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2 A Foundation for Robust Methods > 2.1 Basic Tools for Judging Robustness - Pg. 23

CHAPTER 2 A Foundation for Robust Methods Measures that characterize a distribution, such as measures of location and scale, are said to be robust if slight changes in a distribution have a relatively small effect on their value. As indicated in Chapter 1, the population mean and standard deviation, µ and , as well as the ¯ sample mean and sample standard deviation, X and s 2 , are not robust. This chapter elaborates on this problem by providing a relatively nontechnical description of some of the tools used to judge the robustness of parameters and estimators. Included are some strategies for identifying measures of location and scale that are robust. The emphasis in this chapter is on finding robust analogs of µ and , but the results and criteria described here are directly relevant to judging estimators as well, as will become evident. This chapter also introduces some technical tools that are of use in various situations. This chapter is more technical than the remainder of the book. When analyzing data, it helps to have some understanding of how robustness issues are addressed, and providing a