Information quantities in non-classical settings

Abstract To cope with difficulties met outside the classical framework for likelihood inference various analogue of observed and expected (Fisher) information have been introduced. Here, some of these information quantities are reviewed, exemplified and compared, and their properties are discussed. Besides observed and expected information we consider incremental observed and expected information (in martingale language these are the quadratic variation and quadratic characteristic of the score process), robust observed information, and observed profile information. Extensions of the ideas to estimating equations and to semiparametric models are considered.

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