3.4 Let X1, . . . ,Xn be an independent sample from a population with density f(x...
Question:
3.4 Let X1, . . . ,Xn be an independent sample from a population with density f(x − ) and let T(X1. . . . ,Xn) be a translation equivariant estimator of , then Tn has a continuous distribution function.
Hint: T(x1, . . . , xn) = t if and only if x1 = t−T(0, x2−x1, . . . , xn−x1).
Hence, given X2 − X1, . . . ,Xn − X1 = (y2, . . . , yn) and t 2 R, there is exactly one point x for which T(x) = t. Hence, P{T(X) = t|X2 − X1 =
y2, . . . ,Xn − X1 = yn} = 0 for every (y2, . . . , yn) and t, thus P{T(X) =
t} = 0 8t.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Related Book For
Robust Statistical Methods With R
ISBN: 9781032092607
2nd Edition
Authors: Jana Jurecková, Jan Picek, Martin Schindler
Question Posted: