Statistical Inference for Models with Multivariate t-Distributed Errors

CHAPTER 6

PARALLELISM MODEL

Outline

6.1 Model Specification

6.2 Estimation of the Parameters and Test of Parallelism

6.3 Bias, MSE, and Risk Expressions

6.4 Risk Analysis

6.5 Problems

In this chapter, we discuss the parallelism model in detail, beginning with the estimation of the model parameters and test of hypothesis. In addition, we provide some improved estimators of the parallelism parameters with their dominance properties.

6.1 Model Specification

Consider several laboratories (say, p of them) dealing with similar experiments in the analysis of bioassay data or shelf-life determination of the pharmaceutical products. Generally, the statistical analysis of the data is based on simple linear models with independent normal errors, and the basic problem is the estimation of the intercept and slope parameters of these models and how to combine these results from the concerned laboratories to make improved analysis of the common problem.

In combining the results of several linear models, one may tentatively suspect that the slopes of the linear models may be the same while intercepts are different, yielding to the parallelism models for the analysis and combination of the results from several laboratories. The initial studies of such problems have been initiated by Lambert, Saleh, and Sen (1985); Akritus, Saleh, and Sen (1985); and Saleh and Sen (1985), among others, encompassing normal theory and nonparametric methods. Details of the developments are given in Saleh (2006). Also, ...