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Efficient Semiparametric Prediction Intervals

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  • Bryan W. Brown

    (Rice University)

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    Abstract

    The construction of prediction intervals and regions and their probability content for nonlinear systems with nonparametric disturbances is considered. The semiparametric efficiency bound for estimating the probability content of a known interval (region) and estimators that attain the bound are developed. Semiparametric efficient estimation of optimal prediction intervals (regions) which either (i) maximize probability content given interval length (region area) or (ii) maximize interval length (region area) given probability content is studied. The estimated probability content of (i) is found to have the same limiting behavior as if the interval (region) were known with certainty and hence attains the semiparametric efficiency bound. Further, the estimated probability of the estimated interval (region) approximates the true coverage probability to order root-n for (i) but order smaller than root-n for (ii). A Monte Carlo experiment is conducted to compare the new predictors to competitors.

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    Bibliographic Info

    Paper provided by Econometric Society in its series Econometric Society World Congress 2000 Contributed Papers with number 1633.

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    Date of creation: 01 Aug 2000
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    Handle: RePEc:ecm:wc2000:1633

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    1. Brown, Bryan W & Mariano, Roberto S, 1984. "Residual-Based Procedures for Prediction and Estimation in a Nonlinear Simultaneous System," Econometrica, Econometric Society, vol. 52(2), pages 321-43, March.
    2. Newey, W.K., 1991. "The Asymptotic Variance of Semiparametric Estimators," Working papers 583, Massachusetts Institute of Technology (MIT), Department of Economics.
    3. Mariano, Roberto S & Brown, Bryan W, 1983. "Asymptotic Behavior of Predictors in a Nonlinear Simultaneous System," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 24(3), pages 523-36, October.
    4. Brown, Bryan W. & Mariano, Roberto S., 1989. "Predictors in Dynamic Nonlinear Models: Large-Sample Behavior," Econometric Theory, Cambridge University Press, vol. 5(03), pages 430-452, December.
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