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Empirical saddlepoint approximations of the Studentized mean under simple random sampling

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  • Dai, Wen
  • Robinson, John

Abstract

We obtain a saddlepoint approximation for the Studentized mean of a simple random sample taken without replacement from a finite population. This is only possible if we know the entire population, so we also obtain an empirical saddlepoint approximation based on the sample alone. This empirical approximation can be used for tests of significance and confidence intervals for the population mean. We compare the empirical approximation to the true saddlepoint approximation, both theoretically and numerically. We also compare both approximations to values obtained in a large Monte Carlo simulation for a population of survival times. The comparisons show that good accuracy can be obtained from the empirical saddlepoint approximation. In addition, the approximations are compared numerically to the Edgeworth approximation of Sugden and Smith (Statist. Probab. Lett. 34 (3) (1997) 293-299; Statist. Probab. Lett. 37 (3) (1998) 317), with a correction in Sugden et al. (J. Roy. Statist. Soc. B 62 (2000) 787-794).

Suggested Citation

  • Dai, Wen & Robinson, John, 2001. "Empirical saddlepoint approximations of the Studentized mean under simple random sampling," Statistics & Probability Letters, Elsevier, vol. 53(3), pages 331-337, June.
    • Handle: RePEc:eee:stapro:v:53:y:2001:i:3:p:331-337
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    References listed on IDEAS

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    1. Sugden, R. A. & Smith, T. M. F., 1997. "Edgeworth approximations to the distribution of the sample mean under simple random sampling," Statistics & Probability Letters, Elsevier, vol. 34(3), pages 293-299, June.
    2. R. A. Sugden & T. M. F. Smith & R. P. Jones, 2000. "Cochran's rule for simple random sampling," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 787-793.
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    Cited by:

    1. Hu, Zhishui & Ma, Chunsheng & Robinson, John, 2008. "Empirical saddlepoint approximations of the Studentized mean under stratified random sampling," Statistics & Probability Letters, Elsevier, vol. 78(4), pages 396-401, March.
    2. Agho, Kingsley & Dai, Wen & Robinson, John, 2005. "Empirical saddlepoint approximations of the Studentized ratio and regression estimates for finite populations," Statistics & Probability Letters, Elsevier, vol. 71(3), pages 237-247, March.

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