Davison, A. C.
Fraser, D. A. S.
Reid, N.
Sartori, N.
Accurate Directional Inference for Vector Parameters in Linear Exponential Families
Journal Of The American Statistical Association
0162-1459
10.1080/01621459.2013.839451
109
505
302-314
13
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.
Contingency table;
Covariance selection;
Exponential family model;
Higher-order asymptotics;
Likelihood ratio test;
Logistic regression;
American Statistical Association
Alexandria
2014