Analysis of Properties of Robust Estimates

The aim of this thesis is to analyze the properties of robust estimates and to compare these estimates with regard to the properties between them. The analysis of properties depends on the type of a variable (continuous or discrete), its probability distribution, the range of random sample and the proportion of outliers in random sample. Comparing the properties in different situations will give "guidance" to determine which of the estimates is preferable in specific situations, and which of them should be rather avoided. An adjusted bootstrap method is used to obtain the estimates of properties estimates. The thesis is devided into two parts. In the first part, the parameter estimates, type and design of robust estimators and the bootstrap method are monitored. In the second practical part we determine the suitability of bootstrap to obtain estimates of the properties of robust estimators, followed by obtaining estimates of the properties of the estimates and compare them. At the conclusion of the practical part we observe and compare the values of bootstrap confidence intervals on real data on household income. The results of this thesis shows us, that the bootstrap method does not provide good estimates of the properties of robust estimators in all cases. The results also bring us to the conclusion that from a certain extent of random sample regardless of the number of outliers, you can choose from a robust estimate only on the basis of its value, properties of robust estimates are very similar. Contemplated robust estimates of variability are not suitable estimates in most cases