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Volumn 28, Issue 3, 2000, Pages 922-947

Maximum likelihood estimation of smooth monotone and unimodal densities

Author keywords

Contractions; Least concave majorants; Maximum likelihood estimation; Monotone and unimodal densities

Indexed keywords


EID: 0034362429     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1015952005     Document Type: Article
Times cited : (31)

References (35)
  • 2
    • 21344472936 scopus 로고    scopus 로고
    • Some problems on the estimation of unimodal densities
    • BICKEL, P. J. and FAN, I. (1996). Some problems on the estimation of unimodal densities. Statist. Sinica 6 23-45.
    • (1996) Statist. Sinica , vol.6 , pp. 23-45
    • Bickel, P.J.1    Fan, I.2
  • 3
    • 0038582523 scopus 로고
    • Estimating a density under restrictions: Nonasymptotic minimax risk
    • BIRGÉ, L. (1987a). Estimating a density under restrictions: nonasymptotic minimax risk. Ann. Statist. 15 995-1012.
    • (1987) Ann. Statist. , vol.15 , pp. 995-1012
    • Birgé, L.1
  • 4
    • 0038243770 scopus 로고
    • On the risk of histograms for estimating decreasing densities
    • BIRGÉ, L. (1987b). On the risk of histograms for estimating decreasing densities. Ann. Statist. 15 1113-1022.
    • (1987) Ann. Statist. , vol.15 , pp. 1113-11022
    • Birgé, L.1
  • 5
    • 0000513614 scopus 로고
    • The Grenander estimator: A nonasymptotic approach
    • BIRGÉ, L. (1989). The Grenander estimator: a nonasymptotic approach. Ann. Statist. 17 1532-1549.
    • (1989) Ann. Statist. , vol.17 , pp. 1532-1549
    • Birgé, L.1
  • 6
    • 0031494445 scopus 로고    scopus 로고
    • Estimation of unimodal densities without smoothness assumptions
    • BIRGÉ, L. (1997). Estimation of unimodal densities without smoothness assumptions. Ann. Statist. 25 970-981.
    • (1997) Ann. Statist. , vol.25 , pp. 970-981
    • Birgé, L.1
  • 7
    • 0001336210 scopus 로고
    • Conditional expectation given a σ lattice and applications
    • BRUNK, H. D. (1965). Conditional expectation given a σ lattice and applications. Ann. Math. Statist. 36 1339-1350.
    • (1965) Ann. Math. Statist. , vol.36 , pp. 1339-1350
    • Brunk, H.D.1
  • 10
    • 0002533759 scopus 로고
    • Exponential inequalities in nonparametric estimation
    • (G. Roussas, ed.) Kluwer, Dordrecht
    • DEVROYE, L. (1991). Exponential inequalities in nonparametric estimation. In Nonparametric Functional Estimation and Related Topics (G. Roussas, ed.) 31-44. Kluwer, Dordrecht.
    • (1991) Nonparametric Functional Estimation and Related Topics , pp. 31-44
    • Devroye, L.1
  • 13
    • 0001618486 scopus 로고
    • Optimal kernel estimators of the mode
    • EDDY, W. F. (1980). Optimal kernel estimators of the mode. Ann. Statist. 8 870-882.
    • (1980) Ann. Statist. , vol.8 , pp. 870-882
    • Eddy, W.F.1
  • 15
    • 0032690752 scopus 로고    scopus 로고
    • Best asymptotically normal kernel density entropy estimators for smooth densities
    • EGGERMONT, P. P. B. and LARICCIA, V. N. (1999). Best asymptotically normal kernel density entropy estimators for smooth densities. IEEE Trans Inform. Theory 45 1321-1326.
    • (1999) IEEE Trans Inform. Theory , vol.45 , pp. 1321-1326
    • Eggermont, P.P.B.1    Lariccia, V.N.2
  • 16
    • 0031232379 scopus 로고    scopus 로고
    • Estimation de densités unimodales
    • FOUGÈRES, A.-L. (1997). Estimation de densités unimodales. Canad. J. Statist. 25 375-387.
    • (1997) Canad. J. Statist. , vol.25 , pp. 375-387
    • Fougères, A.-L.1
  • 17
    • 84945603474 scopus 로고
    • On the theory of mortality measurements II
    • GRENANDER, U. (1956). On the theory of mortality measurements II. Skand. Akt. 39 125-153.
    • (1956) Skand. Akt. , vol.39 , pp. 125-153
    • Grenander, U.1
  • 20
    • 2942613978 scopus 로고
    • p error in mode estimation
    • p error in mode estimation. Ann. Statist. 23 2264-2284.
    • (1995) Ann. Statist. , vol.23 , pp. 2264-2284
    • Grund, B.1    Hall, P.2
  • 21
    • 0000944497 scopus 로고
    • A geometrical method for removing edge effects from kernel-type nonparametric regression estimators
    • HALL, P. and WEHRLY, T. E. (1991). A geometrical method for removing edge effects from kernel-type nonparametric regression estimators. J. Amer. Statist. Assoc. 86 665-672.
    • (1991) J. Amer. Statist. Assoc. , vol.86 , pp. 665-672
    • Hall, P.1    Wehrly, T.E.2
  • 23
    • 0000907205 scopus 로고
    • On the composition of unimodal distributions
    • IBRAGIMOV, I. A. (1956). On the composition of unimodal distributions. Theory Probab. Appl. 1 255-260.
    • (1956) Theory Probab. Appl. , vol.1 , pp. 255-260
    • Ibragimov, I.A.1
  • 24
    • 0000362452 scopus 로고
    • Simple boundary corrections for kernel density estimation
    • JONES, M. C. (1993). Simple boundary corrections for kernel density estimation. Statist. Comput. 3 135-146.
    • (1993) Statist. Comput. , vol.3 , pp. 135-146
    • Jones, M.C.1
  • 25
    • 0040703192 scopus 로고
    • On the optimum rate of transmitting information
    • Springer, Berlin
    • KEMPERMAN, J. H. B. (1967). On the optimum rate of transmitting information. Lecture Notes in Math. 23 126-169. Springer, Berlin.
    • (1967) Lecture Notes in Math. , vol.23 , pp. 126-169
    • Kemperman, J.H.B.1
  • 27
    • 0001354703 scopus 로고
    • Estimating a smooth monotone regression function
    • MAMMEN, E. (1991). Estimating a smooth monotone regression function. Ann. Statist. 19 724-740.
    • (1991) Ann. Statist. , vol.19 , pp. 724-740
    • Mammen, E.1
  • 28
    • 0345849742 scopus 로고
    • Discussion on Barlow and van Zwet's paper
    • (M. L. Puri, ed.) Cambridge Univ. Press
    • MARSHALL, A. W. (1970). Discussion on Barlow and van Zwet's paper. In Nonparametric Techniques in Statistical Inference (M. L. Puri, ed.) 175-176. Cambridge Univ. Press.
    • (1970) Nonparametric Techniques in Statistical Inference , pp. 175-176
    • Marshall, A.W.1
  • 29
    • 0001538585 scopus 로고
    • On the boundary kernel method for nonparametric curve estimation near endpoints
    • MÜLLER, H.-G. (1993). On the boundary kernel method for nonparametric curve estimation near endpoints. Scand. J. Statist. 20 313-328.
    • (1993) Scand. J. Statist. , vol.20 , pp. 313-328
    • Müller, H.-G.1
  • 30
    • 0001473437 scopus 로고
    • On estimation of a probability density function and mode
    • PARZEN, E. (1962). On estimation of a probability density function and mode. Ann. Math. Statist. 33 1065-1076.
    • (1962) Ann. Math. Statist. , vol.33 , pp. 1065-1076
    • Parzen, E.1
  • 31
    • 0001377295 scopus 로고
    • Weak and strong uniform consistency of the kernel estimate of a density and its derivatives
    • SILVERMAN, B. W. (1978). Weak and strong uniform consistency of the kernel estimate of a density and its derivatives. Ann. Statist. 6 177-184.
    • (1978) Ann. Statist. , vol.6 , pp. 177-184
    • Silverman, B.W.1
  • 32
    • 0000738873 scopus 로고
    • On the estimation of a probability density function by the maximum penalized likelihood method
    • SILVERMAN, B. W. (1982). On the estimation of a probability density function by the maximum penalized likelihood method. Ann. Statist. 10 795-810.
    • (1982) Ann. Statist. , vol.10 , pp. 795-810
    • Silverman, B.W.1
  • 33
    • 0010629978 scopus 로고
    • Maximum likelihood estimation of a unimodal density II
    • WEGMAN, E. I. (1970). Maximum likelihood estimation of a unimodal density II. Ann. Math. Statist. 6 2169-2174.
    • (1970) Ann. Math. Statist. , vol.6 , pp. 2169-2174
    • Wegman, E.I.1
  • 35
    • 0000067461 scopus 로고
    • A penalized maximum likelihood estimate of f(0+) when f is non-increasing Statist
    • 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) Sinica , vol.3 , pp. 501-515
    • Woodroofe, M.1    Sun, J.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.