Restricted Scheffe Method Using Minimal Cone Approach for Multiple Comparisons

• Activity Number: 189
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Yimin Zhang* and Melinda H. McCann
• Companies: Villanova University and Oklahoma State University
• Keywords: Multiple comparisons ; Familywise error rate ; Simultaneous inference ; Scheffe confidence bands

Abstract

Casella and Strawderman (1980) constructed a Scheffe-type confidence band for multiple regression over a restricted range of the predictor variables, the restricted Scheffe method. We propose applying this restricted Scheffe method to a discrete set of multiple comparisons. This proposed method requires minimal assumptions on the distribution of the estimated parameter vector and gives a less conservative solution than Scheffe's method. A rectangle embedding approach was introduced also by Casella and Strawderman (1980) to find appropriate restricted ranges for practical problem settings. However, this approach, which was developed for regression-type problems, encompasses a large excess of comparisons, and consequently causes rather conservative critical values. A new minimal cone approach is developed to address this issue by utilizing the discreteness of the comparisons to obtain the optimal restricted cone-shaped range. In this talk, we will investigate the restricted Scheffe method utilizing the minimal cone approach in comparison with Sidak's method and a hybrid method in a variety of multiple comparisons problems.