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Asymptotic Statistics by A.W. van der Vaart

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21

Quantiles and Order Statistics

           In this chapter we derive the asymptotic distribution of estimators of quantiles from the asymptotic distribution of the corresponding estimators of a distribution function. Empirical quantiles are an example, and hence we also discuss some results concerning order statistics. Furthermore, we discuss the asymptotics of the median absolute deviation, which is the empirical 1/2-quantile of the observations centered at their 1/2-quantile.

21.1 Weak Consistency

The quantile function of a cumulative distribution function F is the generalized inverse image given by

It is a left-continuous function with range equal ...

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