Multistage point estimation methodologies for a negative exponential location under a modified linex loss function: Illustrations with infant mortality and bone marrow data

References

• Bain, L. J. (1978). Statistical Analysis of Reliability and Life Testing Models, New York: Dekker.
   Google Scholar
• Balakrishnan, N. and Basu, A. P. (1995). The Exponential Distribution: Theory, Methods and Application, edited volume, Amsterdam: Gordon and Breach.
   Google Scholar
• Chattopadhyay, S. (1998). Sequential Estimation of Normal Mean under Asymmetric Loss Function with a Shrinkage Stopping Rule, Metrika 48: 53–59.
   Web of Science ®Google Scholar
• Chattopadhyay, S. (2000). Sequential Estimation of Exponential Location Parameter Using an Asymmetric Loss Function, Communications in Statistics - Theory \textup& Methods 29: 783–795.
   Web of Science ®Google Scholar
• Chattopadhyay, S., Chaturvedi, A., and Sengupta, R. N. (2000). Sequential Estimation of a Linear Function of Normal Means under Asymmetric Loss Function, Metrika 52: 225–235.
   Web of Science ®Google Scholar
• Chattopadhyay, S., Datta, S., and Sengupta, R. N. (2005). Asymmetric Penalized Prediction Using Adaptive Sampling Procedures, Sequential Analysis 24: 23–43.
   Google Scholar
• Chattopadhyay, S. and Sengupta, R. N. (2006). Three-Stage and Accelerated Sequential Point Estimation of the Normal Mean Using LINEX Loss Function, Statistics 40: 39–49.
   Web of Science ®Google Scholar
• Chow, Y. S. and Robbins, H. (1965). On the Asymptotic Theory of Fixed Width Sequential Confidence Intervals for the Mean, Annals of Mathematical Statistics 36: 457–462.
   Google Scholar
• Ghosh, M. and Mukhopadhyay, N. (1975). Asymptotic Normality of Stopping Times in Sequential Analysis, Unpublished Report.
   Google Scholar
• Ghosh, M. and Mukhopadhyay, N. (1981). Consistency and Asymptotic Efficiency of Two-Stage and Sequential Procedures, Sankhya, Series A 43: 220–227.
   Google Scholar
• Ghosh, M., Mukhopadhyay, N., and Sen, P. K. (1997). Sequential Estimation, New York: Wiley.
   Google Scholar
• Hwang, L.-C. and Lee, C.-H. (2012). Bayes Sequential Estimation for One-Parameter Exponential Family under Asymmetric LINEX Loss Function, Sequential Analysis 31: 3–21.
   Web of Science ®Google Scholar
• Isogai, E., Kobayashi, K., and Uno, C. (2011). Higher Order Approximations by a Two-Stage Procedure for a Negative Exponential Distribution, Journal of Statistical Planning and Inference 141: 3304–3312.
   Web of Science ®Google Scholar
• Johnson, N. L. and Kotz, S. (1970). Continuous Univariate Distributions-2, New York: Wiley.
   Google Scholar
• Jokiel-Rokita, A. (2008). A Sequential Estimation Procedure for the Parameter of an Exponential Distribution Under Asymmetric Loss Function, Statistics and Probability Letters 78: 3091–3095.
   Web of Science ®Google Scholar
• Klein, J. P. and Moeschberger, M. L. (2003). Survival Analysis, second edition, New York: Springer.
   Google Scholar
• Lai, T. L. and Siegmund, D. (1977). A Nonlinear Renewal Theory with Applications to Sequential Analysis I, Annals of Statistics 5: 946–954.
   Web of Science ®Google Scholar
• Lai, T. L. and Siegmund, D. (1979). A Nonlinear Renewal Theory with Applications to Sequential Analysis II, Annals of Statistics 7: 60–76.
   Web of Science ®Google Scholar
• Leinhardt, S. and Wasserman, S. S. (1979). Exploratory Data Analysis: An Introduction to Selected Methods, in Sociological Methodology, K. Schuessler ed., pp. 311–365, San Francisco: Jossey-Bass.
   Google Scholar
• Lombard, F. and Swanepoel, J. W. H. (1978). On Finite and Infinite Confidence Sequences, South African Statistical Journal 12: 1–24.
   Web of Science ®Google Scholar
• Mukhopadhyay, N. (1974). Sequential Estimation of Location Parameter in Exponential Distributions, Calcutta Statistical Association Bulletin 23: 85–95.
   Google Scholar
• Mukhopadhyay, N. (1984). Sequential and Two Stage Procedures for Selecting the Better Exponential Population Covering the Case of Unknown and Unequal Scale Parameters, Journal of Statistical Planning and Inference 9: 33–43.
   Web of Science ®Google Scholar
• Mukhopadhyay, N. (1988). Sequential Estimation Problems for Negative Exponential Populations, Communications in Statistics-Theory \textup& Methods, Series A 17: 2471–2506.
   Web of Science ®Google Scholar
• Mukhopadhyay, N. (1995). Two-Stage and Multi-Stage Estimation, in The Exponential Distribution: Theory, Methods and Application, N. Balakrishnan and A. P. Basu eds., pp. 429–452, Amsterdam: Gordon and Breach.
   Google Scholar
• Mukhopadhyay, N. (1999). Higher Than Second Order Approximations Via Two-Stage Sampling, Sankhya, Series A 61: 254–269.
   Google Scholar
• Mukhopadhyay, N., Datta, S., and Chattopadhyay, S. (2004). Applied Sequential Methodologies, edited volume, New York: Dekker.
   Google Scholar
• Mukhopadhyay, N. and de Silva, B. M. (2009). Sequential Methods and Their Applications, Boca Raton: CRC.
   Google Scholar
• Mukhopadhyay, N. and Duggan, W. T. (1997). Can a Two-Stage Procedure Enjoy Second Order Properties? Sankhya, Series A 59: 435–448.
   Google Scholar
• Mukhopadhyay, N. and Duggan, W. T. (1999). On a Two-Stage Procedure Having Second Order Properties with Applications, Annals of Institute of Statistical Mathematics 51: 621–636.
   Web of Science ®Google Scholar
• Mukhopadhyay, N. and Hilton, G. F. (1986). Two Stage and Sequential Procedures for Estimating the Location Parameter of a Negative Exponential Distribution, South African Statistical Journal 20:117–136.
   Web of Science ®Google Scholar
• Mukhopadhyay, N. and Solanky, T. K. S. (1994). Multistage Selection and Ranking Procedures, New York: Dekker.
   Google Scholar
• The New York Times, 28 September, 1975, p. E-3, Table 3.
   Google Scholar
• R Core Team (2014). R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria.
   Google Scholar
• Sen, P. K. (1981). Sequential Nonparametrics, New York: Wiley.
   Google Scholar
• Siegmund, D. (1985). Sequential Analysis: Tests and Confidence Intervals, New York: Springer.
   Google Scholar
• Stein, C. (1945). A Two Sample Test for a Linear Hypothesis Whose Power Is Independent of the Variance, Annals of Mathematical Statistics 16: 243–258.
   Google Scholar
• Stein, C. (1949). Some Problems in Sequential Estimation (abstract), Econometrica 17: 77–78.
   Google Scholar
• Swanepoel, J. W. H. and van Wyk, J. W. J. (1982). Fixed Width Confidence Intervals for the Location Parameter of an Exponential Distribution, Communications in Statistics - Theory \textup& Methods, Series A 11: 1279–1289.
   Web of Science ®Google Scholar
• Takada, Y. (2000). Sequential Point Estimation of Normal Mean under Linex Loss Function, Metrika 52: 163–171.
   Web of Science ®Google Scholar
• Takada, Y. (2001). Bayes Sequential Estimation of Poisson Mean under a LINEX Loss Function, Sequential Analysis 20: 55–64.
   Google Scholar
• Takada, Y. (2006). Multistage Estimation Procedures with Bounded Risk for the Normal Mean Under LINEX Loss Function, Sequential Analysis 25: 227–239.
   Google Scholar
• Takada, Y. and Nagao, H. (2004). Asymptotic Improvement of the Sample Mean Vector for Sequential Point Estimation of a Multivariate Normal Mean with a Linex Loss Function, Sientiae Mathematicae Japonicae Online 10: 71–79.
   Google Scholar
• Varian, H. R. (1975). A Bayesian Approach to Real Estate Assessment, in Studies in Bayesian Econometrics and Statistics, L. J. Savage, S. E. Fienberg, and A. Zellner eds., pp. 195–208, North Holland: Elsevier.
   Google Scholar
• Wiener, N. (1939). The Ergodic Theorem, Duke Mathematical Journal 5: 1–18.
   Google Scholar
• Woodroofe, M. (1977). Second Order Approximation for Sequential Point and Interval Estimation, Annals of Statistics 5: 984–995.
   Web of Science ®Google Scholar
• Woodroofe, M. (1982). Nonlinear Renewal Theory in Sequential Analysis, CBMS 39, Philadelphia: SIAM.
   Google Scholar
• Zacks, S. (2009). Stage-Wise Adaptive Designs, New York: Wiley.
   Google Scholar
• Zacks, S. and Mukhopadhyay, N. (2009). On Exact and Asymptotic Properties of Two-Stage and Sequential Estimation of the Normal Mean under Linex Loss, Communications in Statistics - Theory \textup& Methods 38: 2992–3014.
   Web of Science ®Google Scholar
• Zelen, M. (1966). Application of Exponential Models to Problems in Cancer Research, Journal of Royal Statistical Society 129: 368–398.
   Google Scholar
• Zellner, A. (1986). Bayesian Estimation and Prediction Using Asymmetric Loss Functions, Journal of American Statistical Association 81: 446–451.
   Web of Science ®Google Scholar