Inferences under a stochastic ordering constraint: The k-sample case

dc.contributor.author	El Barmi, Hammou
dc.contributor.author	Mukerjee, Hari
dc.date.accessioned	2012-06-21T18:04:28Z
dc.date.available	2012-06-21T18:04:28Z
dc.date.issued	2005-03
dc.identifier.citation	Barmi, H. E. and H. Mukerjee (2005). "Inferences under a Stochastic Ordering Constraint: The k-Sample Case." Journal of the American Statistical Association 100(469): 252-261.	en_US
dc.identifier.issn	0162-1459
dc.identifier.issn	1537-274X
dc.identifier.uri	http://hdl.handle.net/10057/5217
dc.identifier.uri	http://dx.doi.org/10.1198/016214504000000764
dc.description	Click on the DOI link below to access this article (may not be free)	en_US
dc.description.abstract	If X1 and X2 are random variables with distribution functions F1 and F2, then X1 is said to be stochastically larger than X2 if F1 ≤ F2. Statistical inferences under stochastic ordering for the two-sample case has a long and rich history. In this article we consider the k-sample case; that is, we have k populations with distribution functions F1,F2, . . .,Fk , k ≥ 2, and we assume that F1 ≤ F2 ≤· · ·≤Fk. For k = 2, the nonparametric maximum likelihood estimators of F1 and F2 under this order restriction have been known for a long time; their asymptotic distributions have been derived only recently. These results have very complicated forms and are hard to deal with when making statistical inferences. We provide simple estimators when k ≥ 2. These are strongly uniformly consistent, and their asymptotic distributions have simple forms. If ˆ Fi and ˆ F ∗ i are the empirical and our restricted estimators of Fi , then we show that, asymptotically, P(\| ˆ F ∗ i (x) − Fi (x)\| ≤ u) ≥ P(\| ˆ Fi (x) − Fi (x)\| ≤ u) for all x and all u > 0, with strict inequality in some cases. This clearly shows a uniform improvement of the restricted estimator over the unrestricted one. We consider simultaneous confidence bands and a test of hypothesis of homogeneity against the stochastic ordering of the k distributions. The results have also been extended to the case of censored observations. Examples of application to real life data are provided.	en_US
dc.language.iso	en_US	en_US
dc.publisher	American Statistical Association	en_US
dc.relation.ispartofseries	Journal of the American Statistical Association;v.100 no.469
dc.subject	Censoring	en_US
dc.title	Inferences under a stochastic ordering constraint: The k-sample case	en_US
dc.type	Article	en_US
dc.description.version	Peer reviewed
dc.rights.holder	Copyright American Statistical Association 2005