Bregman and GPL Losses: Identified or Not?

Robert P. Lieli, Maxwell B. Stinchcombe

    Research output: Working paper/PreprintWorking paper

    Abstract (may include machine translation)

    The Bregman class of loss functions is characterized by the property that the con-
    ditional mean is the unrestricted optimal forecast for any Bregman loss. Similarly,
    generalized piecewise linear (GPL) loss functions all give rise to a given quantile as
    the unrestricted optimal forecast. Using the identification theory in Lieli and Stinch-
    combe (2013), we argue that Bregman losses are still potentially distinguishable if
    restrictions are placed on the set of allowable forecasts; e.g., off-support forecasts are
    excluded. In contrast, GPL loss functions remain observationally equivalent even in
    such forecasting environments—here the failure of identification is more fundamental.
    Motivated by these examples, we conclude by asking partly open questions about the
    nonparametric identifiability of loss functions.
    Original languageAmerican English
    PublisherCentral European University, Department of Economics
    StatePublished - 2016

    Publication series

    NameWorking papers

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