REFERENCES

  1. 1. A. Agresti, Categorical Data Analysis, 3rd ed., Wiley, New York, 2012.
  2. 2. T. W. Anderson, Maximum likelihood estimates for a multivariate normal distribution when some observations are missing, J. Am. Stat. Assoc. 52 (1957), 200-203.
  3. 3. J. D. Auble, Extended tables for the Mann-Whitney statistic, Bull. Inst. Educ. Res. 1 (1953), No. i-iii, 1-39.
  4. 4. D. Bernstein, Sur une propriété charactéristique de la loi de Gauss, Trans. Leningrad Polytech. Inst. 3 (1941), 21-22.
  5. 5. P. J. Bickel, On some robust estimators of location, Ann. Math. Stat. 36 (1965), 847-858.
  6. 6. P. Billingsley, Probability and Measure,2nd ed., Wiley, New York, 1986.
  7. 7. D. Birkes, Generalized likelihood ratio tests and uniformly most powerful tests, Am. Stat. 44 (1990), 163-166.
  8. 8. Z. W. Birnbaum and F. H. Tingey, One-sided confidence contours for probability distribution functions, Ann. Math. Stat. 22 (1951), 592-596.
  9. 9. Z. W. Birnbaum, Numerical tabulation of the distribution of Kolmogorov's statistic for finite sample size, J. Am. Stat. Assoc., 17 (1952), 425-441.
  10. 10. D. Blackwell, Conditional expectation and unbiased sequential estimation, Ann. Math. Stat. 18 (1947), 105-110.
  11. 11. J. Boas, A note on the estimation of the covariance between two random variables using extra information on the separate variables, Stat. Neerl. 21 (1967), 291-292.
  12. 12. D. G. Chapman and H. Robbins, Minimum variance estimation without regularity assumptions, Ann. Math. Stat. 22 (1951), 581-586.
  13. 13. S.D. Chatterji, Some elementary characterizations of the Poisson distribution, Am. Math. Mon. 70 (1963), 958-964.
  14. 14. K. L. Chung and P. Erdös, On the application of the Borel-Cantelli lemma, Trans. Am. Math.Soc. 72 (1952), 179–186.
  15. 15. K. L. Chung, A Course in Probability Theory, Harcourt, Brace & World, New York, 1968.
  16. 16. H. Cramér, Über eine Eigenschaft der normalen Verteilungsfunktion, Math. Z. 41 (1936), 405–414.
  17. 17. H. Cramér, Mathematical Methods of Statistics, Princeton University Press, Princeton, N.J.,1946.
  18. 18. H. Cramér, A contribution to the theory of statistical estimation, Skand. Aktuarietidskr. 29 (1946), 85–94.
  19. 19. J. H. Curtiss, A note on the theory of moment generating functions, Ann. Math. Stat. 13 (1942), 430–433.
  20. 20. D. A. Darmois, Sur diverses propriétés charactéristique de la loi de probabilité de Laplace-Gauss, Bull. Int. Stat. Inst. 23 (1951), part II, 79–82.
  21. 21. M. M. Desu, Optimal confidence intervals of fixed width, Am. Stat. 25 (1971), No. 2, 27–29.
  22. 22. B. Efron, Bootstrap methods: Another look at the jackknife. Ann. Stat. 7 (1979), 1–26.
  23. 23. B. Efron and R. J. Tibshirani, An Introduction to Bootstrap, Chapman Hall, New York, 1993.
  24. 24. W. Feller, Über den Zentralen Granzwertsatz der Wahrscheinlichkeitsrechnung, Math. Z. 40 (1935), 521–559; 42 (1937), 301–312.
  25. 25. W. Feller, An Introduction to Probability Theory and Its Applications, Vol.1, 3rd ed., Wiley, New York, 1968.
  26. 26. W. Feller, An Introduction to Probability Theory and Its Applications, Vol. 2, 2nd ed., Wiley, New York, 1971.
  27. 27. K. K. Ferentinos, Shortest confidence intervals for families of distributions involving truncation parameters, Am. Stat. 44 (1990), 40–41.
  28. 28. T. S. Ferguson, Mathematical Statistics, Academic Press, New York, 1967.
  29. 29. T. S. Ferguson, A Course in Large Sample Theory, Chapman & Hall, London, 1996.
  30. 30. R. A. Fisher, On the mathematical foundations of theoretical statistics, Phil. Trans. R. Soc. A222 (1922), 309–386.
  31. 31. M. Fisz, Probability Theory and Mathematical Statistics, 3rd ed., Wiley, 1963.
  32. 32. D. A. S. Fraser, Nonparametric Methods in Statistics, Wiley, New York, 1965.
  33. 33. D. A. S. Fraser, The Structure of Inference, Wiley, New York, 1968.
  34. 34. M. Fréchet, Sur l’extension de certaines evaluations statistiques au cas de petits echantillons, Rev. Inst. Int. Stat. 11 (1943), 182–205.
  35. 35. J. D. Gibbons, Nonparametric Statistical Inference, Dekker, New York, 1985.
  36. 36. B. V. Gnedenko, Sur la distribution limite du terme maximum d'une série aléatoire, Ann. Math. 44 (1943), 423–453.
  37. 37. W. C. Guenther, Shortest confidence intervals, Am. Stat. 23 (1969), No. 1, 22–25.
  38. 38. W. C. Guenther, Unbiased confidence intervals, Am. Stat. 25 (1971), No. 1, 51–53.
  39. 39. E. J. Gumbel, Distributions à plusieurs variables dont les marges sont données, C. R. Acad. Sci. Paris 246 (1958), 2717–2720.
  40. 40. J. H. Hahn and W. Nelson, A problem in the statistical comparison of measuring devices, Technometrics 12 (1970), 95–102.
  41. 41. P. R. Halmos and L. J. Savage, Application of the Radon-Nikodym theorem to the theory of sufficient statistics, Ann. Math. Stat. 20 (1949), 225–241.
  42. 42. P. R. Halmos, Measure Theory, Van Nostrand, New York, 1950.
  43. 43. J. L. Hodges and E. L. Lehmann, Some problems in minimax point estimation, Ann. Math. Stat. 21 (1950), 182–197.
  44. 44. J. L. Hodges, Jr. and E. L. Lehmann, Estimates of location based on rank tests, Ann. Math. Stat. 34(1963), 598–611.
  45. 45. W. Hoeffding, A class of statistics with asymptotically normal distribution, Ann. Math. Stat. 19 (1948), 293–325.
  46. 46. D. Hogben, The distribution of the sample variance from a two-point binomial population, Am. Stat. 22 (1968), No. 5, 30.
  47. 47. V. S. Huzurbazar, The likelihood equation consistency, and maxima of the likelihood function, Ann. Eugen. (London) 14 (1948), 185–200.
  48. 48. M. Kac, Lectures in Probability, The Mathematical Association of America, Washinton, D.C.,1964–1965.
  49. 49. W. C. M. Kallenberg et al., Testing Statistical Hypotheses: Worked Solutions, CWI, Amster-dam, 1980.
  50. 50. J. F. Kemp, A maximal distribution with prescribed marginals, Am. Math. Mon. 80 (1973), 83.
  51. 51. M. G. Kendall, Rank Correlation Methods, 3rd ed., Charles Griffin, London, 1962.
  52. 52. J. Kiefer, On minimum variance estimators, Ann. Math. Stat. 23 (1952), 627–629.
  53. 53. A. N. Kolmogorov, Sulla determinazione empirica di una legge di distribuzione, G. Inst. Ital. Attuari 4(1933), 83–91.
  54. 54. A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis, Vol. 2, Graylock Press, Albany, N.Y., 1961.
  55. 55. C. H. Kraft and C. Van Eeden, A Nonparametric Introduction to Statistics, Macmillan, New York, 1968.
  56. 56. W. Kruskal, Note on a note by C. S. Pillai, Am. Stat. 22 (1968), No. 5, 24–25.
  57. 57. G. Kulldorf, On the condition for consistency and asymptotic efficiency of maximum likelihood estimates, Skand. Aktuarietidskr. 40 (1957), 129–144.
  58. 58. R. G. Laha and V. K. Rohatgi, Probability Theory, Wiley, New York, 1979.
  59. 59. J. Lamperti, Density of random variable, Am. Math. Mon. 66 (1959), 317.
  60. 60. J. Lamperti and W. Kruskal, Solution by W. Kruskal to the problem “Poisson Distribution” posed by J. Lamperti, Am. Math. Mon. 67 (1960), 297–298.
  61. 61. E. L. Lehmann, Nonparametrics: Statistical Methods Based on Ranks, Holden-Day, San Francisco, C.A., 1975.
  62. 62. E. L. Lehmann, An interpretation of completeness and Basu’s theorem, J. Am. Stat. Assoc. 76 (1981), 335–340.
  63. 63. E. L. Lehmann, Theory of Point Estimation, Wiley, New York, 1983.
  64. 64. E. L. Lehmann, Testing Statistical Hypotheses, 2nd ed., Wiley, New York, 1986.
  65. 65. E. L. Lehmann and H. Scheffé, Completeness, similar regions, and unbiased estimation, Sankhya, Ser. A, 10 (1950), 305–340.
  66. 66. M. Loève, Probability Theory, 4th ed., Springer-Verlag, New York, 1977.
  67. 67. E. Lukacs, A characterization of the normal distribution, Ann. Math. Stat. 13 (1942), 91–93.
  68. 68. E. Lukacs, Characterization of populations by properties of suitable statistics, Proc. Third Berkeley Symp. 2 (1956), 195–214.
  69. 69. E. Lukacs, Characteristic Functions, 2nd ed., Hafner, New York, 1970.
  70. 70. E. Lukacs and R. G. Laha, Applications of Characteristic Functions, Hafner, New York, 1964.
  71. 71. H.B. Mann and D. R. Whitney, On a test whether one of two random variables is stochastically larger than the other, Ann. Math. Stat. 18 (1947), 50–60.
  72. 72. F. J. Massey, Distribution table for the deviation between two sample cumulatives, Ann. Math. Stat. 23 (1952), 435–441.
  73. 73. M. V. Menon, A characterization of the Cauchy distribution, Ann. Math. Stat. 33 (1962), 1267–1271.
  74. 74. L. H. Miller, Table of percentage points of Kolmogorov statistics, J. Am. Stat. Assoc. 51 (1956),111–121.
  75. 75. M. G. Natrella, Experimental Statistics, Natl. Bur. Stand. Handb. 91, Washington, D.C., 1963.
  76. 76. J. Neyman and E. S. Pearson, On the problem of the most efficient tests of statistical hypotheses, Phil. Trans. R. Soc. A231 (1933), 289–337.
  77. 77. J. Neyman and E. L. Scott, Consistent estimates based on partially consistent observations, Econometrica 16 (1948), 1–32.
  78. 78. E. H. Oliver, A maximum likelihood oddity, Am. Stat. 26 (1972), No. 3, 43–44.
  79. 79. D. B. Owen, Handbook of Statistical Tables, Addison-Wesley, Reading, M.A., 1962.
  80. 80. E. J. G. Pitman and E. J. Williams, Cauchy-distributed functions of Cauchy variates, Ann. Math. Stat. 38 (1967), 916–918.
  81. 81. J. W. Pratt, Length of confidence intervals, J. Am. Stat. Assoc. 56 (1961), 260–272.
  82. 82. B. J. Prochaska, A note on the relationship between the geometric and exponential distributions, Am. Stat. 27 (1973), 27.
  83. 83. P. S. Puri, On a property of exponential and geometric distributions and its relevance to multivariate failure rate, Sankhya, Ser. A, 35 (1973), 61–68.
  84. 84. D. A. Raikov, On the decomposition of Gauss and Poisson laws (in Russian), Izv. Akad. Nauk. SSSR, Ser. Mat. 2 (1938), 91–124.
  85. 85. R. R. Randles and D. A. Wolfe, Introduction to the Theory of Nonparametric Statistics, Krieger, Melbourne, F.L., 1991.
  86. 86. C. R. Rao, Information and the accuracy attainable in the estimation of statistical parameters, Bull. Calcutta Math. Soc. 37 (1945), 81–91.
  87. 87. C. R. Rao, Sufficient statistics and minimum variance unbiased estimates, Proc. Cambridge Phil. Soc. 45 (1949) 213–218.
  88. 88. C. R. Rao, Linear Statistical Inference and Its Applications, 2nd ed., Wiley, New York, 1973.
  89. 89. S. C. Rastogi, Note on the distribution of a test statistic, Am. Stat. 23 (1969), 40–41.
  90. 90. V. K. Rohatgi, Statistical Inference, Wiley, New York, 1984.
  91. 91. V. K. Rohatgi, On the moments of F(X) when F is discrete, J. Stat. Comp. Simul. 29 (1988), 340–343.
  92. 92. V. I. Romanovsky, On the moments of the standard deviations and of the correlation coefficient in samples from a normal population, Metron 5 (1925), No. 4, 3–46.
  93. 93. L. Rosenberg, Nonnormality of linear combinations of normally distributed random variables, Am. Math. Mon. 72 (1965), 888–890.
  94. 94. J. Roy and S. Mitra, Unbiased minimum variance estimation in a class of discrete distributions, Sankhya 18 (1957), 371–378.
  95. 95. R. Roy, Y. LePage, and M. Moore, On the power series expansion of the moment generating function, Am. Stat. 28 (1974), 58–59.
  96. 96. H. L. Royden, Real Analysis, 2nd ed., Macmillan, New York, 1968.
  97. 97. Y. D. Sabharwal, A sequence of symmetric Bernoulli trials, SIAM Rev. 11 (1969), 406-H)9.
  98. 98. A. Sampson and B. Spencer, Sufficiency, minimal sufficiency, and lack thereof, Am. Stat. 30 (1976) 34-35. Correction, 31 (1977), 54.
  99. 99. P. A. Samuelson, How deviant can you be? J. Am. Stat. Assoc. 63 (1968), 1522–1525.
  100. 100. H. Scheffé, A useful convergence theorem for probability distributions, Ann. Math. Stat. 18 (1947), 434–438.
  101. 101. H. Scheffé, The Analysis of Variance, Wiley, New York, 1961.
  102. 102. R. J. Serfling, Approximation Theorems of Mathematical Statistics, Wiley, New York, 1979.
  103. 103. D. N. Shanbhag and I. V. Basawa, On a characterization property of the multinomial distribution, Ann. Math. Stat. 42 (1971), 2200.
  104. 104. L. Shepp, Normal functions of normal random variables, SIAM Rev. 4 (1962), 255–256.
  105. 105. A. E. Siegel, Film-mediated fantasy aggression and strength of aggression drive, Child Dev. 27 (1956), 365–378.
  106. 106. V. P. Skitovitch, Linear forms of independent random variables and the normal distribution law, Izv. Akad. Nauk. SSSR. Ser. Mat. 18 (1954), 185–200.
  107. 107. N. V. Smirnov, On the estimation of the discrepancy between empirical curves of distributions for two independent samples (in Russian), Bull. Moscow Univ. 2 (1939), 3–16.
  108. 108. N. V. Smirnov, Approximate laws of distribution of random variables from empirical data (in Russian), Usp. Mat. Nauk. 10 (1944), 179–206.
  109. 109. R. C. Srivastava, Two characterizations of the geometric distribution, J. Am. Stat. Assoc. 69 (1974), 267–269.
  110. 110. S. M. Stigler, Completeness and unbiased estimation, Am. Stat. 26 (1972), 28–29.
  111. 111. P. T. Strait, A note on the independence and conditional probabilities, Am. Stat. 25 (1971), No. 2, 17–18.
  112. 112. R. F. Tate and G. W. Klett, Optimum confidence intervals for the variance of a normal distribution, J. Am. Stat. Assoc. 54 (1959), 674–682.
  113. 113. W. A. Thompson, Jr., Applied Probability, Holt, Rinehart and Winston, New York, 1969.
  114. 114. H. G. Tucker, A Graduate Course in Probability, Academic Press, New York, 1967.
  115. 115. A. Wald, Note on the consistency of the maximum likelihood estimate, Ann. Math. Stat. 20 (1949), 595–601.
  116. 116. G. N. Watson, A Treatise on the Theory of Bessel Functions, 2nd ed., Cambridge University Press, Cambridge, 1966.
  117. 117. D. V. Widder, Advanced Calculus, 2nd ed., Prentice-Hall, Englewood Cliffs, N.J., 1961.
  118. 118. S. S. Wilks, Mathematical Statistics, Wiley, New York, 1962.
  119. 119. J. Wishart, The generalized product-moment distribution in samples from a normal multivariate population, Biometrika 20A (1928), 32–52.
  120. 120. C. K. Wong, A note on mutually independent events. Am. Stat. 26 (1972), 27.
  121. 121. S. Zacks, The Theory of Statistical Inference, Wiley, New York, 1971.
  122. 122. P. W. Zehna, Invariance of maximum likelihood estimation, Ann. Math. Stat. 37 (1966), 755.
..................Content has been hidden....................

You can't read the all page of ebook, please click here login for view all page.
Reset
18.222.164.141