Restricted Scheffe Method Using Minimal Cone Approach in Multiple Comparisons

• Activity Number: 376
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Yimin Zhang*+ and Melinda McCann
• Companies: Oklahoma State University and Oklahoma State University
• Keywords: simultaneous confidence intervals ; Scheff\'{e} confidence bands

Abstract

Casella and Strawderman (1980) constructed a Scheff\'{e}-type confidence band for multiple regression over a restricted range of the predictor variables, which is also referred to as the restricted Scheff\'{e} method. We propose applying the restricted Scheff\'{e} method to a discrete set of multiple comparisons. This will give a less conservative solution than Scheff\'{e} method and possibly other alternative methods also. A rectangle embedding approach was also introduced by Casella and Strawderman (1980) to find appropriate restricted ranges that practical problem settings can fit into. However, this approach that is intended for continuous regression, suffers from the over-expansion drawback with multiple discrete comparisons. A new minimal cone approach is developed to obtain the optimal restricted range from the coefficients of multiple comparisons. We investigate the restricted Scheff\'{e} method utilizing the minimal cone approach in comparison with many single-step competitors in a variety of multiple comparisons problems.