Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

A Note on Comparing Multistage Procedures for Fixed-Width Confidence Interval

  • Choi, Ki-Heon (Department of Statistics, Duksung Women's University)
  • Published : 2008.09.30
Download PDF
⟨ Previous Next ⟩

Abstract

Application of the bootstrap to problems in multistage inference procedures are discussed in normal and other related models. After a general introduction to these procedures, here we explore in multistage fixed precision inference in models. We present numerical comparisons of these procedures based on bootstrap critical points for small and moderate sample sizes obtained via extensive sets of simulated experiments. It is expected that the procedure based on bootstrap leads to better results.

Keywords

References

  1. Aerts, M. and Gijbels, I. (1993). A three-stage procedure based on bootstrap critical points, Sequential Analysis, 12, 93-113 https://doi.org/10.1080/07474949308836272
  2. Chow, Y. S. and Robbins, H. (1965). On the Asymptotic Theory of fixed-width sequential confidence intervals for the mean, The Annals of Mathematical Statistics, 36, 457-462 https://doi.org/10.1214/aoms/1177700156
  3. Ghosh, M., Mukhopadhyay, N. and Sen, P. K. (1997). Sequential Estimation, John Wiley & Sons, New York
  4. Hall, P. (1981). Asymptotic theory of triple sampling for sequential estimation of a mean, The Annals of Statistics, 9, 1229-1238 https://doi.org/10.1214/aos/1176345639
  5. Lehmann, E. (1959). Testing Statistical Hypotheses, John Wiley & Sons, New York
  6. Mukhopadhyay, N. (1980). A consistent and asymptotically efficient two-stage procedure to construct fixed-width confidence interval for the mean, Metrika, 27, 281-284 https://doi.org/10.1007/BF01893607
  7. Mukhopadhyay, N. and Duggan, W. T. (1997). Can a two-stage procedure enjoy second-order properties?, Sankhya Ser. A, 59, 435-448
  8. Stein, C. (1945). A two sample test for a linear hypothesis whose power is independent of the variance, The Annals of Mathematical Statistics, 16, 243-258 https://doi.org/10.1214/aoms/1177731088
  9. Swanepoel, J. W. H., van Wijk, J. W. J. and Venter, J. H. (1983). Fixed-width confidence intervals based on bootstrap procedures, Sequential Analysis, 2, 289-310 https://doi.org/10.1080/07474948408836041