1,808 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
Resampling Procedures with Empirical Beta Copulas
The empirical beta copula is a simple but effective smoother of the empirical
copula. Because it is a genuine copula, from which, moreover, it is
particularly easy to sample, it is reasonable to expect that resampling
procedures based on the empirical beta copula are expedient and accurate. In
this paper, after reviewing the literature on some bootstrap approximations for
the empirical copula process, we first show the asymptotic equivalence of
several bootstrapped processes related to the empirical copula and empirical
beta copula. Then we investigate the finite-sample properties of resampling
schemes based on the empirical (beta) copula by Monte Carlo simulation. More
specifically, we consider interval estimation for some functionals such as rank
correlation coefficients and dependence parameters of several well-known
families of copulas, constructing confidence intervals by several methods and
comparing their accuracy and efficiency. We also compute the actual size and
power of symmetry tests based on several resampling schemes for the empirical
copula and empirical beta copula.Comment: 22 pages, 8 table
Multiple Imputation Using Gaussian Copulas
Missing observations are pervasive throughout empirical research, especially
in the social sciences. Despite multiple approaches to dealing adequately with
missing data, many scholars still fail to address this vital issue. In this
paper, we present a simple-to-use method for generating multiple imputations
using a Gaussian copula. The Gaussian copula for multiple imputation (Hoff,
2007) allows scholars to attain estimation results that have good coverage and
small bias. The use of copulas to model the dependence among variables will
enable researchers to construct valid joint distributions of the data, even
without knowledge of the actual underlying marginal distributions. Multiple
imputations are then generated by drawing observations from the resulting
posterior joint distribution and replacing the missing values. Using simulated
and observational data from published social science research, we compare
imputation via Gaussian copulas with two other widely used imputation methods:
MICE and Amelia II. Our results suggest that the Gaussian copula approach has a
slightly smaller bias, higher coverage rates, and narrower confidence intervals
compared to the other methods. This is especially true when the variables with
missing data are not normally distributed. These results, combined with
theoretical guarantees and ease-of-use suggest that the approach examined
provides an attractive alternative for applied researchers undertaking multiple
imputations
Multiplier bootstrap of tail copulas with applications
For the problem of estimating lower tail and upper tail copulas, we propose
two bootstrap procedures for approximating the distribution of the
corresponding empirical tail copulas. The first method uses a multiplier
bootstrap of the empirical tail copula process and requires estimation of the
partial derivatives of the tail copula. The second method avoids this
estimation problem and uses multipliers in the two-dimensional empirical
distribution function and in the estimates of the marginal distributions. For
both multiplier bootstrap procedures, we prove consistency. For these
investigations, we demonstrate that the common assumption of the existence of
continuous partial derivatives in the the literature on tail copula estimation
is so restrictive, such that the tail copula corresponding to tail independence
is the only tail copula with this property. Moreover, we are able to solve this
problem and prove weak convergence of the empirical tail copula process under
nonrestrictive smoothness assumptions that are satisfied for many commonly used
models. These results are applied in several statistical problems, including
minimum distance estimation and goodness-of-fit testing.Comment: Published in at http://dx.doi.org/10.3150/12-BEJ425 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
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