6.3 Let X1, . . . ,Xn be a sample from a population with distribution function F(x−), and F symmetric around 0. The -trimmed mean Tn(), defined in Example 3.2 is asymptotically normally distributed,

Let F be a value minimizing 2(, F). It is unknown, provided that F is unknown. The estimation of F (adaptive choice of the trimmed mean)
was considered by Tukey and McLaughlin (1963), Jaeckel (1971), and Hall (1981).

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L{(T(a))}N(0,0 (a,F)) where F-1 (1-a) 2(a,F)= == r2dF(x)+2a(F-1(1) (1-2a) -1(a)