Ancillaries and Third Order Signiicance
نویسندگان
چکیده
SUMMARY For a variable and parameter of the same dimension, the tangent exponential model (Fraser, 1988) approximates an asymptotic model to third order in a rst derivative neighbourhood of the data point and to second order otherwise. For the more usual case of a variable of larger dimension than the parameter, we obtain a unique expression for the third order ancillary distribution as projected to the observed maximum likelihood surface, obtain the tangent directions for a second order ancillary, and then show that third order inference needs only the observed likelihood and the tangent directions for a second order ancillary. These results are then combined and a unique third order distribution is obtained for testing a component parameter; for testing a real parameter a simple expression is obtained for the third order observed signiicance level.Dec 30, 1993
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