., 43210, Columbus, OH aut NATIONALLICENCE 773 0- Environmental and Ecological Statistics Kluwer Academic Publishers 7/4(2000-12-01), 343-356 1352-8505 7:4<343 2000 7 10651 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer