![]() ![]() Typically, this estimator would have to be transformed ( e.g., “standardized”) to make it “pivotal” – that is, having a sampling distribution that does not depend on any other unknown parameters. Usually, this would be a statistic that had already been found to be a “good” estimator of the parameter under test. We combine the sample values into a single statistic. ![]() For example, we might use simple random sampling, so that all sample values are mutually independent of each other. Then we take a carefully constructed sample from the population of interest.We call this the “alternative hypothesis”. We also state clearly what situation will prevail if the hypothesis to be tested is not true.We want to test the validity of statement (“null hypothesis”) about a parameter associated with a well-defined underlying population.The whole procedure would have been presented, more or less, along the following lines: It would have just been “statistical hypothesis testing”. It probably wasn’t described to you in so many words. I’m sure that the first exposure that you had to this was actually in terms of “classical”, Neyman-Pearson, testing. When you took your first course in economic statistics, or econometrics, no doubt you encountered some of the basic concepts associated with testing hypotheses. This might seem a bit redundant, but it will help us to see how permutation tests differ from the sort of tests that we usually use in econometrics. Let’s begin with some background discussion to set the scene. Permutation tests, which I’ll be discussing in this post, aren’t that widely used by econometricians. ![]()
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