0162-1459
Accurate Directional Inference for Vector Parameters in Linear Exponential Families
Davison
A. C.
Ecole Polytech Fed Lausanne, EPFL FSB MATHAA STAT, CH-1015 Lausanne, Switzerland
Fraser
D. A. S.
Univ Toronto, Dept Stat, Toronto, ON M5S 3G3, Canada
Reid
N.
Univ Toronto, Dept Stat, Toronto, ON M5S 3G3, Canada
Sartori
N.
2014
We consider inference on a vector-valued parameter of interest in a linear exponential family, in the presence of a finite-dimensional nuisance parameter. Based on higher-order asymptotic theory for likelihood, we propose a directional test whose p-value is computed using one-dimensional integration. The work simplifies and develops earlier research on directional tests for continuous models and on higher-order inference for discrete models, and the examples include contingency tables and logistic regression. Examples and simulations illustrate the high accuracy of the method, which we compare with the usual likelihood ratio test and with an adjusted version due to Skovgaard. In high-dimensional settings, such as covariance selection, the approach works essentially perfectly, whereas its competitors can fail catastrophically.
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