7,209 research outputs found
Approximate Bayesian inference in semiparametric copula models
We describe a simple method for making inference on a functional of a
multivariate distribution. The method is based on a copula representation of
the multivariate distribution and it is based on the properties of an
Approximate Bayesian Monte Carlo algorithm, where the proposed values of the
functional of interest are weighed in terms of their empirical likelihood. This
method is particularly useful when the "true" likelihood function associated
with the working model is too costly to evaluate or when the working model is
only partially specified.Comment: 27 pages, 18 figure
Penalized variable selection procedure for Cox models with semiparametric relative risk
We study the Cox models with semiparametric relative risk, which can be
partially linear with one nonparametric component, or multiple additive or
nonadditive nonparametric components. A penalized partial likelihood procedure
is proposed to simultaneously estimate the parameters and select variables for
both the parametric and the nonparametric parts. Two penalties are applied
sequentially. The first penalty, governing the smoothness of the multivariate
nonlinear covariate effect function, provides a smoothing spline ANOVA
framework that is exploited to derive an empirical model selection tool for the
nonparametric part. The second penalty, either the
smoothly-clipped-absolute-deviation (SCAD) penalty or the adaptive LASSO
penalty, achieves variable selection in the parametric part. We show that the
resulting estimator of the parametric part possesses the oracle property, and
that the estimator of the nonparametric part achieves the optimal rate of
convergence. The proposed procedures are shown to work well in simulation
experiments, and then applied to a real data example on sexually transmitted
diseases.Comment: Published in at http://dx.doi.org/10.1214/09-AOS780 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Efficient semiparametric estimation and model selection for multidimensional mixtures
In this paper, we consider nonparametric multidimensional finite mixture
models and we are interested in the semiparametric estimation of the population
weights. Here, the i.i.d. observations are assumed to have at least three
components which are independent given the population. We approximate the
semiparametric model by projecting the conditional distributions on step
functions associated to some partition. Our first main result is that if we
refine the partition slowly enough, the associated sequence of maximum
likelihood estimators of the weights is asymptotically efficient, and the
posterior distribution of the weights, when using a Bayesian procedure,
satisfies a semiparametric Bernstein von Mises theorem. We then propose a
cross-validation like procedure to select the partition in a finite horizon.
Our second main result is that the proposed procedure satisfies an oracle
inequality. Numerical experiments on simulated data illustrate our theoretical
results
Building and using semiparametric tolerance regions for parametric multinomial models
We introduce a semiparametric ``tubular neighborhood'' of a parametric model
in the multinomial setting. It consists of all multinomial distributions lying
in a distance-based neighborhood of the parametric model of interest. Fitting
such a tubular model allows one to use a parametric model while treating it as
an approximation to the true distribution. In this paper, the Kullback--Leibler
distance is used to build the tubular region. Based on this idea one can define
the distance between the true multinomial distribution and the parametric model
to be the index of fit. The paper develops a likelihood ratio test procedure
for testing the magnitude of the index. A semiparametric bootstrap method is
implemented to better approximate the distribution of the LRT statistic. The
approximation permits more accurate construction of a lower confidence limit
for the model fitting index.Comment: Published in at http://dx.doi.org/10.1214/08-AOS603 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Copulas in finance and insurance
Copulas provide a potential useful modeling tool to represent the dependence structure
among variables and to generate joint distributions by combining given marginal
distributions. Simulations play a relevant role in finance and insurance. They are used to
replicate efficient frontiers or extremal values, to price options, to estimate joint risks, and so
on. Using copulas, it is easy to construct and simulate from multivariate distributions based
on almost any choice of marginals and any type of dependence structure. In this paper we
outline recent contributions of statistical modeling using copulas in finance and insurance.
We review issues related to the notion of copulas, copula families, copula-based dynamic and
static dependence structure, copulas and latent factor models and simulation of copulas.
Finally, we outline hot topics in copulas with a special focus on model selection and
goodness-of-fit testing
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