Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.

Full text of review: PDF   This review is available free of charge.
Book Information:

Authors: Galen R. Shorack and Jon A. Wellner
Title: Empirical processes with applications to statistics
Additional book information: Wiley Series in Probability and Mathematical Statistics, John Wiley and Sons, New York, Chichester, Brisbane, Toronto, Singapore, 1986, xxvii + 938 pp., $59.95. ISBN 0-471-86725-X.

References [Enhancements On Off] (What's this?)

  • R. R. Bahadur (1966), A note on quantiles in large samples, Ann. Math. Statist. 37, 577-580. MR 189095
  • J. Bernoulli (1713), Ars Coniectandi. I-II, III-IV, Oswald's Klassiker der Exacten Wissenschaften, No. 108, W. Engelmann, Leipzig, 1899.
  • P. Billingsley (1968), Convergence of probability measures, Wiley, New York. MR 233396
  • L. Brieman (1968), Probability, Addison-Wesley, Reading, Mass.
  • J. Bretagnolle, Statistique de Kolmogorov-Smirnov pour un échantillon non équiréparti, Statistical and physical aspects of Gaussian processes (Saint-Flour, 1980), Colloq. Internat. CNRS, vol. 307, CNRS, Paris, 1981, pp. 39–44 (French, with English summary). MR 716526
  • D. R. Brillinger (1969), The asymptotic representation of the sample distribution function, Bull. Amer. Math. Soc. 75, 545-547. MR 243659
  • F. P. Cantelli (1933), Sulla determinazione empirica delle leggi di probabilità, Giorn. 1st. Ital. Attuari 4, 421-424.
  • Miklós Csörgő, Quantile processes with statistical applications, CBMS-NSF Regional Conference Series in Applied Mathematics, vol. 42, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1983. MR 745130
  • Miklós Csörgő, Sándor Csörgő, and Lajos Horváth, An asymptotic theory for empirical reliability and concentration processes, Lecture Notes in Statistics, vol. 33, Springer-Verlag, Berlin, 1986. MR 856407
  • M. Csörgő and P. Révész, A new method to prove strassen type laws of invariance principle. II, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 31 (1975), no. 4, 261–269. MR 1554018,
  • M. Csörgő and P. Révész, Strong approximations in probability and statistics, Probability and Mathematical Statistics, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1981. MR 666546
  • M. Donsker (1951), An invariance principle for certain probability limit theorems, Mem. Amer. Math. Soc. 6, 1-12. MR 40613
  • M. Donsker (1952), Justification and extension of Doob's heuristic approach to the Kolmogorov-Smirnov theorems, Ann. Math. Statist. 23, 277-281. MR 47288
  • J. L. Doob (1949), Heuristic approach to the Kolmogorov-Smirnov theorems, Ann. Math. Statist. 20, 393-403. MR 30732
  • R. M. Dudley, A course on empirical processes, École d’été de probabilités de Saint-Flour, XII—1982, Lecture Notes in Math., vol. 1097, Springer, Berlin, 1984, pp. 1–142. MR 876079,
  • P. Erdős and M. Kac (1946), On certain limit theorems of the theory of probability, Bull. Amer. Math. Soc. 52, 292-302. MR 15705
  • W. Feller (1948), On the Kolmogorov-Smirnov limit theorems for empirical distributions, Ann. Math. Statist. 19, 177-189. MR 25108
  • Peter Gänssler, Empirical processes, Institute of Mathematical Statistics Lecture Notes—Monograph Series, vol. 3, Institute of Mathematical Statistics, Hayward, CA, 1983. MR 744668
  • V. Glivenko (1933), Sulla determinazione empirica della legge di probabilità, Giorn. Ist. Ital. Attuari 4, 92-99.
  • B. V. Gnedenko and V. S. Korolyuk (1951), On the maximum discrepancy between two empirical distributions, Selected Transl. Math. Statist. Prob. 1 (1961), 13-16; original in Dokl. Akad. Nauk SSSR 80, 525. MR 116418
  • M. Kac (1946), On the average of a certain Wiener functional and a related limit theorem in calculus of probability, Trans. Amer. Math. Soc. 59, 404-414. MR 16570
  • M. Kac and A. J. F. Siegert (1947), An explicit representation of a stationary Gaussian process, Ann. Math. Statist. 18, 438-442. MR 21672
  • J. Kiefer (1967), On Bahadur's representation of sample quantiles, Ann. Math. Statist. 38, 1323-1342. MR 217844
  • J. Kiefer (1969), On the deviations in the Skorokhod-Strassen approximation scheme, Z. Wahrsch. Verw. Gebiete 13, 321-332. MR 256461
  • J. Kiefer (1970), Deviations between the sample quantile process and the sample df, Nonparametric Techniques in Statistical Inference (M. L. Puri, éd. ), Cambridge Univ. Press, Cambridge. MR 277071
  • J. Kiefer, Skorohod embedding of multivariate RV’s, and the sample DF, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 24 (1972), no. 1, 1–35. MR 1554013,
  • A. N. Kolmogorov (1931), Eine Verallgemeinerung des Laplace-Liapunovschen Stazes, Izv. Akad. Nauk SSSR Ser. Fiz-Mat., 959-962.
  • A. N. Kolmogorov (1933a), Grundbegriffe der Wahrscheinlichkeitsrechnung, Springer-Verlag, Berlin and New York. MR 494348
  • A. N. Kolmogorov (1933b), Sulla determinazione empirica di una legge di distribuzione, Giorn. 1st. Ital. Attuari 4, 83-91.
  • A. N. Kolmogorov (1933c), Über die Grenzwertsätze der Wahrscheinlichkeitsrechnung, Izv. Akad. Nauk SSSR Ser. Fiz-Mat., 363-372.
  • J. Komlós, P. Major and G. Tusnády (1975; 1976), An approximation of partial sums of independent rv's and the sample df. I, II, Z. Wahrsch. Verw. Gebiete 32, 111-131; 34, 33-58.
  • M. Loève (1955), Probability theory, Van Nostrand, New York. MR 203748
  • K. R. Parthasarathy (1967), Probability measures on metric spaces, Academic Press, New York. MR 226684
  • E. J. G. Pitman, Some basic theory for statistical inference, Chapman and Hall, London; A Halsted Press Book, John Wiley & Sons, New York, 1979. Monographs on Applied Probability and Statistics. MR 549771
  • David Pollard, Convergence of stochastic processes, Springer Series in Statistics, Springer-Verlag, New York, 1984. MR 762984
  • Yu. V. Prohorov (1956), Convergence of random processes and limit theorems in probability theory, Theory Probab. Appl. 1, 157-214. MR 84896
  • A. V. Skorokhod (1956), Limit theorems for stochastic processes, Theory Probab. Appl. 1, 261-290. MR 84897
  • A. V. Skorokhod (1961), Studies in the theory of random processes, Kiev Univ.; Addison-Wesley, Reading, Mass., 1965 (translation). MR 185620
  • N. V. Smirnov (1939a), Ob uklonenijah empiričeskoi krivoi raspredelenija, Recueil Mathématique (Matematičeskii Sbornik) N. S. 6 (48), 3-26.
  • N. V. Smirnov (1939b), An estimate of divergence between empirical curves of a distribution in two independent samples, Vestnik Moskov. Univ. 2, 3-14. (Russian)
  • N. V. Smirnov (1944), Approximate laws of distribution of random variables from empirical data, Uspekhi Mat. Nauk 10, 179-206. (Russian) MR 12387
  • V. Strassen (1964), An invariance principle for the law of the iterated logarithm, Z. Wahrsch. Verw. Gebiete 3, 211-226. MR 175194
  • V. Strassen (1967), Almost sure behaviour of sums of independent random variables and martingales, Proc. Fifth Berkeley Sympos. Math. Statist. and Probab., vol. 2, pp. 315-343, Univ. of California Press, Berkeley, Calif. MR 214118

Review Information:

Reviewer: Miklós Csörgő
Journal: Bull. Amer. Math. Soc. 17 (1987), 189-200
American Mathematical Society