Increasing reliability of the test for outliers whose magnitude is small

Abstract

The power and level breakdown points measure the global reliability of a test in robust statistics. However, they cannot give enough information about the reliability of a test if outliers are small. Hence, mean success rate (MSR) of a test for outliers (such as data snooping, tau-test) was introduced. But, the MSRs of tests for outliers are small. To increase the MSRs (of tests for outliers, we propose a new repetitive test procedure where the weights of the randomly chosen m observations are increased to the same large value such as 4. m(max) is the number of all possible outliers. The test procedure is repeated for a given number of times and tested on a linear regression by a simulation. One hundred generated samples with random errors distributed normally were chosen. Random and influential outliers are considered in the tail regions and in the whole region of a sample. These outliers are randomly generated 100 times for each simulated sample. Repeating the new test procedure only 20 times, the MSR of data snooping and also the MSR of tau-test are increased for one outlier lying between 3 sigma and 6 sigma at a rate of 10% and 20% respectively.