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, τ -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 mmax observations are increased to the same large value such as 4. mmax 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 τ-test are increasedfor one outlier lying between 3σ and 6σ at a rate of 10% and 20% respectively.