Ancillaries and Conditional Inference

Improved Likelihood Inference for Discrete Data

“…This appears in discussions of ancillarity by Fisher (1956), Basu (1964), Fraser (1979) and Fraser (2004) and has the unusual feature that the row totals and column totals are each ancillary statistics for θ but the combination of them is not ancillary. The construction below however is conditional on an approximate ancillary statistic that is not needed explicitly.…”

Coherent Frequentism: A Decision Theory Based on Confidence Sets

“…Given the ubiquity of recognizable subsets (Buehler and Feddersen, 1963;Bondar, 1977), this strategy uses pre-data confidence as an approximation to post-data confidence in the sense in which expected Fisher information approximates observed Fisher information (Efron and Hinkley, 1978), aiming not at exact inference but at a pragmatic use of the limited resources available for any particular data analysis. Certain situations may instead call for careful applications of conditional inference (Goutis and Casella, 1995;Sundberg, 2003;Fraser, 2004) or of minimum description length (Bickel, 2011b) for basing decisions more directly on the data actually observed.…”

Three Examples of Accurate Likelihood Inference

“…. , V n in (7) are d ×1 vectors that are tangent to the ancillary statistic and that show how changing the parameter θ changes y (Fraser 2004); we discuss them further below. Expression (6), which is appreciably easier to deal with than the somewhat forbidding expression (5), shows that in order to compute ϕ(θ) we require the expected information matrix and the score statistic, and the derivatives of the latter and of the log-likelihood with respect to the observation.…”