STAT 4201 Midterm: STAT 421 OSU NonparametricTests
31 Jan 2019
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In chapter 12-13 we discussed tests of hypotheses in a parametric statistics framework: Which assumes that the functional form of the (population) probability distribution of the measurement. X is known, except for a small number of unknown parameter(s), whose value(s) determine the underlying distribution, e. g. , X gamma one or both the parameters are unknown. F is assumed to belong to a family of distributions defined by possible values of the parameter(s) in a defined set. Parameter is the basis for forming hypothesis of interest. As long as the assumption about f is correct, these tests are optimal, in some statistical sense, e. g. , for a fixed level test, n-p lemma gives the most powerful test to detect a false null. The concept called robustness studies the effect of violations of the underlying assumption, and suggests methods of estimation and hypothesis tests that do not require these parametric assumption(s). Estimation - suppose that the measurement x has a symmetric distribution.
