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Partially Adaptive Estimation via Maximum Entropy Densities

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  • Thanasis Stengos
  • Ximing Wu

Abstract

We propose a partially adaptive estimator based on information theoretic maximum entropy estimates of the error distribution. The maximum entropy (maxent) densities have simple yet flexible functional forms to nest most of the mathematical distributions. Unlike the nonparametric fully adaptive estimators, our parametric estimators do not involve choosing a bandwidth or trimming, and only require estimating a small number of nuisance parameters, which is desirable when the sample size is small. Monte Carlo simulations suggest that the proposed estimators fare well with non-normal error distributions. When the errors are normal, the efficiency loss due to redundant nuisance parameters is negligible as the proposed error densities nest the normal. The proposed partially adaptive estimator compares favorably with existing methods, especially when the sample size is small. We apply the estimator to a bio-pharmaceutical example and a stochastic frontier model.

Suggested Citation

  • Thanasis Stengos & Ximing Wu, 2005. "Partially Adaptive Estimation via Maximum Entropy Densities," University of Cyprus Working Papers in Economics 6-2005, University of Cyprus Department of Economics.
    • Handle: RePEc:ucy:cypeua:6-2005
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    Cited by:

    1. Theodore Panagiotidis & Georgios Papapanagiotou, 2024. "A note on the determinants of NFTs returns," Discussion Paper Series 2024_02, Department of Economics, University of Macedonia, revised Feb 2024.
    2. Usta, Ilhan & Kantar, Yeliz Mert, 2011. "On the performance of the flexible maximum entropy distributions within partially adaptive estimation," Computational Statistics & Data Analysis, Elsevier, vol. 55(6), pages 2172-2182, June.
    3. Rompolis, Leonidas S., 2010. "Retrieving risk neutral densities from European option prices based on the principle of maximum entropy," Journal of Empirical Finance, Elsevier, vol. 17(5), pages 918-937, December.
    4. Steven Caudill & James Long, 2010. "Do former athletes make better managers? Evidence from a partially adaptive grouped-data regression model," Empirical Economics, Springer, vol. 39(1), pages 275-290, August.
    5. Wu, Ximing & Perloff, Jeffrey M., 2005. "GMM Estimation of a Maximum Distribution With Interval Data," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt7jf5w1ht, Department of Agricultural & Resource Economics, UC Berkeley.
    6. Steven Caudill, 2012. "A partially adaptive estimator for the censored regression model based on a mixture of normal distributions," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 21(2), pages 121-137, June.
    7. Thanasis Stengos & Ximing Wu, 2010. "Information-Theoretic Distribution Test with Application to Normality," Econometric Reviews, Taylor & Francis Journals, vol. 29(3), pages 307-329.
    8. Katherine G. Yewell & Steven B. Caudill & Franklin G. Mixon, Jr., 2014. "Referee Bias and Stoppage Time in Major League Soccer: A Partially Adaptive Approach," Econometrics, MDPI, vol. 2(1), pages 1-19, February.
    9. Emanuele Taufer & Sudip Bose & Aldo Tagliani, 2009. "Optimal predictive densities and fractional moments," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(1), pages 57-71, January.
    10. Sella Lisa, 2008. "Old and New Spectral Techniques for Economic Time Series," Department of Economics and Statistics Cognetti de Martiis. Working Papers 200809, University of Turin.
    11. Pendharkar, Parag C., 2008. "Maximum entropy and least square error minimizing procedures for estimating missing conditional probabilities in Bayesian networks," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3583-3602, March.

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