A Tribute to Frank Anscombe and Random Central Limit Theorem from 1952

REFERENCES

• Anscombe , F. J. ( 1946 ). Linear Sequential Rectifying Inspection for Controlling Fraction Defective , Journal of Royal Statistical Society, Supplement 8 : 216 – 222 .
   Google Scholar
• Anscombe , F. J. ( 1948a ). The Transformation of Poisson, Binomial and Negative-Binomial Data , Biometrika 35 : 246 – 254 .
   Web of Science ®Google Scholar
• Anscombe , F. J. ( 1948b ). The Validity of Comparative Experiments , Journal of Royal Statistical Society, Series A 111 : 181 – 211 .
   Google Scholar
• Anscombe , F. J. ( 1949a ). Large-Sample Theory of Sequential Estimation , Biometrika 36 : 455 – 458 .
   PubMed Web of Science ®Google Scholar
• Anscombe , F. J. ( 1949b ). The Statistical Analysis of Insect Counts Based on the Negative Binomial Distribution , Biometrics 5 : 165 – 173 .
   PubMed Web of Science ®Google Scholar
• Anscombe , F. J. (1950). Sampling Theory of the Negative Binomial and Logarithmic Series Distribution, Biometrika 37: 358–382.
   PubMed Web of Science ®Google Scholar
• Anscombe , F. J. ( 1952 ). Large-Sample Theory of Sequential Estimation , Proceedings of Cambridge Philosophical Society 48 : 600 – 607 .
   Web of Science ®Google Scholar
• Anscombe , F. J. ( 1953 ). Sequential Estimation , Journal of Royal Statistical Society, Series B 15 : 1 – 29 .
   Google Scholar
• Anscombe , F. J. ( 1973 ). Graphs in Statistical Analysis , American Statistician 27 : 17 – 21 .
   Web of Science ®Google Scholar
• Anscombe , F. J. ( 1981 ). Computing in Statistical Science through APL , New York : Springer .
   Google Scholar
• Anscombe , F. J. and Aumann , R. J. ( 1963 ). A Definition of Subjective Probability , Annals of Mathematical Statistics 34 : 199 – 205 .
   Google Scholar
• Anscombe , F. J. and Tukey , J. W. ( 1963 ). The Examination and Analysis of Residuals , Technometrics 5 : 141 – 160 .
   Web of Science ®Google Scholar
• Barnard , G. A. ( 1946 ). Sequential Tests in Industrial Statistics , Journal of Royal Statistical Society Supplement 8 : 1 – 26 .
   Google Scholar
• Barrigossi , J. A. F. ( 1997 ). Development of an IPM System for the Mexican Bean Beetle (Epilachna varivestis Mulsant) as a Pest of Dry Bean (Phaseolus vulgaris L.), Ph.D. diss., University of Nebraska, Lincoln, Nebraska.
   Google Scholar
• Bhattacharyya , P. K. and Mallik , A. ( 1973 ). Asymptotic Normality of the Stopping Times of Some Sequential Procedures , Annals of Statistics 1 : 1203 – 1211 .
   Web of Science ®Google Scholar
• Caliński , T. and Kageyama , S. ( 2000 ). Block Designs: A Randomization Approach: Vol. I. Analysis , Lecture Notes in Statistics 150 , New York : Springer .
   Google Scholar
• Callaert , H. and Janssen , P. ( 1978 ). The Berry-Esseen Theorem for U-Statistics , Annals of Statistics 6 : 417 – 421 .
   Web of Science ®Google Scholar
• Callaert , H. and Janssen , P. ( 1981 ). The Convergence Rate of Fixed-Width Sequential Confidence Intervals for the Mean , Sankhya, Series A 43 : 211 – 219 .
   Google Scholar
• Callaert , H. and Veraverbeke , N. ( 1981 ). The Order of Normal Approximation for a Studentized U-Statistic , Annals of Statistics 8 : 194 – 200 .
   Google Scholar
• Carroll , R. J. ( 1977 ). On the Asymptotic Normality of Stopping Times Based on Robust Estimators , Sankhya, Series A 39 : 355 – 377 .
   Google Scholar
• Chow , Y. S. , Hsiung , C. , and Lai , T. L. ( 1979 ). Extended Renewal Theory and Moment Convergence in Anscombe's Theorem , Annals of Probability 7 : 304 – 318 .
   Web of Science ®Google Scholar
• Chow , Y. S. and Martinsek , A. T. ( 1982 ). Bounded Regret of a Sequential Procedure for Estimation of the Mean , Annals of Statistics 10 : 909 – 914 .
   Web of Science ®Google Scholar
• Chow , Y. S. and Robbins , H. ( 1965 ). On the Asymptotic Theory of Fixed Width Confidence Intervals for the Mean , Annals of Mathematical Statistics 36 : 457 – 462 .
   Google Scholar
• Chow , Y. S. and Yu , K. F. ( 1981 ). The Performance of a Sequential Procedure for the Estimation of the Mean , Annals of Statistics 9 : 184 – 188 .
   Web of Science ®Google Scholar
• Csenki , A. ( 1980 ). On the Convergence Rate of Fixed-Width Sequential Confidence Intervals, Scandinavian Actuarial Journal 107–111.
   Google Scholar
• Csörgõ , M. and Rychlik , Z. ( 1980 ). Weak Convergence of Sequences of Random Elements with Random Indices , Mathematical Proceedings of Cambridge Philosophical Society 88 : 171 – 174 .
   Web of Science ®Google Scholar
• Csörgõ , M. and Rychlik , Z. ( 1981 ). Asymptotic Properties of Randomly Indexed Sequences of Random Variables , Canadian Journal of Statistics 9 : 101 – 107 .
   Google Scholar
• Geertsema , J. C. ( 1970 ). Sequential Confidence Intervals Based on Rank Tests , Annals of Mathematical Statistics 41 : 1016 – 1026 .
   Google Scholar
• Ghosh , B. K. and Sen , P. K. ( 1991 ). Handbook of Sequential Analysis , edited volume , New York : Dekker .
   Google Scholar
• Ghosh , M. ( 1980 ). Rate of Convergence to Normality for Random Means: Applications to Sequential Estimation , Sankhya, Series A 42 : 231 – 240 .
   Google Scholar
• Ghosh , M. and DasGupta , R. ( 1980 ). Berry-Esseen Theorems for U-Statistics in the Non IID Case, in Proceedings of Nonparametric Statistical Inference, pp. 219–313, Budapest, Hungary.
   Google Scholar
• Ghosh , M. and Mukhopadhyay , N. (1975). Asymptotic Normality of Stopping Times in Sequential Analysis, unpublished manuscript, Indian Statistical Institute, Calcutta, India.
   Google Scholar
• Ghosh , M. and Mukhopadhyay , N. ( 1976 ). On Two Fundamental Problems of Sequential Estimation , Sankhya, Series B 38 : 203 – 218 .
   Google Scholar
• Ghosh , M. and Mukhopadhyay , N. ( 1979 ). Sequential Point Estimation of the Mean When the Distribution is Unspecified , Communications in Statistics-Theory & Methods, Series A 8 : 637 – 652 .
   Web of Science ®Google Scholar
• Ghosh , M. , Mukhopadhyay , N. , and Sen , P. K. ( 1997 ). Sequential Estimation , New York : Wiley .
   Google Scholar
• Ghosh , M. and Sen , P. K. ( 1971 ). Sequential Confidence Intervals for the Regression Coefficient Based on Kendall's Tau , Calcutta Statistical Association Bulletin 20 : 23 – 36 .
   Google Scholar
• Ghosh , M. and Sen , P. K. ( 1972 ). On Bounded Length Confidence Intervals for the Regression Coefficient Based on a Class of Rank Statistics , Sankhya, Series A 34 : 33 – 52 .
   Google Scholar
• Gut , A. ( 2009 ). Stopped Random Walks, , 2nd ed. , New York : Springer .
   Google Scholar
• Hoeffding , W. ( 1948 ). A Class of Statistics with Asymptotically Normal Distribution , Annals of Mathematical Statistics 19 : 293 – 325 .
   Google Scholar
• Hoeffding , W. ( 1961 ). The Strong Law of Large Numbers for U-Statistics, Mimeo Series Number 302, Institute of Statistics, University of North Carolina, Chapel Hill.
   Google Scholar
• Johnson , N. L. and Kotz , S. ( 1969 ). Distributions in Statistics: Discrete Distributions , New York : Wiley .
   Google Scholar
• Khan , R. A. ( 1969 ). A General Method of Determining Fixed-Width Confidence Intervals , Annals of Mathematical Statistics 40 : 704 – 709 .
   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
• Landers , D. and Rogge , L. ( 1976 ). The Exact Order in the Central-Limit-Theorem for Random Summation, Zeitschrift Wahrscheinlichkeitstheorie Verw Gebiete 36: 269–283.
   Google Scholar
• Mahalanobis , P. C. ( 1940 ). A Sample Survey of Acreage under Jute in Bengal, with Discussion on Planning of Experiments, in Proceedings of Second Indian Statistical Conference, Calcutta, India: Statistical Publishing Society.
   Google Scholar
• Mukhopadhyay , N. ( 1975 ). Sequential Methods in Estimation and Prediction, Ph.D. diss., Indian Statistical Institute, Calcutta.
   Google Scholar
• Mukhopadhyay , N. ( 1978 ). Sequential Point Estimation of the Mean When the Distribution is Unspecified, Technical Report Number 312, University of Minnesota, Minneapolis.
   Google Scholar
• Mukhopadhyay , N. ( 2000 ). Probability and Statistical Inference , New York : Dekker .
   Google Scholar
• Mukhopadhyay , N. ( 2002 ). Sequential Sampling , in Encyclopedia of Environmetrics , vol. 4, A. H. Shaarawi and W. W. Piegorsch , eds., pp. 1983 – 1988 , Chichester : Wiley .
   Google Scholar
• Mukhopadhyay , N. ( 2011 ). Sequential Sampling , in International Encyclopedia of Statistical Science , M. Lovric , ed., pp. 1311 – 1314 , Berlin : Springer .
   Google Scholar
• Mukhopadhyay , N. , Datta , S. , and Chattopadhyay , S. ( 2004 ). Applied Sequential Methodologies , New York : Dekker .
   Google Scholar
• Mukhopadhyay , N. and de Silva , B. M. ( 2005 ). Two-Stage Estimation of Mean in a Negative Binomial Distribution with Applications to Mexican Bean Beetle Data , Sequential Analysis 24 : 99 – 137 .
   Google Scholar
• Mukhopadhyay , N. and de Silva , B. M. ( 2009 ). Sequential Methods and Their Applications , Boca Raton : CRC Press .
   Google Scholar
• Mukhopadhyay , N. and Diaz , J. ( 1985 ). Two-Stage Sampling for Estimating the Mean of a Negative Binomial Distribution , Sequential Analysis 4 : 1 – 18 .
   Google Scholar
• Mukhopadhyay , N. and Solanky , T. K. S. ( 1994 ). Multistage Selection and Ranking Procedures , New York : Dekker .
   Google Scholar
• Mukhopadhyay , N. and Vik , G. (1985). Asymptotic Results for Stopping Times Based on U-Statistics, Sequential Analysis 4: 83–110.
   Google Scholar
• Mulekar , M. S. and Young , L. J. ( 2004 ). Sequential Estimation in the Agricultural Sciences , in Applied Sequential Methodologies , N. Mukhopadhyay , S. Datta and S. Chattopadhyay , eds., pp. 293 – 318 , New York : Dekker .
   Google Scholar
• Ray , W. D. ( 1957 ). Sequential Confidence Intervals for the Mean of a Normal Population with Unknown Variance , Journal of Royal Statistical Society, Series B 10 : 133 – 143 .
   Google Scholar
• Rényi , A. ( 1957 ). On the Asymptotic Distribution of the Sum of a Random Number of Independent Random Variables , Acta Mathematica Academiae Scientiarum Hungaricae 8 : 193 – 199 .
   Google Scholar
• Robbins , H. ( 1959 ). Sequential Estimation of the Mean of a Normal Population , in Probability and Statistics , H. Cramer volume , U. Grenander , ed., pp. 235 – 245 , Uppsala : Almquist and Wiksell .
   Google Scholar
• Sen , P. K. ( 1981 ). Sequential Nonparametrics , New York : Wiley .
   Google Scholar
• Sen , P. K. ( 1985 ). Theory and Applications of Sequential Nonparametrics , CBMS Lecture Notes # 49 , Philadelphia : SIAM .
   Google Scholar
• Sen , P. K. and Ghosh , M. ( 1971 ). On Bounded Length Sequential Confidence Intervals Based on One-Sample Rank Order Statistics , Annals of Mathematical Statistics 42 : 189 – 203 .
   Google Scholar
• Serfling , R. J. ( 1980 ). Approximation Theorems of Mathematical Statistics , New York : Wiley .
   Google Scholar
• Shiryaev , A. N. ( 1969 ). Statistical Sequential Analysis: Optimal Stopping Rules , Moscow : Nauka (in Russian) .
   Google Scholar
• Siegmund , D. ( 1968 ). On the Asymptotic Normality of One-Sided Stopping Times , Annals of Mathematical Statistics 39 : 1493 – 1497 .
   Google Scholar
• Siegmund , D. ( 1985 ). Sequential Analysis: Tests and Confidence Intervals , New York : Springer .
   Google Scholar
• Sproule , R. N. ( 1969 ). A Sequential Fixed-Width Confidence Interval for the Mean of a U-Statistic, Ph.D. diss., Department of Statistics, University of North Carolina, Chapel Hill.
   Google Scholar
• Sproule , R. N. ( 1974 ). Asymptotic Properties of U-Statistics , Transactions of American Mathematical Society 199 : 55 – 64 .
   Web of Science ®Google Scholar
• Sproule , R. N. ( 1985 ). Sequential Nonparametric Fixed-Width Confidence Intervals for U-Statistics , Annals of Statistics 13 : 228 – 235 .
   Web of Science ®Google Scholar
• Sriram , T. N. ( 1987 ). Sequential Estimation of the Mean of a First-Order Stationary Autoregressive Process , Annals of Statistics 15 : 1079 – 1090 .
   Web of Science ®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 , Econometrica 17 : 77 – 78 .
   Google Scholar
• Taylor L. R., Woiwood , I. P. and Perry , J. N. ( 1978 ). The Density Dependence of Spatial Behavior and the Rarity of Randomness , Journal of Animal Ecology 16 : 426 – 482 .
   Google Scholar
• Wald , A. ( 1945 ). Sequential Tests of Statistical Hypotheses , Annals of Mathematical Statistics 16 : 426 – 482 .
   Google Scholar
• Wald , A. ( 1947 ). Sequential Analysis , New York : Wiley .
   Google Scholar
• Wald , A. and Wolfowitz , J. ( 1948 ). Optimum Character of the Sequential Probability Ratio Test , Annals of Mathematical Statistics 19 : 326 – 339 .
   Google Scholar
• Wijsman , R. ( 1991 ). Stopping Times: Termination, Moments, Distribution , in Handbook of Sequential Analysis , B. K. Ghosh and P. K. Sen , eds., pp. 67 – 119 , New York : Dekker .
   Google Scholar
• Willson , L. J. ( 1981 ). Estimation and Testing Procedures for the Parameters of the Negative Binomial Distribution, Ph.D. diss., Department of Statistics, Oklahoma State University, Stillwater.
   Google Scholar
• Willson , L. J. and Folks , J. L. ( 1983 ). Sequential Estimation of the Mean of the Negative Binomial Distribution , Sequential Analysis 2 : 55 – 70 .
   Google Scholar
• Woodroofe , M. ( 1977 ). Second Order Approximations 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 Lecture Notes #39 , Philadelphia : SIAM.
   Google Scholar
• Young , L. J. ( 2004 ). Sequential Testing in the Agricultural Sciences , in Applied Sequential Methodologies , N. Mukhopadhyay , S. Datta and S. Chattopadhyay , eds., pp. 381 – 410 , New York : Dekker .
   Google Scholar
• Young , L. J. and Young , J. H. ( 1998 ). Statistical Ecology , Boston : Kluwer .
   Google Scholar
• Zacks , S. ( 2009 ). Stage-Wise Adaptive Designs , New York : Wiley .
   Google Scholar
• Zou , G. ( 1998 ). Weed Population Sequential Sampling Plan and Weed Seedling Emergence Pattern Prediction, Ph.D. diss., Department of Plant Science, University of Connecticut, Storrs.
   Google Scholar
• Recommended by T. K. S. Solanky
   Google Scholar