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A composite likelihood is a non-genuine likelihood function that allows to make inference on limited aspects of a model, such as marginal or conditional distributions. Composite likelihoods are not proper likelihoods and need therefore calibration for their use in inference, from both a frequentist and a Bayesian perspective. The maximizer to the composite likelihood can serve as an estimator and its variance is assessed by means of a suitably defined sandwich matrix. In the Bayesian setting, the composite likelihood can be adjusted by means of magnitude and curvature methods. Magnitude methods imply raising the likelihood to a constant, while curvature methods imply evaluating the likelihood at a different point by translating, rescaling and rotating the parameter vector. Some authors argue that curvature methods are more reliable in general, but others proved that magnitude methods are sufficient to recover, for instance, the null distribution of a test statistic. We propose a simple calibration for the marginal posterior distribution of a scalar parameter of interest which is invariant to monotonic and smooth transformations. This can be enough for instance in medical statistics, where a single scalar effect measure is often the target.
This paper investigates the high-dimensional linear regression with highly correlated covariates. In this setup, the traditional sparsity assumption on the regression coefficients often fails to hold, and consequently many model selection procedures
In a network meta-analysis, some of the collected studies may deviate markedly from the others, for example having very unusual effect sizes. These deviating studies can be regarded as outlying with respect to the rest of the network and can be influ
As an effective nonparametric method, empirical likelihood (EL) is appealing in combining estimating equations flexibly and adaptively for incorporating data information. To select important variables and estimating equations in the sparse high-dimen
Ideally, a meta-analysis will summarize data from several unbiased studies. Here we consider the less than ideal situation in which contributing studies may be compromised by measurement error. Measurement error affects every study design, from rando
Objective Bayesian inference procedures are derived for the parameters of the multivariate random effects model generalized to elliptically contoured distributions. The posterior for the overall mean vector and the between-study covariance matrix is