REFERENCES

1. D.J.Aigner and G.G.Judge, Application of pre-test and Stein estimation to economic data, Econometrica, 1977, pp 1279--1288.

2. S.A.Aivazian, I.S.Yenyukov, and L.D.Meshalkin. Applied Statistics (in Russian), vol. 2: Investigation of dependencies, "Finansy i Statistika", Moscow, 1985.

3. S.A.Aivazian, V.M.Buchstaber, I.S.Yenyukov, L.D.Meshalkin. Applied Statistics (in Russian). vol. 3: Classification and Reduction of Dimension, "Finansy i Statistika", Moscow, 1989.

4. T.W.Anderson and R.R.Bahadur, Classification into multivariate normal distributions with different covariance matrices, Ann. Math. Statist. 1962, vol. 32, 2.

5. T.Anderson, An Introduction to Multivariate Statistical Analysis, John Wiley, N.Y., 1958.

6. L.V.Arkharov, Yu.N.Blagoveshchenskii, A.D.Deev, Limit theorems of multivariate statistics, Theory Probab. Appl. 1971, vol. 16, 3.

7. L.V.Arkharov, Limit theorems for characteristic roots of sample covariance matrices, Soviet Math. Doklady 1971, vol. 12, 1206--1209.

8. Z.D.Bai, Convergence rate of the expected spectral distribution of large random matrices, Ann. Probab. 1993, vol. 21, pp 649--672.

9. Z.D.Bai, J.W.Silverstein, No eigenvalues outside the support of the limiting spectral distribution of large-dimensional sample covariance matrices, Ann. Probab. 1998, vol. 26, pp 316--345.

10. A.J.Baranchik, A family minimax estimators of the mean of a multivariate normal distribution, Ann. Math. Statist., 1970, vol. 41, pp 642--645.

11. T.A.Baranova, On asymptotic residual for a generalized ridge regression, Fifth Internat. Conf. on Probab. and Statistics (Vilnius), 1989, vol. 3.

12. T.A.Baranova, I.F.Sentiureva, On the accuracy of asymptotic expressions for spectral functions and the resolvent of sample covariance matrices, in: Random Analysis, Moscow State University, Moscow 1987, pp 17--24.

13. A.C.Brandwein and W.E.Strawderman, Stein estimation: the spherically symmetric case. Statist. Sci., 1990, vol. 5, pp 356--369.

14. M.L.Clevenson and J.V.Zidek, Simultaneous estimation of the means for independent Poisson law, J. American Statist. Assoc., 1975, vol. 70, pp 698--705.

15. A.Cohen, Improved confidence intervals for the variance of a normal distribution, J. American Statist. Assoc., 1972, vol. 67, pp 382--387.

16. M.J.Daniels, R.E.Kass, Shrinkage estimators for covariance matrices, Biometrics, 2001, vol. 57, pp 1173--1184.

17. A.D.Deev, Representation of statistics of discriminant analysis, and asymptotic expansion when space dimensions are comparable with sample size, Soviet Math. Doklady, 1970, vol. 11, 1547--1550.

18. A.D.Deev, A discriminant function constructed from independent blocks, Engrg. Cybernetics, 1974, vol. 12, 153--156.

19. M.H.DeGroot. Optimal Statistical Decisions. McGraw-Hill, NY, 1970.

20. R.A.Fischer, The use of multiple measurements in taxonomic problems, Ann. Eugenics 7, 1936, pt.2, pp 179--188. Also in: Contribution to Mathematical Statistics, J. Wiley, N.Y., 1950.

21. V.L.Girko, An introduction to general statistical analysis. Theory Probab. Appl. 1987, vol. 32, p. 229--242.

22. V.L.Girko, Spectral Theory of Random Matrices (in Russian), "Nauka", Moscow, 1988.

23. V.L.Girko, General equation for the eigenvalues of empirical covariance matrices, Random Operators and Stochastic Equations, 1994, vol. 2, pt1: pp 13--24; pt2: pp 175--188.

24. V.L.Girko. Theory of Random Determinants, Kluwer Academic Publishers, 1990.

25. V.L.Girko. Statistical Analysis of Observations of Increasing Dimension, Kluwer Academic Publishers, Dordrecht, 1995.

26. V.L.Girko. Theory of Stochastic Equations. vol. 1 and 2. Kluwer Academic Publishers, Dordrecht/Boston/London, 2001.

27. C.Goutis and G.Casella, improved invariant confidence intervals for a normal variance, Ann. Statist., 1991, vol. 19, pp 2015--2031.

28. E.Green and W.E.Strawderman, A James--Stein type estimator for combining unbiased and possibly unbiased estimators, J. American Statist. Assoc., 1991, vol. 86, pp 1001--1006.

29. M.H.J.Gruber. Improving Efficiency by Shrinkage. Marcel Dekker Inc., N. Y., 1998.

30. Das Gupta and B.K.Sinha, A new general interpretation of the Stein estimators and how it adapts: Application, J. Statist. Plann. Inference, 1999, vol. 75, pp 247--268.

31. Y.Y.Guo and N.Pal, A sequence of improvements over the James--Stein estimator, J. Multiv. Analysis, 1992, vol. 42, pp 302--312.

32. K.Hoffmann, Improved estimation of distribution parameters: Stein-type estimators, Teubner, Leipzig 1992 (Teubner-Texte zur Mathematik, Bd 128).

33. K.Hoffmann, Stein estimation -- a review, Statistical Papers, 2000, vol. 41, pp 127--158.

34. P.Hebel, R.Faivre, B.Goffinat, and D.Wallach, Shrinkage estimators applied to prediction of French winter wheat yields, Biometrics, 1993, vol. 40, pp 281--293.

35. I.A.Ibragimov, R.Z.Khas'minski. Statistical Estimation. Asymptotical Theory. Springer, Berlin, 1981.

36. W.James, C.Stein, Estimation with the quadratic loss, In: Proc. Fourth Berkley Symposium Math. Statist. Probab., 1960, vol. 2; pp 361--379.

37. G.Judge and M.E.Bock. The Statistical Implication of Pretest and Stein Rule Estimators in Econometrics, North Holland, Amsterdam, 1978.

38. T.Kubokawa, An approach to improving the James--Stein estimator, J. Multiv. Anal., 1991, vol. 36, pp 121--126.

39. T.Kubokawa, Shrinkage and modification techniques in estimation, Commun. Stat. Theory and Appl., 1999, vol. 28, pp 613--650.

40. T.Kubokawa, M.S.Srivastava, Estimating the covariance mat-rix: A new approach. J. Multiv. Anal., 2003, vol. 86, pp 28--47.

41. A.N.Kolmogorov, Problems of the Probability Theory (in Russian), Probab. Theory Appl., 1993, vol. 38, 2.

42. J.M.Maata and G.Casella, Development in decision-theoretical variance estimation, Statist. Sci., 1990, vol. 5, pp 90--120.

43. V.A.Marchenko and L.A.Pastur, Distribution of eigenvalues in some sets of random matrices, Math. USSR Sbornik 1967, vol. 1, pp 457--483.

44. A.S.Mechenov. Pseudosoltions of Linear Functional Equations. Springer Verlag, NY LLC, 2005.

45. L.D.Meshalkin, V.I.Serdobolskii, Errors in the classification of multivariate observations, Theory Probab. Appl., 1978, vol. 23, pp 741--750.

46. L.D.Meshalkin, Assignement of numeric values to nominal variables (in Russian), Statist. Problems of Control, Vilnius, 1976, vol. 14, pp 49--55.

47. L.D.Meshalkin, The increasing dimension asymptotics in multivariate analysis, The First World Congress of the Bernoulli Society, vol. 1, "Nauka", Moscow, 1986, pp 197--199.

48. N.Pal, B.K.Sinha, Estimation of a common mean of a several multivariate normal populations: a review. Far East J. Math. Sci. 1996, Special volume, pt 1, pp 97--110.

49. N.Pal and A.Eflesi, Improved estimation of a multivariate normal mean vector and the dispersion matrix: how one effects the other, Sankhya series A, 1996, vol. 57, pp 267--286.

50. L.A.Pastur, Spectra of random self-adjoint operators, Russian Math. Surveys, 1969, vol. 28, 1.

51. Sh.Raudys, Results in statistical discriminant analysis: a review of the former Soviet Union literature, J. Multiv. Analysis, 2004, vol. 89, 1, pp 1--35.

52. G.G.Roussas, Contiguity of Probability Measures, Camb. University Press, Cambridge, 1972.

53. S.K.Sarkar, Stein-type improvements of confidence intervals for the generalized variance, Ann. Inst. Statist. Math., 1991, vol. 43, pp 369--375.

54. A.V.Serdobolskii. The asymptotically optimal Bayes solution to systems of a large number of linear algebraic equations, 53th IMS Ann. Meeting Second Bernoulli Soc. World Congress, Uppsala, Sweden, 1990, CP-387, pp. 177--178.

55. A.V.Serdobolskii, Solution of empirical SLAE unimprovable in the mean (in Russian), Review of Applied and Industrial Mathematics, 2001, vol. 8, 1, p. 321.

56. A.V.Serdobolskii, Unimprovable solution to systems of empirical linear algebraic equations, Statist. Probab. Letters, 2002, vol. 60, 1--6;
Article full text PDF (95.9 KB) pp 1--6

57. A.V.Serdobolskii, V.I.Serdobolskii, Estimation of the solution of high-order random systems of linear algebraic equations, J. Math. Sci., 2004, vol. 119, 3, pp 315--320.

58. A.V.Serdobolskii, V.I.Serdobolskii, Estimation of solutions of random sets of simultaneous linear algebraic equations of high order, J. Math. Sci., 2005, vol. 126, 1, pp 961--967.

59. V.I.Serdobolskii, On classification errors induced by sampling, Theory Probab. Appl., 1979, vol. 24, p. 130--144.

60. V.I.Serdobolskii, Discriminant Analysis of Observations of High Dimension (in Russian), publ. by Sci. Council on the Joint Problem "Cybernetics", USSR Acad. Sci., Moscow, 1979, pp 1--57.

61. V.I.Serdobolskii, Discriminant analysis for a large number of variables, Soviet Math. Doklady, 1980, vol. 22, 314--319.
62. V.I.Serdobolskii, The effect of weighting of variables in the discriminant function, Third Intern. Conf. on Probab. Theory and Math. Statistics (Vilnius), 1981, vol. 2, pp 147--148.

63. V.I.Serdobolskii, On minimum error probability in discriminant analysis, Soviet Math. Doklady, 1983, vol. 27, pp 720--725.

64. V.I.Serdobolskii, On estimation of the expectation values under increasing dimension, Theory of Probab. Appl., 1984, vol. 29, 1.

65. V.I.Serdobolskii, The resolvent and spectral functions of sample covariance matrices of increasing dimension, Russian Math. Surveys, 1985, 40:2, pp 232--233.

66. V.I.Serdobolskii, A.V.Serdobolskii, Asymptotically optimal regularization for the solution of systems of linear algebraic equations with random coefficients, Moscow State University Vestnik, "Computational Math. and Cybernetics", Moscow, 1991, vol. 15, 2.

67. V.I.Serdobolskii, Spectral properties of sample covariance matrices, Theory Probab. Appl., 1995, vol. 40, p. 777.

68. V.I.Serdobolskii, Main part of the quadratic risk for a class of essentially multivariate regressions, Intern. Conf. "Asymptotic Methods in Probabability Theory and Mathematical Statistics", St. Peterburg, 1998, 247--250.

69. V.I.Serdobolskii, Theory of essentially multivariate statistical analysis, Russian Math. Surveys, 1999, vol. 54, 2, pp 351--379.

70. V.I.Serdobolskii, Constructive foundations of randomness, in: "Foundations of Probability and Physics", World Scientific, New Jersey--London, 2000, pp 335--349.

71. V.I.Serdobolskii. Multivariate Statistical Analysis. A High-Dimensional Approach. Kluwer Academic Publishers, 2000.

72. V.I.Serdobolskii, Normal model for distribution free multivariate analysis, Statist. and Probab. Letters, 2000, vol. 48, pp 353--360.
See also: V.I.Serdobolskii, Normalization in estimation of the multivariate procedure quality, Soviet Math. Doklady, 1995, v.343.

73. V.I.Serdobolskii, A.I.Glusker, Spectra of Large-Dimensional Sample Covariance Matrices, preprint 2002, 1--19
at: www.mathpreprints.com/math/Preprint/vadim/20020622/1

74. V.I.Serdobolskii, Estimators shrinkage to reduce the quadratic risk, Doklady Mathematics, ISSN 1064-5624, 2003, vol. 67, 2, pp 196--202.

75. V.I.Serdobolskii, Matrix shrinkage of high-dimensional expectation vectors, Journal of Multivariate Analysis, 2005, vol. 92, pp 281--297.

76. A.N.Shiryaev. Probability. Springer Verlag, N.Y.- Berlin, 1984.

77. J.W.Silverstein and Z.D.Bai, On the empirical distributions of eigenvalues of a class of large-dimensional random matrices, J. Multiv. Analysis 1995, vol. 54, pp 175--192.

78. J.W.Silverstein and S.I.Choi, Analysis of the limiting spectra of large dimensional random matrices, J. Multiv. Analysis 1995, vol. 54, pp 295--309.

79. C.Stein, Inadmissibility of the usual estimator for the mean of a multivariate normal distribution, Proc. of the Third Berkeley Symposium, Math. Statist. Probab., 1956, vol. 1, pp 197--206.

80. C.Stein, Inadmissibility of the usual estimator for the variance of a normal distribution with unknown mean, Ann. Inst. Statist. Math., 1964, vol. 16, pp 155--160.

81. C.Stein, Estmation of the mean of a multivariate normal distribution, Ann. Statist., 1981, vol. 9, pp 1135--1151.

82. V.S.Stepanov. Some Properties of High Dimension Linear Discriminant Analysis (in Russian), Author's summary, Moscow, Moscow States University, 1987.

83. A.N.Tikhonov and V.Ya.Arsenin. Solution of Ill-Posed Problem. Wiley, N.Y., 1977.

84. H.D.Vinod, Improved Stein-rule estimator for regression problems, J. Econometrics, 1980, vol. 12, pp 143--150.

85. A.Wald, On a statistical problem arising in the classification of an individual in one of two groups, Ann. Math. Statist., 1944, vol. 15, pp 147--163.

86. A.Wald, Estimation of a parameter when the number of unknown parameters increases indefinitely with the number of observations, Ann. Math. Statist., 1948, vol. 19, pp 220--227.

87. A.Wald. Statistical Decision Functions. Wiley, NY, 1970.

88. E.P.Wigner, On the distribution of roots of certain symmetric matrices, Ann. Math., 1958, vol. 67, pp 325--327.

89. E.P.Wigner, Random matrices in physics, Ann. of Inst. Math. Statistics, 1967, vol. 9, 1.

90. Q.Yin and P.R.Krishnaiah, On limit of the largest eigenvalue of the large-dimensional sample covariance matrix, Probab. Theory Related Fields, 1988, vol. 78, pp 509--521.

91. S.Zachs. The Theory of Statistical Inference, J.Wiley, 1971.

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