Project Fact File

Title: Testing after pretest
Category: statistics
Area: Improved Tests
No. of units: 1 or 2 or 4
Supervisor: Shahjahan Khan (Staff Profile)
Description:

The idea of using non-sample prior information in the form of pretesting for improving properties of estimators is applied in the testing regime to achieve better power of the ultimate test. 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 intercept. The impact of the pretest on the performance (power and size) of the ultimate test is studied. Defining unrestricted test (UT), restricted test (RT) and pretest test (PTT) the critical region and power functions are derived. Analytical and graphical comparisons of the three tests are obtained by studying the power functions. 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-pretest based test, the PTT based on pretest performs better and its power function behaves similar to the quadratic risk function of the preliminary test estimator (PTE).

Student: