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(9.143) Here the summation is to be performed over the complex exponentials only. Thus, by using (9.144) we achieve
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Event photography covers a huge range of subjects and photographic opportunities. Everything from a birthday party to a parade falls under the umbrella of event photography. Some types of speci c events, like weddings and concerts, are covered in other sections of this chapter, but the basic idea remains the same. The photos from the event need to tell a story or have a unifying theme. Each photo should be able to stand on its own merits and tell a story or evoke a feeling relating to that type of event.
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The motivation behind our claim is the following basic resistance requirement. Take a linear statistic of the form (1.10) and make a small change in the sample, that is, make either small changes in all of the observations z, (rounding, grouping) or large changes in a few of them (gross errors, blunders). If $ is bounded and continuous, then this will result in a small change of T(F,) = j $ dF,. But if $ is not bounded, then a single, strategically placed gross error can completely upset T(F,). If 4 is not continuous, and if F, happens to put mass onto discontinuity points, then small changes in many of the z, may produce a large change in T(F,). We conclude from this that our vague, intuitive notion of resistance or robustness should be made precise as follows: a linear functional T is robust everywhere if and only if (iff) the corresponding .Ic, is bounded and continuous, that is, iff T is weakly continuous. We could take this last property as our definition and call a (not necessarily linear) statistical functional T robust if it is weakly continuous. But, following Hampel (1971), we prefer to adopt a slightly more general definition. Let the observations 2, be independent identically distributed, with common distribution F , and let (T,) be a sequence of estimates or test statistics T, = T,(zl.. . . . IC,). Then this sequence is called robust at F = FOif the sequence of maps of distributions F CF(G), (1.17)
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If F is continuous and strictly monotone, the two formulas (3.65) and (3.66) are equivalent. For discontinuous distributions, for instance if we insert the empirical distributions F, and Gn corresponding to the x-and y-samples, the exact equivalence is destroyed. Moreover, (3.65) is no longer well defined (its value depends on the arbitrary convention about the value of H = LF i G at its jump points). If we standardize H ( z ) = i H ( z - 0) Z H ( x 0), then (3.65) combined with 1 the scores (3.63) gives (3.61). In any case, (3.66) with (3.64) gives (3.61); we assume that there are no ties between z- and y-values. To fix the ideas, from now on we work with (3.66) and (3.64). We also assume once and for all that
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CHAPTER 3. THE BASIC TYPES OF ESTIMATES
To use the Add To New Folder tool, right-click a component or mate (or selection of components or mates) and select Add To New Folder from the menu. This moves the component or mate into the folder. Folders do not affect the assembly in any functional way; they are simply for organization, to speed browsing and selection.
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