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Abstract:
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Inference for vector parameters is often based on the likelihood ratio statistic, with p-values computed using the Chi-squared approximation. Davison et al (2014) and Fraser et al (2016) proposed a directional test and showed how p-values for this test could be accurately computed. The calculations are particularly simple for linear hypotheses in exponential families. In some common situations the directional approach yields p-values that are equivalent to those obtained from well known test statistics. For example, the directional test of a linear constraint on the regression vector in normal theory linear regression is equivalent to the usual F-test, thus giving a new view on this classical test. We examine the performance of directional inference in several examples. Simulations are presented showing that directional p-values are uniformly distributed under the null hypothesis, and can be more accurate than usual first order approximations.
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