Asymptotics Of Extremes And Order Statistics
PROBABILITY FOR STATISTICS AND MACHINE LEARNING: FUNDAMENTALS AND ADVANCED TOPICS(2010)
摘要
We discussed the importance of order statistics and sample percentiles in detail in Chapter 6. The exact distribution theory
of one or several order statistics was presented there. Although closed-form in principle, the expressions are complicated,
except in some special cases, such as the uniform and the exponential. However, once again it turns out that just like sample
means, order statistics and sample percentiles also have a very structured asymptotic distribution theory. We present a selection
of the fundamental results on the asymptotic theory for order statistics and sample percentiles, including the sample extremes.
Principal references for this chapter are David (1980), Galambos (1987), Serfling (1980), Reiss (1989), de Haan (2006), and
DasGupta (2008); other references are given in the sections. First, we recall some notation for convenience.
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