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On the structure of undominated statistical experiments: sufficiency, invariance, and optimality in unbiased estimation (extended abstract)

In: Tatra Mountains Mathematical Publications, vol. 26, no. 2
Immanuel M. Bomze
Detaily:
Rok, strany: 2003, 255 - 267
O článku:
There are three different (although equivalent) ways to define the $L$-space $L(E)$ of a statistical experiment $E=(Ω, F, P)$, where $P$ is an (arbitrarily complex) set of probability measures on a measurable space $(Ω, F)$. This $L(E)$ is an ordered Banach lattice substitute of $L1(Q)$ if $Q$ is a probability measure on $(Ω, F)$ equivalent to all considered probabilities $PinP$ of the experiment in case that $E$ (i.e., $P)$ is dominated by a $σ$-finite measure. The (topological) dual $M(E) = [L(E) ]*$ is called $M$-space of $E$, and generalizes the space of all bounded random variables in the experiment. We discuss relations between measure-theoretic properties of $P$ like (weak) domination, and functional-analytic ones of the $L$- and $M$-spaces as (order complete) Banach lattices. It will turn out, that many structural properties which facilitate analysis of sufficiency, invariance and optimality in unbiased estimation carry over from the dominated to the undominated case. This way, following LeCam's decision theoretic approach [L. LeCam: Asymptotic Methods in Statistical Decision Theory, Springer-Verlag, New York, 1986], functional analytic means are employed to avoid involved measure theoretic arguments.
Ako citovať:
ISO 690:
Bomze, I. 2003. On the structure of undominated statistical experiments: sufficiency, invariance, and optimality in unbiased estimation (extended abstract). In Tatra Mountains Mathematical Publications, vol. 26, no.2, pp. 255-267. 1210-3195.

APA:
Bomze, I. (2003). On the structure of undominated statistical experiments: sufficiency, invariance, and optimality in unbiased estimation (extended abstract). Tatra Mountains Mathematical Publications, 26(2), 255-267. 1210-3195.