115,537 research outputs found
On asymptotically optimal tests under loss of identifiability in semiparametric models
We consider tests of hypotheses when the parameters are not identifiable
under the null in semiparametric models, where regularity conditions for
profile likelihood theory fail. Exponential average tests based on integrated
profile likelihood are constructed and shown to be asymptotically optimal under
a weighted average power criterion with respect to a prior on the
nonidentifiable aspect of the model. These results extend existing results for
parametric models, which involve more restrictive assumptions on the form of
the alternative than do our results. Moreover, the proposed tests accommodate
models with infinite dimensional nuisance parameters which either may not be
identifiable or may not be estimable at the usual parametric rate. Examples
include tests of the presence of a change-point in the Cox model with current
status data and tests of regression parameters in odds-rate models with right
censored data. Optimal tests have not previously been studied for these
scenarios. We study the asymptotic distribution of the proposed tests under the
null, fixed contiguous alternatives and random contiguous alternatives. We also
propose a weighted bootstrap procedure for computing the critical values of the
test statistics. The optimal tests perform well in simulation studies, where
they may exhibit improved power over alternative tests.Comment: Published in at http://dx.doi.org/10.1214/08-AOS643 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Deep Random based Key Exchange protocol resisting unlimited MITM
We present a protocol enabling two legitimate partners sharing an initial
secret to mutually authenticate and to exchange an encryption session key. The
opponent is an active Man In The Middle (MITM) with unlimited computation and
storage capacities. The resistance to unlimited MITM is obtained through the
combined use of Deep Random secrecy, formerly introduced and proved as
unconditionally secure against passive opponent for key exchange, and universal
hashing techniques. We prove the resistance to MITM interception attacks, and
show that (i) upon successful completion, the protocol leaks no residual
information about the current value of the shared secret to the opponent, and
(ii) that any unsuccessful completion is detectable by the legitimate partners.
We also discuss implementation techniques.Comment: 14 pages. V2: Updated reminder in the formalism of Deep Random
assumption. arXiv admin note: text overlap with arXiv:1611.01683,
arXiv:1507.0825
The semiparametric Bernstein-von Mises theorem
In a smooth semiparametric estimation problem, the marginal posterior for the
parameter of interest is expected to be asymptotically normal and satisfy
frequentist criteria of optimality if the model is endowed with a suitable
prior. It is shown that, under certain straightforward and interpretable
conditions, the assertion of Le Cam's acclaimed, but strictly parametric,
Bernstein-von Mises theorem [Univ. California Publ. Statist. 1 (1953) 277-329]
holds in the semiparametric situation as well. As a consequence, Bayesian
point-estimators achieve efficiency, for example, in the sense of H\'{a}jek's
convolution theorem [Z. Wahrsch. Verw. Gebiete 14 (1970) 323-330]. The model is
required to satisfy differentiability and metric entropy conditions, while the
nuisance prior must assign nonzero mass to certain Kullback-Leibler
neighborhoods [Ghosal, Ghosh and van der Vaart Ann. Statist. 28 (2000)
500-531]. In addition, the marginal posterior is required to converge at
parametric rate, which appears to be the most stringent condition in examples.
The results are applied to estimation of the linear coefficient in partial
linear regression, with a Gaussian prior on a smoothness class for the
nuisance.Comment: Published in at http://dx.doi.org/10.1214/11-AOS921 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
- …