Ordered classification rules for inverse gaussian populations with unknown parameters. Issue 14 (22nd September 2019)

• Record Type: Journal Article
• Authors: Jana, Nabakumar; Kumar, Somesh
• Is Part Of: Journal of statistical computation and simulation. Volume 89:Issue 14(2019)
• Page Start: 2597
• Page End: 2620
• Publication Date: 2019-09-22
• Subjects: Mixed estimator -- bayes classification rule -- common mean -- coefficient of variation -- likelihood ratio -- probability of correct classification; 62H30 -- 62F30; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5028505
• DOI: 10.1080/00949655.2019.1628233
• Languages: English
• ISSNs: 0094-9655

Abstract

ABSTRACT: Let Π 1, Π 2, …, Π k be k ( ≥ 2 ) populations with Π i having an inverse Gaussian distribution with unknown mean μ i and unknown scale-like parameter λ i, respectively. We study the problem of classification of an observation when prior information suggests some orderings on parameters. When the means are equal but unknown, we derive plug-in Bayes classification rules based on the maximum likelihood estimator (MLE), Graybill-Deal type estimator and shrinkage estimator of the common mean. When all parameters are unknown and unequal, we also derive likelihood ratio-based classification rules. For more than two populations, we suggest ordered rules when λ i s follow an ordering. When the means are unequal, we also derive rules assuming ordering among either λ i s or μ i s. Extensive simulations are carried out to compare the proposed rules with respect to expected probabilities of correct classification. Applications of these classification rules are described using real data sets.