SUBSET-SELECTION WITH ADDITIONAL ORDER INFORMATION

Traditional subset selection procedures were developed without assumin g any order information about the response variable. However, in some applications there is additional, even though incomplete, order inform ation about the treatment effects at increasing treatment levels. One important example is the up-then-down umbrella ordering with an unknow n peak. This type of additional order information is utilized explicit ly in this paper to construct subset selection procedures for several settings studied in the literature where only order restricted tests a re known to exist. This paper also proposes a straightforward algorith m to compute the isotonic regression with respect to umbrella ordering s, which can be used to carry out the proposed procedures. Examples ar e given to illustrate the procedures and algorithm.