4,749 research outputs found
Multivariate Bernoulli distribution
In this paper, we consider the multivariate Bernoulli distribution as a model
to estimate the structure of graphs with binary nodes. This distribution is
discussed in the framework of the exponential family, and its statistical
properties regarding independence of the nodes are demonstrated. Importantly
the model can estimate not only the main effects and pairwise interactions
among the nodes but also is capable of modeling higher order interactions,
allowing for the existence of complex clique effects. We compare the
multivariate Bernoulli model with existing graphical inference models - the
Ising model and the multivariate Gaussian model, where only the pairwise
interactions are considered. On the other hand, the multivariate Bernoulli
distribution has an interesting property in that independence and
uncorrelatedness of the component random variables are equivalent. Both the
marginal and conditional distributions of a subset of variables in the
multivariate Bernoulli distribution still follow the multivariate Bernoulli
distribution. Furthermore, the multivariate Bernoulli logistic model is
developed under generalized linear model theory by utilizing the canonical link
function in order to include covariate information on the nodes, edges and
cliques. We also consider variable selection techniques such as LASSO in the
logistic model to impose sparsity structure on the graph. Finally, we discuss
extending the smoothing spline ANOVA approach to the multivariate Bernoulli
logistic model to enable estimation of non-linear effects of the predictor
variables.Comment: Published in at http://dx.doi.org/10.3150/12-BEJSP10 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
A sieve M-theorem for bundled parameters in semiparametric models, with application to the efficient estimation in a linear model for censored data
In many semiparametric models that are parameterized by two types of
parameters---a Euclidean parameter of interest and an infinite-dimensional
nuisance parameter---the two parameters are bundled together, that is, the
nuisance parameter is an unknown function that contains the parameter of
interest as part of its argument. For example, in a linear regression model for
censored survival data, the unspecified error distribution function involves
the regression coefficients. Motivated by developing an efficient estimating
method for the regression parameters, we propose a general sieve M-theorem for
bundled parameters and apply the theorem to deriving the asymptotic theory for
the sieve maximum likelihood estimation in the linear regression model for
censored survival data. The numerical implementation of the proposed estimating
method can be achieved through the conventional gradient-based search
algorithms such as the Newton--Raphson algorithm. We show that the proposed
estimator is consistent and asymptotically normal and achieves the
semiparametric efficiency bound. Simulation studies demonstrate that the
proposed method performs well in practical settings and yields more efficient
estimates than existing estimating equation based methods. Illustration with a
real data example is also provided.Comment: Published in at http://dx.doi.org/10.1214/11-AOS934 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Naturalness and a light
Models with a light, additional gauge boson are attractive extensions of the
standard model. Often these models are only considered as effective low energy
theory without any assumption about an UV completion. This leaves not only the
hierarchy problem of the SM unsolved, but introduces a copy of it because of
the new fundamental scalars responsible for breaking the new gauge group. A
possible solution is to embed these models into a supersymmetric framework.
However, this gives rise to an additional source of fine-tuning compared to the
MSSM and poses the question how natural such a setup is. One might expect that
the additional fine-tuning is huge, namely, . In
this paper we point out that this is not necessarily the case. We show that it
is possible to find a focus point behaviour also in the new sector in
co-existence to the MSSM focus point. We call this 'Double Focus Point
Supersymmetry'. Moreover, we stress the need for a proper inclusion of
radiative corrections in the fine-tuning calculation: a tree-level estimate
would lead to predictions for the tuning which can be wrong by many orders of
magnitude. As showcase, we use the extended MSSM and discuss
possible consequence of the observed anomaly. However, similar
features are expected for other models with an extended gauge group which
involve potentially large Yukawa-like interactions of the new scalars.Comment: 11 pages, 4 figures, two column format, reference update
Neutralino Dark Matter in Gauge Mediation After Run I of LHC and LUX
Neutralino can be the dark matter candidate in the gauge-mediated
supersymmetry breaking models if the conformal sequestered mechanism is assumed
in the hidden sector. In this paper, we study this mechanism by using the
current experimental results after the run I of LHC and LUX. By adding new
Yukawa couplings between the messenger fields and Higgs fields, we find that
this mechanism can predict a neutralino dark matter with correct relic density
and a Higgs boson with mass around 125 GeV. All our survived points have some
common features. Firstly, the Higgs sector falls into the decoupling limit. So
the properties of the light Higgs boson are similar to the predictions of the
Standard Model one. Secondly, the correct EWSB hints a relatively small
-term, which makes the lightest neutralino lighter than the lightest stau.
So a bino-higgsino dark matter with correct relic density can be achieved. And
the relatively small -term results in a small fine-tuning. Finally, this
bino-higgsino dark matter can pass all current bounds, including both
spin-independent and spin-dependent direct searches. The spin-independent cross
section of our points can be examined by further experiments.Comment: Minor changes, version to appear in Phys. Lett.
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