Abstract

In Chap. 2, we used isotonic regression to estimate the order- restricted means. Chapter 3 is devoted to order-restricted inference in a dose-response setting. We formulate the null hypothesis and the ordered alternatives and we discuss the test statistics proposed by Williams (Biometrics 27:103–117, 1971; Biometrics 28:519–531, 1972) and Marcus (Biometrika 63:177–83, 1976); both are “t-test”-type test statistics that can be used to compare each nonzero dose level to the zero dose (i.e., the control) under order constraints. In the last part of the chapter we discuss the likelihood ratio test (Barlow et al., Statistical inference under order restriction. Wiley, New York, 1972; Robertson et al., Order restricted statistical inference. Wiley, New York, 1988).

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.