A broader class of modified two-stage minimum risk point estimation procedures for a normal mean

References

• Abramowitz, M., and I. A. Stegun. 1972. Handbook of mathematical functions, tenth printing. New York: Dover.
   Google Scholar
• Babu, G. J., and C. R. Rao. 1992. Expansions for statistics involving the mean absolute deviations. Annals of the Institute of Statistical Mathematics 44 (2):387–403.
   Web of Science ®Google Scholar
• Chattopadhyay, B., and N. Mukhopadhyay. 2013. Two-stage fixed-width confidence intervals for a normal mean in the presence of suspect outliers. Sequential Analysis 32 (2):134–57.
   Web of Science ®Google Scholar
• Ghosh, M., and N. Mukhopadhyay. 1981. Consistency and asymptotic efficiency of two-stage and sequential procedures. Sankhyā, Series A 43:220–27.
   Google Scholar
• Gini, C. 1912. Variabilità e mutabilità, contributo allo studio delle distribuzioni e delle relazioni statistiche. In Studi Economico-giuridici della Regia Facoltà Giurisprudenza, anno III, parte II. Bologna: Cuppini.
   Google Scholar
• Hand, D. J., F. Daly, K. McConway, D. Lunn, and E. Ostrowski. 1993. A handbook of small data sets, edited volume. New York: Chapman & Hall.
   Google Scholar
• Hoeffding, W. 1948. A class of statistics with asymptotically normal distribution. The Annals of Mathematical Statistics 19 (3):293–325.
   Google Scholar
• Hoeffding, W. 1961. The strong law of large numbers for U-Statistics. Institute of Statistics Mimeo Series #302, University of North Carolina, Chapel Hill.
   Google Scholar
• Hu, J., and N. Mukhopadhyay. 2019. Second-order asymptotics in a class of purely sequential minimum risk point estimation (MRPE) methodologies. Japanese Journal of Statistics and Data Science 2 (1):81–104.
   Google Scholar
• Mukhopadhyay, N. 1980. A consistent and asymptotically efficient two-stage procedure to construct fixed-width confidence intervals for the mean. Metrika 27 (1):281–84.
   Google Scholar
• Mukhopadhyay, N. 1982. Stein’s two-stage procedure and exact consistency. Scandinavian Actuarial Journal 1982 (2):110–22.
   Google Scholar
• Mukhopadhyay, N. 1999. Higher than second-order approximations via two-stage sampling. Sankhyā, Series A 61:254–69.
   Google Scholar
• Mukhopadhyay, N., and B. M. de Silva. 2009. Sequential methods and their applications. Boca Ratton, FL: CRC.
   Google Scholar
• Mukhopadhyay, N., and W. T. Duggan. 1997. Can a two-stage procedure enjoy second-order properties? Sankhyā, Series A 59:435–48.
   Google Scholar
• Mukhopadhyay, N., and J. Hu. 2017. Confidence intervals and point estimators for a normal mean under purely sequential strategies involving Gini’s mean difference and mean absolute deviation. Sequential Analysis 36 (2):210–39.
   Web of Science ®Google Scholar
• Mukhopadhyay, N., and J. Hu. 2018. Gini’s mean difference and mean absolute deviation based two-stage estimation for a normal mean with known lower bound of variance. Sequential Analysis 37 (2):204–21.
   Web of Science ®Google Scholar
• Mukhopadhyay, N., and Y. Zhuang. 2019. Two-sample two-stage and purely sequential methodologies for tests of hypotheses with applications: Comparing normal means when the two variances are unknown and unequal. Sequential Analysis 38 (1):69–114.
   Web of Science ®Google Scholar
• Nair, U. S. 1936. The standard error of Gini’s mean difference. Biometrika 28 (3–4):428–36.
   Google Scholar
• Robbins, H. 1959. Sequential estimation of the mean of a normal population. In Probability and statistics, H. Cramér volume, ed. U. Grenander, 235–45. Uppsala: Almquist & Wiksell.
   Google Scholar
• Starr, N. 1966. On the asymptotic efficiency of a sequential procedure for estimating the mean. The Annals of Mathematical Statistics 37 (5):1173–85.
   Google Scholar
• Stein, C. 1945. A two sample test for a linear hypothesis whose power is independent of the variance. The Annals of Mathematical Statistics 16 (3):243–58.
   Google Scholar
• Tukey, J. W. 1938. On the distribution of the fractional part of a statistical variable. Matematicheskii Sbornik 4:561–62.
   Google Scholar
• Yitzhaki, S. 2003. Gini’s mean difference: A superior measure of variability for non-normal distributions. Metron 61:285–316.
   Google Scholar
• Zhuang, S., and S. R. Bapat. 2020. On comparing locations of two-parameter exponential distributions using sequential sampling with applications in cancer research. Communications in Statistics - Simulation and Computation. Advance online publication. doi:10.1080/03610918.2020.1794007
   Web of Science ®Google Scholar