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On the Approximation of Saddlepoint Expansions in Statistics

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  • Lieberman, Offer

Abstract

The saddlepoint approximation as developed by Daniels [3] is an extremely accurate method for approximating probability distributions. Econometric and statistical applications of the technique to densities of statistics of interest are often hindered by the requirements of explicit knowledge of the c.g.f. and the need to obtain an analytical solution to the saddlepoint defining equation. In this paper, we show the conditions under which any approximation to the saddlepoint is justified and suggest a convenient solution. We illustrate with an approximate saddlepoint expansion of the Durbin-Watson test statistic.

Suggested Citation

  • Lieberman, Offer, 1994. "On the Approximation of Saddlepoint Expansions in Statistics," Econometric Theory, Cambridge University Press, vol. 10(5), pages 900-916, December.
    • Handle: RePEc:cup:etheor:v:10:y:1994:i:05:p:900-916_00
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    Cited by:

    1. Glasserman, Paul & Kim, Kyoung-Kuk, 2009. "Saddlepoint approximations for affine jump-diffusion models," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 15-36, January.
    2. La Vecchia, Davide & Ronchetti, Elvezio, 2019. "Saddlepoint approximations for short and long memory time series: A frequency domain approach," Journal of Econometrics, Elsevier, vol. 213(2), pages 578-592.
    3. Ai[dieresis]t-Sahalia, Yacine & Yu, Jialin, 2006. "Saddlepoint approximations for continuous-time Markov processes," Journal of Econometrics, Elsevier, vol. 134(2), pages 507-551, October.
    4. Mengzhe Zhang & Leunglung Chan, 2016. "Saddlepoint approximations to option price in a regime-switching model," Annals of Finance, Springer, vol. 12(1), pages 55-69, February.
    5. Wendong Zheng & Yue Kuen Kwok, 2014. "Saddlepoint Approximation Methods for Pricing Derivatives on Discrete Realized Variance," Applied Mathematical Finance, Taylor & Francis Journals, vol. 21(1), pages 1-31, March.

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