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Statistical Analysis of Curved Probability Densities

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  • Taniguchi, M.
  • Watanabe, Y.

Abstract

Suppose that pn(· ; [theta]) is the joint probability density of n observations which are not necessarily i.i.d. In this paper we discuss the estimation of an unknown parameter u of a family of "curved probability densities" defined by M = {pn(· ; [theta](u)), dim u

Suggested Citation

  • Taniguchi, M. & Watanabe, Y., 1994. "Statistical Analysis of Curved Probability Densities," Journal of Multivariate Analysis, Elsevier, vol. 48(2), pages 228-248, February.
    • Handle: RePEc:eee:jmvana:v:48:y:1994:i:2:p:228-248
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    Cited by:

    1. Marsh, Patrick, 2001. "Edgeworth expansions in Gaussian autoregression," Statistics & Probability Letters, Elsevier, vol. 54(3), pages 233-241, October.
    2. Tomonari Sei & Fumiyasu Komaki, 2008. "Information geometry of small diffusions," Statistical Inference for Stochastic Processes, Springer, vol. 11(2), pages 123-141, June.
    3. Kakizawa, Yoshihide, 2010. "Comparison of Bartlett-type adjusted tests in the multiparameter case," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1638-1655, August.
    4. In-Bong Choi & Masanobu Taniguchi, 2003. "Prediction Problems for Square-Transformed Stationary Processes," Statistical Inference for Stochastic Processes, Springer, vol. 6(1), pages 43-64, January.
    5. Haruhiko Ogasawara, 2012. "Asymptotic expansions for the ability estimator in item response theory," Computational Statistics, Springer, vol. 27(4), pages 661-683, December.
    6. 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.
    7. Yuji Sakamoto & Nakahiro Yoshida, 2004. "Asymptotic expansion formulas for functionals of ε-Markov processes with a mixing property," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 56(3), pages 545-597, September.
    8. Ogasawara, Haruhiko, 2016. "Asymptotic expansions for the estimators of Lagrange multipliers and associated parameters by the maximum likelihood and weighted score methods," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 20-37.

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