Statistics 240 Lecture Notes
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چکیده
So far, we have been concerned with nonparametric tests and procedures: tests and procedures with minimal assumptions about the probability distribution that gives rise to the data. Examples of the kinds of assumptions we have made in various places are that the distribution is continuous, that the observations are iid, that subjects are randomized into treatment and control, etc. We now consider assumptions that are more restrictive, but still less restrictive than the parametric assumptions common to much of statistical theory. In a loose sense, an estimator or test is robust if its performance is good over a neighborhood of distributions including the family in which the truth is modeled to lie. Virtually every real data set has some “gross errors,” which are in some sense corrupted measurements. Data can be transcribed incorrectly, bits can be corrupted in transmission or storage, cosmic rays can hit satellite-borne instruments, power supplies can have surges, operators can miss their morning cups of coffee, etc. Hampel et al. (1986) quote studies that find gross errors comprise
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