Available in electronic format
Available in print format
Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)
     

Book Review

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

Retrieve article in: PDF

Book Information

Author(s): 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:

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 (1980), Statistique de Kolmogorov-Smirnov pour un enchantillon nonequireparti, Colloq. Internat. CNRS 307, 39-44. 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.

M. Csörgő (1983), Quantile processes with statistical applications, Regional Conf. Ser. on Appl. Math. vol. 42, SIAM, Philadelphia, Pa. MR 745130

M. Csörgő, S. Csörgő and L. Horváth (1986), An asymptotic theory for empirical reliability and concentration processes, Lecture Notes in Statistics, vol. 33, Springer-Verlag, Berlin and New York. MR 856407

M. Csörgő and P. Révész (1975), A new method to prove Strassen-type laws of invariance principle. I, II, Z. Wahrsch. Verw. Gebiete 31, 255-260; 261-269. MR 1554018

M. Csörgő and P. Révész (1981), Strong approximations in probability and statistics, Akadémiai Kiadó, Budapest-Academic Press, New York, 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 (1984), A course on empirical processes, Lecture Notes in Math., vol. 1097, Springer-Verlag, Berlin and New York. 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

P. Gaenssler (1983), Empirical processes, IMS Lecture Notes-Monograph Series, vol. 3, Institute of Mathematical Statistics, Hayward, Calif. 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 (1972), Skorohod embedding of multivariate RV's and the sample DF, Z. Wahrsch. Verw. Gebiete 24, 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. Pitman (1979), Some basic theory for statistical inference, Chapman & Hall, London. MR 549771

D. Pollard (1984), Convergence of stochastic processes, Springer-Verlag, Berlin and New York. 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


Additional Information:

Reviewer(s):
Miklós Csörgő

Review Information:
Journal: Bull. Amer. Math. Soc. 17 (1987), 189-200.
DOI: 10.1090/S0273-0979-1987-15560-1
PII: S 0273-0979(1987)15560-1


  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2008, American Mathematical Society
Privacy Statement
Search the AMSPowered by Google