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Approximate maximum entropy on the mean for instrumental variable regression

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  • Loubes, Jean-Michel
  • Rochet, Paul

Abstract

We want to estimate an unknown finite measure μX from a noisy observation of generalized moments of μX, defined as the integral of a continuous function Φ with respect to μX. Assuming that only a quadratic approximation Φm is available, we define an approximate maximum entropy solution as a minimizer of a convex functional subject to a sequence of convex constraints. We establish asymptotic properties of the approximate solution under regularity assumptions on the convex functional, and we study an application of this result to instrumental variable estimation.

Suggested Citation

  • Loubes, Jean-Michel & Rochet, Paul, 2012. "Approximate maximum entropy on the mean for instrumental variable regression," Statistics & Probability Letters, Elsevier, vol. 82(5), pages 972-978.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:5:p:972-978
    DOI: 10.1016/j.spl.2012.02.006
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    References listed on IDEAS

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    1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    2. Henryk Gzyl & Noam Zeev, 2002. "Probabilistic Approach to an Image Reconstruction Problem," Methodology and Computing in Applied Probability, Springer, vol. 4(3), pages 279-290, September.
    3. Hansen, Lars Peter & Singleton, Kenneth J, 1982. "Generalized Instrumental Variables Estimation of Nonlinear Rational Expectations Models," Econometrica, Econometric Society, vol. 50(5), pages 1269-1286, September.
    4. Gamboa F., 1999. "New Bayesian Methods For Ill Posed Problems," Statistics & Risk Modeling, De Gruyter, vol. 17(4), pages 315-338, April.
    5. Newey, Whitney K, 1990. "Efficient Instrumental Variables Estimation of Nonlinear Models," Econometrica, Econometric Society, vol. 58(4), pages 809-837, July.
    6. Chamberlain, Gary, 1987. "Asymptotic efficiency in estimation with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 34(3), pages 305-334, March.
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    Cited by:

    1. Yuri S. Popkov, 2021. "Qualitative Properties of Randomized Maximum Entropy Estimates of Probability Density Functions," Mathematics, MDPI, vol. 9(5), pages 1-13, March.

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