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XV. References
Badrikian, A.: Seminaire sur les Fonctions Aleatoires Lineaires et les Mesures Cylindriques. Springer Lecture Notes 139 (1970).
_____, and Chevet, S.: Mesures cylindriques, Espaces de Wiener et Fonctions Aleatoires Gaussienes. Springer Lecture Notes 379 (1974).
Beran, R. J.: Estimating a distribution function. Ann. Stat. 5, 400–404 (1977).
_____: Efficient robust estimation for parametric models. Z. Wahr. (1981).
_____: Estimated sampling distributions: the bootstrap and its competitors. Preprint, 1981.
Bickel, P.: Quelques aspects de la statistique robuste. Ecole d’Ete St. Flour. To appear, 1979.
_____, and Doksum, K.: Mathematical Statistics: Basic Ideas and Selected Topics. Holden-Day, San Francisco, 1977.
_____ and Lehmann, E.: Descriptive statistics for nonparametric models I, II. Ann. Stat. 3, 1038–1069 (1975).
Bolthausen, E.: Convergence in distribution of minimum distance estimators. Metrika 24, 215–227 (1977).
Billingsley, P.: Convergence of Probability Measures. Wiley, New York 1968.
Blackwell, D.: Equivalent comparisons of experiments. Ann. Math. Stat. 24, 265–272 (1953).
Davies, R. B.: Asymptotic inference in time series. Adv. Appl. Prob. 5, 469–497 (1973).
Dunford, N., and Schwartz, J.: Linear Operators, vol. I. Interscience, New York, 1964.
Dvoretsky, A., Kiefer, J., and Wolfowitz, J.: Asymptotic minimax character of the sample distribution function and the classical multinomial estimator. Ann. Math. Stat. 27, 642–669 (1956).
Ferguson, T. S.: Mathematical Statistics. Academic Press, New York, 1967.
Gross, L.: Abstract Wiener spaces. Proc. Fifth Berkeley Symp. 2, 31–42 (1965).
Hajek, J.: Local asymptotic minimax and admissibility in estimation. Proc. Sixth Berkeley Symp. I 175–194 (1972).
_____: A characterization of limiting distributions of regular estimates. Z. Wahr. 14, 323–330 (1970).
_____, and Sidak, Z.: Theory of Rank Tests. Academic Press, New York, 1967.
Hasminskii, R. Z.: Lower bound for the risk of nonparametric estimates of the mode. Contrib. to Stat. (Hajek memorial volume) 91–97, Prague, 1979.
Huber, P. J.: Robust Statistical Procedures. SIAM Series in Appl. Math. (1977).
_____: Robust statistics: a review. Ann. Math. Stat. 43, 1041–1067 (1972).
Ibragimov, A.: Estimation of the spectral function of a stationary Gaussian process. Theory of Prob. 8, 391–430 (1963).
Johanssen, S.: Introduction to the Theory of Regular Exponential Families. University of Copenhagen, 1979.
Kato
Kiefer, J., and Wolfowitz, J.: On the deviation of the empirical distribution function of a vector chance variable. T. A. M. S. (1958).
_____: Asymptotically minimax estimation of concave and convex distribution functions. Z. Wahr. 34, 73–85 (1976).
Koshevnik, Ya. A, and Levit, B. Ya.: On a non parametric analogue of the information matrix. Theor. Prob. Appl. 21, 738–753 (1976).
Kuo, Hui-Hsiung: Gaussian Measures in Banach Space. Springer, 1975.
La Riccia, U. N.: Asymptotic properties of weighted L2 quantile distance estimators. Preprint, 1981.
Le Cam, L.: On some asymptotic properties of maximum likelihood estimates and related Bayes estimates. Univ. of Calif. Publ. Stat. I, 277–330 (1953).
_____: An extension of Wald’s theory of statistical decision functions. A.M.S. 26, 69–81 (1955).
_____: On the asymptotic theory of estimation and testing hypotheses. Proc. 3rd Berkeley Symp. I, 129–156 (1956).
_____: Sufficiency and asymptotic sufficiency. A.M.S. 35, 1419–1455 (1964).
_____: Theorie asymptotique de la decision statistique. Presses de l’Universite de Montreal (1969).
_____: Limits of experiments. Proc. 6th Berkeley Symp. I (1972).
_____: Convergence of estimates under dimensionality restrictions. Ann. Stat. 1, 38–53 (1973).
_____: On the assumptions used to prove asymptotic normality of maximum likelihood estimates. A.M.S. 41, 802–828 (1970).
Levit, B. Ya.: Efficiency of a class of non parametric estimates. Theor. Prob. Appl. 20, 723–740 (1975).
_____: Infinite dimensional information lower bounds. Theor. Prob. Appl. 23, 371–377 (1978).
_____, and Samarov, A. M.: Estimation of spectral functions. Problems of Information Transmission, 120–124 (1978).
Loeve, M.: Probability. Van Nostrand.
Millar, P. W.: Asymptotic minimax theorems for the sample distribution function. Z. Wahr. 48, 233–252 (1979).
_____: Robust estimation via minimum distance methods. Z. Wahr. 55, 73–89 (1971).
_____: Non parametric applications of an infinite dimensional convolution theorem. Preprint, 1982.
_____: An abstract minimax theorem, with applications to minimum distance estimation. Preprint, 1982.
_____: Optimal estimation of a general regression function. To appear, Ann. Stat., 1982.
_____: Robust tests of statistical hypotheses. Preprint, 1982.
Neveu, J.: Mathematical Foundations of the Calculus of Probability. Holden-Day, San Francisco, 1965.
Parr, W. C.: Minimum distance estimation: a bibliography. Preprint, 1980.
_____, and Schucany, W. R.: Minimum distance and robust estimation. J.A.S.A. (1981).
_____, and de Wet, T.: On minimum weighted Cramér-von Mises statistic estimation. Preprint, 1980.
Parthasarathy, K. R.: Probability Measures on Metric Spaces. Academic Press, 1967.
Pollard, D.: The minimum distance method of testing. Metrika 27, 43–70 (1980).
Prohorov, Yu. V.: Convergence of random processes and limit theorems in probability theory. Theor. Prob. Appl. (1956).
Reeds, J.: On the definition of von Mises functionals. To appear, Univ. of Chicago Press.
Roussas, G. G.: Contiguous Probability Measures: Some Applications in Statistics. Cambridge Univ. Press, 1972.
Schaeffer, H. H.: Topological Vector Spaces. Springer, 1970.
Serfling, R. J.: Approximation Theorems of Mathematical Statistics. John Wiley & Sons, New York, 1980.
Shorack, G.: Convergence of quantile and spacings processes with applications. A.M.S. 43, 1400–1411 (1972).
Skorokhod, A. V.: Integration in Hilbert Space. K. Wickwire, transl. Springer, New York, 1974.
Staudte, R. G.: Robust estimation. Queen’s Papers in Pure and Applied Math. #53 (1980).
Veitch, J.: Thesis, Univ. of Calif., 1982.
Wald, A.: Statistical Decision Functions. Wiley, New York, 1950.
Wellner, J. A.: Estimating a distribution function with random censorship. Preprint, 1981.
Wolfowitz, J.: The minimum distance method. A.M.S. 28, 75–88 (1957).
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Millar, P.W. (1983). The minimax principle in asymptotic statistical theory. In: Ecole d’Eté de Probabilités de Saint-Flour XI — 1981. Lecture Notes in Mathematics, vol 976. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0067986
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