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Higher-order asymptotic theory of shrinkage estimation for general statistical models

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  • Shiraishi, Hiroshi
  • Taniguchi, Masanobu
  • Yamashita, Takashi

Abstract

In this study, we develop a higher-order asymptotic theory of shrinkage estimation for general statistical models, which includes dependent processes, multivariate models, and regression models (i.e., non-independent and identically distributed models). We introduce a shrinkage estimator of the maximum likelihood estimator (MLE) and compare it with the standard MLE by using the third-order mean squared error. A sufficient condition for the shrinkage estimator to improve the MLE is given in a general setting. Our model is described as a curved statistical model p(⋅;θ(u)), where θ is a parameter of the larger model and u is a parameter of interest with dimu

Suggested Citation

  • Shiraishi, Hiroshi & Taniguchi, Masanobu & Yamashita, Takashi, 2018. "Higher-order asymptotic theory of shrinkage estimation for general statistical models," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 198-211.
    • Handle: RePEc:eee:jmvana:v:166:y:2018:i:c:p:198-211
    DOI: 10.1016/j.jmva.2018.03.006
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    References listed on IDEAS

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    1. Masanobu Taniguchi & Junichi Hirukawa, 2005. "The Stein–James estimator for short- and long-memory Gaussian processes," Biometrika, Biometrika Trust, vol. 92(3), pages 737-746, September.
    2. Velasco, Carlos & Robinson, Peter M., 2001. "Edgeworth Expansions For Spectral Density Estimates And Studentized Sample Mean," Econometric Theory, Cambridge University Press, vol. 17(3), pages 497-539, June.
    3. Ledoit, Olivier & Wolf, Michael, 2003. "Improved estimation of the covariance matrix of stock returns with an application to portfolio selection," Journal of Empirical Finance, Elsevier, vol. 10(5), pages 603-621, December.
    4. Jorion, Philippe, 1986. "Bayes-Stein Estimation for Portfolio Analysis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 21(3), pages 279-292, September.
    5. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    6. Hiroshi Shiraishi & Masanobu Taniguchi, 2008. "Statistical estimation of optimal portfolios for non-Gaussian dependent returns of assets," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 27(3), pages 193-215.
    7. Taniguchi, M. & Watanabe, Y., 1994. "Statistical Analysis of Curved Probability Densities," Journal of Multivariate Analysis, Elsevier, vol. 48(2), pages 228-248, February.
    8. Senda, Motohiro & Taniguchi, Masanobu, 2006. "James-Stein estimators for time series regression models," Journal of Multivariate Analysis, Elsevier, vol. 97(9), pages 1984-1996, October.
    9. Frost, Peter A. & Savarino, James E., 1986. "An Empirical Bayes Approach to Efficient Portfolio Selection," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 21(3), pages 293-305, September.
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