4,801 research outputs found
Reliable inference for complex models by discriminative composite likelihood estimation
Composite likelihood estimation has an important role in the analysis of
multivariate data for which the full likelihood function is intractable. An
important issue in composite likelihood inference is the choice of the weights
associated with lower-dimensional data sub-sets, since the presence of
incompatible sub-models can deteriorate the accuracy of the resulting
estimator. In this paper, we introduce a new approach for simultaneous
parameter estimation by tilting, or re-weighting, each sub-likelihood component
called discriminative composite likelihood estimation (D-McLE). The
data-adaptive weights maximize the composite likelihood function, subject to
moving a given distance from uniform weights; then, the resulting weights can
be used to rank lower-dimensional likelihoods in terms of their influence in
the composite likelihood function. Our analytical findings and numerical
examples support the stability of the resulting estimator compared to
estimators constructed using standard composition strategies based on uniform
weights. The properties of the new method are illustrated through simulated
data and real spatial data on multivariate precipitation extremes.Comment: 29 pages, 4 figure
Empirical and Simulated Adjustments of Composite Likelihood Ratio Statistics
Composite likelihood inference has gained much popularity thanks to its
computational manageability and its theoretical properties. Unfortunately,
performing composite likelihood ratio tests is inconvenient because of their
awkward asymptotic distribution. There are many proposals for adjusting
composite likelihood ratio tests in order to recover an asymptotic chi square
distribution, but they all depend on the sensitivity and variability matrices.
The same is true for Wald-type and score-type counterparts. In realistic
applications sensitivity and variability matrices usually need to be estimated,
but there are no comparisons of the performance of composite likelihood based
statistics in such an instance. A comparison of the accuracy of inference based
on the statistics considering two methods typically employed for estimation of
sensitivity and variability matrices, namely an empirical method that exploits
independent observations, and Monte Carlo simulation, is performed. The results
in two examples involving the pairwise likelihood show that a very large number
of independent observations should be available in order to obtain accurate
coverages using empirical estimation, while limited simulation from the full
model provides accurate results regardless of the availability of independent
observations.Comment: 15 page
Approximate Bayesian Computation with composite score functions
Both Approximate Bayesian Computation (ABC) and composite likelihood methods
are useful for Bayesian and frequentist inference, respectively, when the
likelihood function is intractable. We propose to use composite likelihood
score functions as summary statistics in ABC in order to obtain accurate
approximations to the posterior distribution. This is motivated by the use of
the score function of the full likelihood, and extended to general unbiased
estimating functions in complex models. Moreover, we show that if the composite
score is suitably standardised, the resulting ABC procedure is invariant to
reparameterisations and automatically adjusts the curvature of the composite
likelihood, and of the corresponding posterior distribution. The method is
illustrated through examples with simulated data, and an application to
modelling of spatial extreme rainfall data is discussed.Comment: Statistics and Computing (final version
Composite Likelihood Inference by Nonparametric Saddlepoint Tests
The class of composite likelihood functions provides a flexible and powerful
toolkit to carry out approximate inference for complex statistical models when
the full likelihood is either impossible to specify or unfeasible to compute.
However, the strenght of the composite likelihood approach is dimmed when
considering hypothesis testing about a multidimensional parameter because the
finite sample behavior of likelihood ratio, Wald, and score-type test
statistics is tied to the Godambe information matrix. Consequently inaccurate
estimates of the Godambe information translate in inaccurate p-values. In this
paper it is shown how accurate inference can be obtained by using a fully
nonparametric saddlepoint test statistic derived from the composite score
functions. The proposed statistic is asymptotically chi-square distributed up
to a relative error of second order and does not depend on the Godambe
information. The validity of the method is demonstrated through simulation
studies
Multiple Comparisons using Composite Likelihood in Clustered Data
We study the problem of multiple hypothesis testing for multidimensional data
when inter-correlations are present. The problem of multiple comparisons is
common in many applications. When the data is multivariate and correlated,
existing multiple comparisons procedures based on maximum likelihood estimation
could be prohibitively computationally intensive. We propose to construct
multiple comparisons procedures based on composite likelihood statistics. We
focus on data arising in three ubiquitous cases: multivariate Gaussian, probit,
and quadratic exponential models. To help practitioners assess the quality of
our proposed methods, we assess their empirical performance via Monte Carlo
simulations. It is shown that composite likelihood based procedures maintain
good control of the familywise type I error rate in the presence of
intra-cluster correlation, whereas ignoring the correlation leads to erratic
performance. Using data arising from a diabetic nephropathy study, we show how
our composite likelihood approach makes an otherwise intractable analysis
possible
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