Empirical estimation of the power of test in outlier detection problem

Abstract

Classical outlier detection test methods such as Baarda test and Pope test are generally preferred in geodetic problems. They depend on the Least Square Estimation (LSE) and LSE is very sensitive to the variations of the model. The capacity of the LSE changes depending on the different significance level, different type of outlier, the number of outlier, magnitude of outlier, number of observations and the number of unknowns. In statistics, the power of test is the probability of rejecting the null hypothesis when the null hypothesis is false. It is a theoretical assumption and depends on the significance level (Type I error) and (Type II error). The different types of the outliers, such as random or non-random, affect the results of the test methods; but the power of test is the same for all different types of the outliers. In this study, empirical estimation of the power of test is presented as Mean Success Rate (MSR). The theoretical power of test and empirical MSR have been estimated for univariate model and linear model by using Baarda test; according to the obtained results, MSR can be used as empirical value of the power of test and capacity of the test models. Also, MSR reflects more realistic results than the theoretical power of test.