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ABRAM KAGAN - University of Maryland

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” On the Nile Problem by Sir Ronald Fisher”
17 October 2013 from 4:00 PM to 5:00 PM
201 Thomas Bldg.
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The Nile problem by Ronald Fisher may be interpreted as the problem of
making statistical inference for a special curved exponential family when the
minimal sufficient statistic is incomplete. The problem itself and its versions
for general curved expenential families pose a mathematical-statistical challenge:
studying the subalgebras of ancillary statistics within the σ-algebra of the (incomplete)
minimal sufficient statistics and closely related questions of the structure of UMVUEs.

In the talk a new method is presented that proves, in particular, that in
the classical Nile problem no statistic subject to mild natural conditions is
a UMVUE. The method almost solves an old problem of the existence of
UMVUEs. The method is purely statistical (vs. analytical) and works for
any family possessing an ancillary statistic. It complements an analytical
method that uses only the first order ancillarity (and does not require the
existence of ancillary sualgebras) and works for curved exponential families
with polynomial constraints on the parameters covering the Nile problem.
(It is a joint work with Yaakov Malinovsky of UMBC).