Trends and Perspectives in Linear Statistical Inference by Müjgan Tez & Dietrich von Rosen

Author:Müjgan Tez & Dietrich von Rosen
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

then

and so

Of course,

so that we have obtained the following result:

Theorem 3.2

Under the linear model , where is predictable, the following decomposition holds (with probability 1):

Next, we consider the -sufficiency of for .

Theorem 3.3

The statistic is -sufficient for under if and only if any of the following equivalent conditions holds:(a)

(b)

(c) with probability 1.

(d)There exists at least one representation of of under which is also under the transformed model .

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