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How should parameter estimation be tailored to the objective?
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DOI：10.1016/j.jeconom.2020.12.014.png)
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摘要
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We study parameter estimation from the sample X, when the objective is to maximize the expected value of a criterion function, Q, for a distinct sample, Y. This is the situation that arises when a model is estimated for the purpose of describing other data than those used for estimation, such as in forecasting problems. A natural candidate for solving maxT is an element of Sigma(X)EQ(Y, T) is the innate estimator, theta circumflex accent = arg max theta Q(X, theta). While the innate estimator has certain advantages, we show that the asymptotically efficient estimator takes the form theta tilde = arg max theta Q tilde (X, theta), where Q tilde is defined from a likelihood function in conjunction with Q. The likelihood-based estimator is, however, fragile, as misspecification is harmful in two ways. First, the likelihood-based estimator may be inefficient under misspecification. Second, and more importantly, the likelihood approach requires a parameter transformation that depends on the true model, causing an improper mapping to be used under misspecification.(c) 2021 Elsevier B.V. All rights reserved.
Keyword:
Estimation
Model selection
LinEx loss
Multistep forecasting
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4
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5.2K
被引数:
3.0W
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