Bulletin of the American Mathematical Society

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Book Information:

Author: Martin Jacobsen
Title: Statistical analysis of counting processes
Additional book information: Lecture Notes in Statistics, Vol. 12, Springer-Verlag, New York, 1982, vii + 226 pp., $14.80. ISBN 0-3879-0769-6.

Odd O. Aalen, Weak convergence of stochastic integrals related to counting processes, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 38 (1977), no. 4, 261–277. MR 448552, DOI 10.1007/BF00533158

Per Kragh Andersen, Ørnulf Borgan, Richard Gill, and Niels Keiding, Linear nonparametric tests for comparison of counting processes, with applications to censored survival data, Internat. Statist. Rev. 50 (1982), no. 3, 219–258 (English, with French summary). With discussion, and with a reply by the authors. MR 693219, DOI 10.2307/1402489

P. K. Andersen and R. D. Gill, Cox’s regression model for counting processes: a large sample study, Ann. Statist. 10 (1982), no. 4, 1100–1120. MR 673646

4.

D. Bernoulli, Essai d'une nouvelle analyse de la mortalité causée par la petite vérole et les avantages de l'inoculation pour la prévenir, Histoire de l'Académie Royale des Sciences, 1960, pp. 1-45.

R. Boel, P. Varaiya, and E. Wong, Martingales on jump processes. I. Representation results, SIAM J. Control 13 (1975), no. 5, 999–1021. MR 0400379

6.

G. Cardano, Opus Novuum de Proportionibvs Nvmerorvm, 1570, Basel.

D. R. Cox, Regression models and life-tables, J. Roy. Statist. Soc. Ser. B 34 (1972), 187–220. MR 341758

Benjamin Epstein and Milton Sobel, Life testing, J. Amer. Statist. Assoc. 48 (1953), 486–502. MR 56898

9.

L. Euler, Recherches générales sur la mortalité et la multiplication du genre humaine, Histoire de l'Académie Royale des Sciences et Belles Lettres 16 (1760), 144-164; English transl. by N. and B. Keyfitz in Theoret. Population Biol. 1 (1970), 307-314.[Note]

Thomas R. Fleming, Judith R. O’Fallon, Peter C. O’Brien, and David P. Harrington, Modified Kolmogorov-Smirnov test procedures with application to arbitrarily right-censored data, Biometrics 36 (1980), no. 4, 607–625 (English, with French summary). MR 672339, DOI 10.2307/2556114

R. D. Gill, Censoring and stochastic integrals, Mathematical Centre Tracts, vol. 124, Mathematisch Centrum, Amsterdam, 1980. MR 596815

12.

E. Halley, An estimate of the degrees of mortality of mankind..., Philos. Trans. Roy. Soc. London Ser. A 17 (1693), 596-610, 653-656.

Max Halperin, Maximum likelihood estimation in truncated samples, Ann. Math. Statistics 23 (1952), 226–238. MR 48760, DOI 10.1214/aoms/1177729439

D. P. Harrington, T. R. Fleming, and S. J. Green, Procedures for serial testing in censored survival data, Survival analysis (Columbus, Ohio, 1981) IMS Lecture Notes Monogr. Ser., vol. 2, Inst. Math. Statist., Hayward, CA, 1982, pp. 269–286. MR 734208, DOI 10.1214/lnms/1215464855

E. L. Kaplan and Paul Meier, Nonparametric estimation from incomplete observations, J. Amer. Statist. Assoc. 53 (1958), 457–481. MR 93867

Samuel Karlin and Howard M. Taylor, A first course in stochastic processes, 2nd ed., Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1975. MR 0356197

17.

N. Mantel, Evaluations of survival data and two new rank order statistics arising in its consideration, Cancer Chemother. Rep. 50 (1966), 163-170.

R. Rebolledo, Sur les applications de la théorie des martingales à l’étude statistique d’une famille de processus ponctuels, Journées de Statistique des Processus Stochastiques (Grenoble, 1977), Lecture Notes in Math., vol. 636, Springer, Berlin, 1978, pp. 27–70 (French). MR 498944

Anastasios A. Tsiatis, A large sample study of Cox’s regression model, Ann. Statist. 9 (1981), no. 1, 93–108. MR 600535

1.

O. O. Aalen, Weak convergence of stochastic integrals related to counting processes, Z. Wahrsch. Verw. Gebiete 38 (1977), 261-277. MR 0448552

2.

P. K. Andersen, O. Borgan, R. D. Gill and N. Keiding, Linear nonparametric tests for comparison of counting processes, with applications to censored survival data, Internat. Statist. Rev. 50 (1982), 219-258. MR 693219

3.

P. K. Andersen and R. D. Gill, Cox's regression model for counting processes: a large sample study, Ann. Statist. 10 (1982), 1100-1120. MR 673646

4.

D. Bernoulli, Essai d'une nouvelle analyse de la mortalité causée par la petite vérole et les avantages de l'inoculation pour la prévenir, Histoire de l'Académie Royale des Sciences, 1960, pp. 1-45.

5.

R. Boel, P. Varaiya and E. Wong, Martingales on jump processes. I: Representation results, SIAM J. Control Optim. 13 (1975), 999-1021. MR 400379

6.

G. Cardano, Opus Novuum de Proportionibvs Nvmerorvm, 1570, Basel.

7.

D. R. Cox, Regression models and lifetables, J. Roy. Statist. Soc. Ser. B 34 (1972), 187-220. (with discussion) MR 341758

8.

B. Epstein and M. Sobel, Life-testing, J. Amer. Statist. Assoc. 48 (1953), 486-502. MR 56898

9.

L. Euler, Recherches générales sur la mortalité et la multiplication du genre humaine, Histoire de l'Académie Royale des Sciences et Belles Lettres 16 (1760), 144-164; English transl. by N. and B. Keyfitz in Theoret. Population Biol. 1 (1970), 307-314.[Note]

10.

T. R. Fleming, J. R. O'Fallon, P. C. O'Brien and D. P. Harrington, Modified Kolmogorov-Smirnov test procedures with application to arbitrarily right censored data, Biometrics 36 (1980), 607-625. MR 672339

11.

R. D. Gill, Censoring and stochastic integrals, Math. Centre Tracts 124, Math. Centrum, Amsterdam, 1980. MR 596815

12.

E. Halley, An estimate of the degrees of mortality of mankind..., Philos. Trans. Roy. Soc. London Ser. A 17 (1693), 596-610, 653-656.

13.

M. Halperin, Maximum likelihood estimation in truncated samples, Ann. Math. Statist. 23 (1952), 226-238. MR 48760

14.

D. P. Harrington, T. R. Fleming and S. J. Green, Procedures for serial testing in censored survival data, Survival Analysis (J. Crowley and R. A. Johnson, eds.), IMS Lecture Notes-Monograph Ser., Vol. 2, 1982, pp. 269-286. MR 734208

15.

E. L. Kaplan and P. Meier, Nonparametric estimation from incomplete observations, J. Amer. Statist. Assoc. 53 (1958), 457-481. MR 93867

16.

S. Karlin and H. M. Taylor, A first course in stochastic processes, 2nd ed., Academic Press, New York, 1975. MR 356197

17.

N. Mantel, Evaluations of survival data and two new rank order statistics arising in its consideration, Cancer Chemother. Rep. 50 (1966), 163-170.

18.

R. Rebolledo, Sur les applications de la theorie des martingales à l'étude statistique d'une famille de processus ponctuels, Journées de Statistique des Processus Stochastiques (Proc. Conf., Grenoble, 1977), Lecture Notes in Math., Vol. 636, Springer-Verlag, Berlin, 1978. MR 498944

19.

A. A. Tsiatis, A large sample study of Cox's regression model, Ann. Statist. 9 (1981), 93-108. MR 600535