Marginal densities of the least concave majorant of Brownian motion

Annals of Statistics

Volumn 29, Issue 6, 2001, Pages 1732-1750

  Carolan, Chris ^a   Dykstra, Richard ^b  

^a EAST CAROLINA UNIVERSITY   (United States)

^b University of Iowa   (United States)

Author keywords

Brownian motion; Least concave majorant; Likelihood ratio ordering; Stochastic ordering

Indexed keywords

EID: 0035528168     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1015345960     Document Type: Article

References (16)

1. BARLOW, R. E., BARTHOLOMEW, D. J., BREMNER, J. M. and BRUNK, H. D. (1972). Statistical Inference under Order Restrictions. Wiley, London.
2. BASS, R. F. (1983). Markov processes and convex minorants. Seminaire de Probabilities XVIII. Lecture Notes in Math. 1059 29-41. Springer, Berlin.
3. BRUNK, H. D., FRANCK, W. E., HANSON, D. L. and HOGG, R. V. (1966). Maximum likelihood estimation of the distributions of two stochastically ordered random variables. J. Amer. Amer. Statist. Assoc. 61 1067-1080.
4. DYKSTRA, R. (1982). Maximum likelihood estimation of survival functions of stochastically ordered random variables. J. Amer. Amer. Statist. Assoc. 77 621-628.
5. DYKSTRA, R., KOCHAR, S. and ROBERTSON, T. (1995). Inference for likelihood ratio ordering in the two-sample problem. J. Amer. Amer. Statist. Assoc. 90 1034-1040.
6. GRENANDER, U. (1956). On the theory of mortality measurement. Part II. Skand. Akt. 39 125-153.
7. GROENEBOOM, P. (1983). The concave majorant of Brownian motion. Ann. Probab. 11 1016-1027.
8. GROENEBOOM, P. (1985). Estimating a monotone density. In Proceedings of the Berkeley Conference in Honor of Jerzy Neyman and Jack Kiefer (L. M. LeCam and R. A. Olshen, eds.) 2 529-555. Wadsworth, Belmont, CA.
9. ITÔ, K. and MCKEAN, H. P. Jr. (1974). Diffusion prossesses and Their Sample Paths, 2nd ed. Springer, Berlin.
10. MARSHALL, A. W. and PROSCHAN, F. (1965). Maximum likelihood estimation for distributions with monotone failure rates. Ann. Math. Statist. 36 69-77.
11. PITMAN, J. W. (1983). Remarks on the convex minorant of Brownian motion. In Seminar on Stochastic Processes (E. Çinlar, K. L. Chung and R. K. Getoor, eds.) 219-228. Birkhäuser, Boston.
12. PRAESTGAARD, J. T. and HUANG, J. (1996). Asymptotic theory for Nnnparametric estimation of survival curves under order restrictions. Ann. Statist. 24 1679-1716.
13. PRAKASA RAO, B. L. S. (1969). Estimation of a unimodal density. Sankhyā Ser. A 31 23-36.
14. ROBERTSON, T. and WRIGHT, F. T. (1981). Likelihood ratio tests for and against stochastic ordering between multinomial populations. Ann. Statist. 9 1248-57.
15. ROBERTSON, T., WEIGHT, F T. and DYKSTRA, R. L. (1988). Order Restricted Inference. Wiley, New York.
16. WILLIAMS, D. (1974). Path decomposition and continuity of local time for one-dimensional diffusions, I. Proc. London Math. Soc. Ser. 3 28 738-768.