72,949 research outputs found
Phi-divergence statistics for the likelihood ratio order: an approach based on log-linear models
When some treatments are ordered according to the categories of an ordinal
categorical variable (e.g., extent of side effects) in a monotone order, one
might be interested in knowing wether the treatments are equally effective or
not. One way to do that is to test if the likelihood ratio order is strictly
verified. A method based on log-linear models is derived to make statistical
inference and phi-divergence test-statistics are proposed for the test of
interest. Focussed on loglinear modeling, the theory associated with the
asymptotic distribution of the phi-divergence test-statistics is developed. An
illustrative example motivates the procedure and a simulation study for small
and moderate sample sizes shows that it is possible to find phi-divergence
test-statistic with an exact size closer to nominal size and higher power in
comparison with the classical likelihood ratio
Prior distributions for objective Bayesian analysis
We provide a review of prior distributions for objective Bayesian analysis. We start by examining some foundational issues and then organize our exposition into priors for: i) estimation or prediction; ii) model selection; iii) highdimensional models. With regard to i), we present some basic notions, and then move to more recent contributions on discrete parameter space, hierarchical models, nonparametric models, and penalizing complexity priors. Point ii) is the focus of this paper: it discusses principles for objective Bayesian model comparison, and singles out some major concepts for building priors, which are subsequently illustrated in some detail for the classic problem of variable selection in normal linear models. We also present some recent contributions in the area of objective priors on model space.With regard to point iii) we only provide a short summary of some default priors for high-dimensional models, a rapidly growing area of research
Generalized Wald-type Tests based on Minimum Density Power Divergence Estimators
In testing of hypothesis the robustness of the tests is an important concern.
Generally, the maximum likelihood based tests are most efficient under standard
regularity conditions, but they are highly non-robust even under small
deviations from the assumed conditions. In this paper we have proposed
generalized Wald-type tests based on minimum density power divergence
estimators for parametric hypotheses. This method avoids the use of
nonparametric density estimation and the bandwidth selection. The trade-off
between efficiency and robustness is controlled by a tuning parameter .
The asymptotic distributions of the test statistics are chi-square with
appropriate degrees of freedom. The performance of the proposed tests are
explored through simulations and real data analysis.Comment: 26 pages, 10 figures. arXiv admin note: substantial text overlap with
arXiv:1403.033
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