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Volumn 29, Issue 6, 2001, Pages 1653-1698

Estimation of a convex function: Characterizations and asymptotic theory

Author keywords

Convex; Density estimation; Integrated Brownian motion; Least squares; Maximum likelihood; Regression function

Indexed keywords


EID: 0035528158     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1015345958     Document Type: Article
Times cited : (196)

References (31)
  • 3
    • 0001278729 scopus 로고
    • On the estimation of parameters restricted by inequalities
    • BRUNK, H. D. (1958). On the estimation of parameters restricted by inequalities. Ann. Math. Statist. 29 437-454.
    • (1958) Ann. Math. Statist. , vol.29 , pp. 437-454
    • Brunk, H.D.1
  • 4
    • 0001772469 scopus 로고
    • Estimation of isotonic regression
    • (M. L. Puri, ed.) Cambridge Univ. Press
    • BRUNK, H. D. (1970). Estimation of isotonic regression. In Nonparametric Techniques in Statistical Inference (M. L. Puri, ed.) 177-195. Cambridge Univ. Press.
    • (1970) Nonparametric Techniques in Statistical Inference , pp. 177-195
    • Brunk, H.D.1
  • 5
    • 0010946490 scopus 로고
    • Technical Report 137, Dept. Statistics, Univ. Calfornia, Berkeley
    • DONOHO, D. L. and LIU, R. C. (1987). Geometric rates of convergence, I. Technical Report 137, Dept. Statistics, Univ. Calfornia, Berkeley.
    • (1987) Geometric Rates of Convergence , vol.1
    • Donoho, D.L.1    Liu, R.C.2
  • 6
    • 84945603474 scopus 로고
    • On the theory of mortality measurement, part II
    • GRENANDER, U. (1956). On the theory of mortality measurement, part II. Skandinavisk Aktuarietidskrift 39 125-153.
    • (1956) Skandinavisk Aktuarietidskrift , vol.39 , pp. 125-153
    • Grenander, U.1
  • 8
    • 0002641355 scopus 로고
    • Brownian motion with a parabolic drift and Airy functions
    • GROENEBOOM, P. (1988). Brownian motion with a parabolic drift and Airy functions. Probab. Theory Related Fields 81 79-109.
    • (1988) Probab. Theory Related Fields , vol.81 , pp. 79-109
    • Groeneboom, P.1
  • 13
    • 0002670649 scopus 로고
    • Design, modelling and analysis of some biological datasets
    • (C. L. Mallows, ed.) Wiley, New York
    • HAMPEL, F. R. (1987). Design, modelling and analysis of some biological datasets. In Design, Data and Analysis, by Some Friends of Cuthbert Daniel (C. L. Mallows, ed.) 111-115. Wiley, New York.
    • (1987) Design, Data and Analysis, by Some Friends of Cuthbert Daniel , pp. 111-115
    • Hampel, F.R.1
  • 14
    • 0007192362 scopus 로고
    • Consistency in concave regression
    • HANSON, D. L. and PLEDGER, G. (1976). Consistency in concave regression. Ann. Statist. 4 1038-1050.
    • (1976) Ann. Statist. , vol.4 , pp. 1038-1050
    • Hanson, D.L.1    Pledger, G.2
  • 15
    • 0000717251 scopus 로고
    • Point estimators of ordinates of concave functions
    • HILDRETH, C. (1954). Point estimators of ordinates of concave functions. J. Amer. Statist. Assoc. 49 598-619.
    • (1954) J. Amer. Statist. Assoc. , vol.49 , pp. 598-619
    • Hildreth, C.1
  • 17
    • 0032375434 scopus 로고    scopus 로고
    • The iterative convex minorant algorithm for nonparametric estimation
    • JONGBLOED, G. (1998). The iterative convex minorant algorithm for nonparametric estimation. J. Comput. Graph. Statist. 7 310-321.
    • (1998) J. Comput. Graph. Statist. , vol.7 , pp. 310-321
    • Jongbloed, G.1
  • 18
    • 0007259913 scopus 로고    scopus 로고
    • Minimax lower bounds and moduli of continuity
    • JONGBLOED, G. (2000). Minimax lower bounds and moduli of continuity. Statist. Probab. Lett. 50 279-284.
    • (2000) Statist. Probab. Lett. , vol.50 , pp. 279-284
    • Jongbloed, G.1
  • 19
    • 0001315354 scopus 로고
    • Cube root asymptotics
    • KIM, J. and POLLARD, D. (1990). Cube root asymptotics. Ann. Statist. 18 191-219.
    • (1990) Ann. Statist. , vol.18 , pp. 191-219
    • Kim, J.1    Pollard, D.2
  • 20
    • 0026301132 scopus 로고
    • For how long do trans-Saharan migrants stop over at an oasis?
    • LAVEE, D., SAFRIE, U. N. and MEILIJSON, I. (1991). For how long do trans-Saharan migrants stop over at an oasis? Ornis Scandinavica 22 33-44.
    • (1991) Ornis Scandinavica , vol.22 , pp. 33-44
    • Lavee, D.1    Safrie, U.N.2    Meilijson, I.3
  • 21
    • 0000899362 scopus 로고
    • Nonparametric regression under qualitative smoothness assumptions
    • MAMMEN, E. (1991). Nonparametric regression under qualitative smoothness assumptions. Ann. Statist. 19 741-759.
    • (1991) Ann. Statist. , vol.19 , pp. 741-759
    • Mammen, E.1
  • 23
    • 0002727835 scopus 로고
    • Estimation of a unimodal density
    • PRAKASA RAO, B. L. S. (1969). Estimation of a unimodal density. Sankhyā Ser. A 31 23-36.
    • (1969) Sankhyā Ser. A , vol.31 , pp. 23-36
    • Prakasa Rao, B.L.S.1
  • 27
    • 0000661267 scopus 로고
    • Maximum likelihood estimation of ordered probabilities
    • VAN EEDEN, C. (1956). Maximum likelihood estimation of ordered probabilities. Proc. Konink. Nederl. Akad. Wetensch. A 59 444-455.
    • (1956) Proc. Konink. Nederl. Akad. Wetensch. A , vol.59 , pp. 444-455
    • Van Eeden, C.1
  • 28
    • 0000516045 scopus 로고
    • Maximum likelihood estimation of partially ordered probabilities, I
    • VAN EEDEN, C. (1957). Maximum likelihood estimation of partially ordered probabilities, I. Proc. Konink. Nederl. Akad. Wetensch. A 60 128-136.
    • (1957) Proc. Konink. Nederl. Akad. Wetensch. A , vol.60 , pp. 128-136
    • Van Eeden, C.1
  • 30
    • 0000067461 scopus 로고
    • A penalized maximum likelihood estimate of f(0+) when f is non-increasing
    • WOODROOFE, M. and SUN, J. (1993). A penalized maximum likelihood estimate of f(0+) when f is non-increasing. Statist. Sinica 3 501-515.
    • (1993) Statist. Sinica , vol.3 , pp. 501-515
    • Woodroofe, M.1    Sun, J.2
  • 31
    • 0000350091 scopus 로고
    • The asymptotic behavior of monotone regression estimates
    • WRIGHT, F. T. (1981). The asymptotic behavior of monotone regression estimates. Ann. Statist. 9 443-448.
    • (1981) Ann. Statist. , vol.9 , pp. 443-448
    • Wright, F.T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.