The idea of using non-sample prior information in the form of pre-testing for improving properties of estimators is applied in the testing regime to achieve better power of the ultimate test in this project. For example, to test the intercept of a simple regression model, prior information from previous investigations or expert knowledge on the suspected value of the slope is potentially beneficial. Any uncertainty on the value of the slope is removed by performing a pre-test before testing the significance of the intercept. The impact of the pre-test on the performance (power and size) of the ultimate test will be studied. Defining unrestricted test (UT), restricted test (RT) and pre-test test (PTT) corresponding to the unrestricted (UE), restricted (RE), and preliminary test estimators (PTE) in the estimation case, the critical region and power functions are derived. Analytical and graphical comparisons of the three tests are obtained by studying the power functions with respect to size and power of the tests. It is shown that PTT achieves a reasonable dominance over the others asymptotically. The problem can be addressed for both parametric and non-parametric set ups. Robust procedure based on M-estimator can also be used to formulate a test and deriving its power function. In comparison to the other non-pre-test based test, the PTT based on pre-test performs better and its power function behaves similar to the quadratic risk function of the preliminary test estimator (PTE). Guidelines in choosing appropriate value of nominal sizes of pre-test for appropriate value of size of the PTT subject to the values of the slope can also be investigated in this project.

Professor Shahjahan Khan

• Dr Trevor Langlands

• Centre for Health Sciences Research
• School of Agricultural and Environmental Sciences

• Other Medical and Health Sciences
• Statistics

• Doctor of Philosophy (DPHD)
• Master of Research (MRES)