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Volumn 20, Issue 1-4, 2002, Pages 355-378

Optimal Choice of Nonparametric Estimates of A Density And of its Derivatives

Author keywords

Asymptotic optimal estimate; Bandwidth choice; Canonical kernel; Density estimates; Derivatives estimation; Kernel order choice; Polynomial kernels

Indexed keywords


EID: 84995442764     PISSN: 21931402     EISSN: 21967040     Source Type: Journal    
DOI: 10.1524/strm.2002.20.14.355     Document Type: Article
Times cited : (12)

References (33)
  • 2
    • 21144479450 scopus 로고
    • Hierarchies of higher order kernels
    • Berlinet, A., 1993. Hierarchies of higher order kernels. Probab. Theory Related Fields, 94, 489-504.
    • (1993) Probab. Theory Related Fields , vol.94 , pp. 489-504
    • Berlinet, A.1
  • 7
    • 0001257368 scopus 로고
    • Non-parametric estimation of regression functions and their derivatives by the kernel method
    • Gasser, T., Müller, H.G., 1984. Non-parametric estimation of regression functions and their derivatives by the kernel method. Scand. J. Statist., 11, 171-185.
    • (1984) Scand. J. Statist. , vol.11 , pp. 171-185
    • Gasser, T.1    Müller, H.G.2
  • 8
    • 0000587756 scopus 로고
    • Optimizing kernel methods: A unifying variational principle
    • Granovsky, B.L., Müller, H.G., 1991. Optimizing kernel methods: A unifying variational principle. International Statistical Review, 59, 3, 378-388.
    • (1991) International Statistical Review , vol.59 , pp. 378-388
    • Granovsky, B.L.1    Müller, H.G.2
  • 11
    • 0001234940 scopus 로고
    • On amount of noise inherent in bandwidth selection for a kernel density estimation
    • Hall, P., Marron, J.S., 1987a. On amount of noise inherent in bandwidth selection for a kernel density estimation. Ann. Statist., 15, 163-181.
    • (1987) Ann. Statist. , vol.15 , pp. 163-181
    • Hall, P.1    Marron, J.S.2
  • 12
    • 0000156647 scopus 로고
    • Choice of kernel order in density estimation
    • Hall, P., Marron, J.S., 1987b. Choice of kernel order in density estimation. Ann. Statist., 16, 161-173.
    • (1987) Ann. Statist. , vol.16 , pp. 161-173
    • Hall, P.1    Marron, J.S.2
  • 13
    • 38249035197 scopus 로고
    • Estimation of integrated squared density derivatives
    • Hall, P., Marron, J.S., 1987c. Estimation of integrated squared density derivatives. Statist. ' Probab. Lett., 6, 109-115.
    • (1987) Statist. ' Probab. Lett. , vol.6 , pp. 109-115
    • Hall, P.1    Marron, J.S.2
  • 15
    • 84972969036 scopus 로고
    • On kernel density derivative estimation
    • Jones, C., 1994. On kernel density derivative estimation. Comm. Statist. Theory Method, 23, 2133-2139.
    • (1994) Comm. Statist. Theory Method , vol.23 , pp. 2133-2139
    • Jones, C.1
  • 16
    • 38249014444 scopus 로고
    • Asymptotic effectiveness of some higher order kernels
    • Jones, C., Wand, M., 1992. Asymptotic effectiveness of some higher order kernels. J. Statist. Plann. Inference, 31, 15-21.
    • (1992) J. Statist. Plann. Inference , vol.31 , pp. 15-21
    • Jones, C.1    Wand, M.2
  • 17
    • 85025302379 scopus 로고
    • A note on kernels of order v, k. In Proceedings of the fourth Prague symposium on asymptotic statistics, Charles University
    • Mammitzch, V., 1988. A note on kernels of order v, k. In Proceedings of the fourth Prague symposium on asymptotic statistics, Charles University, Prague, 405-412.
    • (1988) Prague , pp. 405-412
    • Mammitzch, V.1
  • 18
    • 0000693311 scopus 로고
    • A comparison of cross-validation techniques in density estimation
    • Marron, J.S., 1987. A comparison of cross-validation techniques in density estimation. Ann. Statist., 15, 152-162.
    • (1987) Ann. Statist. , vol.15 , pp. 152-162
    • Marron, J.S.1
  • 19
    • 38249028534 scopus 로고
    • Canonical kernels for density estimation
    • Marron, J.S., Nolan, D., 1989. Canonical kernels for density estimation. Statist. ' Probab. Lett., 7, 195-199.
    • (1989) Statist. ' Probab. Lett. , vol.7 , pp. 195-199
    • Marron, J.S.1    Nolan, D.2
  • 20
    • 0004004008 scopus 로고
    • Nonparametric regression analysis of longitudinal data
    • Springer
    • Mϋller H.G., 1988. Nonparametric regression analysis of longitudinal data. Lecture Notes in Statistics 46, Springer Verlag Berlin, Heidelberg
    • (1988) Lecture Notes in Statistics 46
    • Mϋller, H.G.1
  • 21
    • 38249005286 scopus 로고
    • On nonparametric regression with higher order kernels
    • Schucany, W., 1991. On nonparametric regression with higher order kernels. J. Statist. Plann. Inference, 23, 145-151.
    • (1991) J. Statist. Plann. Inference , vol.23 , pp. 145-151
    • Schucany, W.1
  • 23
    • 0000997747 scopus 로고
    • Spline smoothing: the equivalent kernel method
    • Silverman, B., 1984. Spline smoothing: the equivalent kernel method. Ann. Statist., 12, 898-916.
    • (1984) Ann. Statist. , vol.12 , pp. 898-916
    • Silverman, B.1
  • 24
    • 0003443397 scopus 로고
    • Density estimation for statistics and data analysis
    • Chapman ' Hall, London.
    • Silverman, B., 1986. Density estimation for statistics and data analysis. Chapman ' Hall, London.
    • (1986)
    • Silverman, B.1
  • 26
    • 0001048793 scopus 로고
    • An asymptotically optimal window selection rule for kernel density estimation
    • Stone, C.J., 1984. An asymptotically optimal window selection rule for kernel density estimation. Ann. Statist., 12, 1285-1297.
    • (1984) Ann. Statist. , vol.12 , pp. 1285-1297
    • Stone, C.J.1
  • 27
    • 0004073954 scopus 로고
    • Orthogonal polynomials
    • Amer. Math. Society, Colloquium Publications. Providence, Rhode Island.
    • Szegö, G., 1991. Orthogonal polynomials. Amer. Math. Society, Colloquium Publications. Providence, Rhode Island.
    • (1991)
    • Szegö, G.1
  • 28
    • 0001438056 scopus 로고
    • The maximal smoothing principle in density estimation
    • Terrell, G.R., 1990. The maximal smoothing principle in density estimation. Journal of the Am. Stat. Assoc., 85, 470-477
    • (1990) Journal of the Am. Stat. Assoc. , vol.85 , pp. 470-477
    • Terrell, G.R.1
  • 30
    • 0000888197 scopus 로고    scopus 로고
    • A note on density mode estimation
    • Vieu, Ph., 1996. A note on density mode estimation. Statist. ' Probab. Lett., 26, 297-307.
    • (1996) Statist. ' Probab. Lett. , vol.26 , pp. 297-307
    • Vieu, P.1
  • 31
    • 0033240218 scopus 로고    scopus 로고
    • Multiple kernel procedure: an asymptotic support
    • Vieu, Ph., 1999. Multiple kernel procedure: an asymptotic support. Scand. J. Statist., 26, 61-72.
    • (1999) Scand. J. Statist. , vol.26 , pp. 61-72
    • Vieu, P.1


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