TY - EJOUR
DO - 10.1080/01621459.2013.839451
AB - 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.
T1 - Accurate Directional Inference for Vector Parameters in Linear Exponential Families
IS - 505
DA - 2014
AU - Davison, A. C.
AU - Fraser, D. A. S.
AU - Reid, N.
AU - Sartori, N.
JF - Journal Of The American Statistical Association
SP - 302-314
VL - 109
EP - 302-314
PB - American Statistical Association
PP - Alexandria
ID - 198639
KW - Contingency table
KW - Covariance selection
KW - Exponential family model
KW - Higher-order asymptotics
KW - Likelihood ratio test
KW - Logistic regression
SN - 0162-1459
ER -