Information, Ancillarity and Conditional Inference
The present chapter studies the amount of information carried by a statistic t(x) from the geometrical point of view. The amount of information plays a fundamental role in parameter estimation and statistical hypothesis testing. Higher-order asymptotic sufficiency, higher-order asymptotic ancillarity, and conditional information are defined in the beginning. Then, the performance of asymptotic conditional inference is studied, and the role of an asymptotic ancillary statistic is elucidated therefrom. We give an answer at least from the asymptotic point of view to the problem on which ancillary statistics one should condition when there are a number of ancillaries. Finally, the sufficient vector statistic x is decomposed into component statistics of geometrical character according as the magnitude of the amount of information.
KeywordsFisher Information Information Loss Exponential Family Conditional Covariance Curvature Direction
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