4,705 research outputs found
What does intrinsic mean in statistical estimation?
In this paper we review different meanings of the word intrinsic in statistical estimation, focusing our attention on the use of this word in the analysis of the properties of an estimator.We review the intrinsic versions of the bias and the mean square error and results analogous to the Cram'er-Rao inequality and Rao-Blackwell theorem. Different results related to the Bernoulli and normal distributions are also considered
Long runs under a conditional limit distribution
This paper presents a sharp approximation of the density of long runs of a
random walk conditioned on its end value or by an average of a function of its
summands as their number tends to infinity. In the large deviation range of the
conditioning event it extends the Gibbs conditional principle in the sense that
it provides a description of the distribution of the random walk on long
subsequences. An approximation of the density of the runs is also obtained when
the conditioning event states that the end value of the random walk belongs to
a thin or a thick set with a nonempty interior. The approximations hold either
in probability under the conditional distribution of the random walk, or in
total variation norm between measures. An application of the approximation
scheme to the evaluation of rare event probabilities through importance
sampling is provided. When the conditioning event is in the range of the
central limit theorem, it provides a tool for statistical inference in the
sense that it produces an effective way to implement the Rao-Blackwell theorem
for the improvement of estimators; it also leads to conditional inference
procedures in models with nuisance parameters. An algorithm for the simulation
of such long runs is presented, together with an algorithm determining the
maximal length for which the approximation is valid up to a prescribed
accuracy.Comment: Published in at http://dx.doi.org/10.1214/13-AAP975 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org). arXiv admin note: text
overlap with arXiv:1010.361
Conditional limit laws for goodness-of-fit tests
We study the conditional distribution of goodness of fit statistics of the
Cram\'{e}r--von Mises type given the complete sufficient statistics in testing
for exponential family models. We show that this distribution is close, in
large samples, to that given by parametric bootstrapping, namely, the
unconditional distribution of the statistic under the value of the parameter
given by the maximum likelihood estimate. As part of the proof, we give uniform
Edgeworth expansions of Rao--Blackwell estimates in these models.Comment: Published in at http://dx.doi.org/10.3150/11-BEJ366 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Conditional Estimation in Two-stage Adaptive Designs
We consider conditional estimation in two-stage sample size adjustable
designs and the following bias. More specifically, we consider a design which
permits raising the sample size when interim results look rather promising,
and, which keeps the originally planned sample size when results look very
promising. The estimation procedures reported comprise the unconditional
maximum likelihood, the conditionally unbiased Rao-Blackwell estimator, the
conditional median unbiased estimator, and the conditional maximum likelihood
with and without bias correction. We compare these estimators based on
analytical results and by a simulation study. We show in a real clinical trial
setting how they can be applied
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