메뉴 건너뛰기




Volumn 77, Issue 7, 2007, Pages 693-703

A note on uniform consistency of monotone function estimators

Author keywords

Function estimator; Kernel method; Monotonicity; Uniform convergence

Indexed keywords


EID: 33947131133     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spl.2006.11.004     Document Type: Article
Times cited : (12)

References (38)
  • 1
    • 0035457247 scopus 로고    scopus 로고
    • Nonparametric estimation of the residual distribution
    • Akritas M., and Van Keilegom I. Nonparametric estimation of the residual distribution. Scand. J. Statist. 28 (2001) 549-567
    • (2001) Scand. J. Statist. , vol.28 , pp. 549-567
    • Akritas, M.1    Van Keilegom, I.2
  • 3
    • 33947119541 scopus 로고    scopus 로고
    • Birke, M., Dette, H., 2005. A note on estimating a monotone regression by combining kernel and density estimates. Technical Report Ruhr-Universität Bochum 〈http://www.rub.de/mathematik3/preprint.htm〉.
  • 4
    • 0001278729 scopus 로고
    • On the estimation of parameters restricted by inequalities
    • Brunk H.D. On the estimation of parameters restricted by inequalities. Ann. Math. Statist. 29 (1958) 437-454
    • (1958) Ann. Math. Statist. , vol.29 , pp. 437-454
    • Brunk, H.D.1
  • 5
    • 33947133568 scopus 로고
    • On the strong consistency of density estimation by orthogonal series methods
    • Chen T.W. On the strong consistency of density estimation by orthogonal series methods. Tamkang J. Math. 12 (1981) 265-268
    • (1981) Tamkang J. Math. , vol.12 , pp. 265-268
    • Chen, T.W.1
  • 6
    • 0033245255 scopus 로고    scopus 로고
    • Nonparametric density estimation under unimodality and monotonicity constraints
    • Cheng M.-Y., Gasser T., and Hall P. Nonparametric density estimation under unimodality and monotonicity constraints. J. Comput. Graph. Statist. 8 (1999) 1-21
    • (1999) J. Comput. Graph. Statist. , vol.8 , pp. 1-21
    • Cheng, M.-Y.1    Gasser, T.2    Hall, P.3
  • 7
    • 33947159966 scopus 로고
    • Convergence uniforme d'estimateurs de la fonction de hasard pour des observations dépendantes: méthodes du noyau et des k-points les plus proches
    • Collomb G., Hassani S., Sarda P., and Vieu P. Convergence uniforme d'estimateurs de la fonction de hasard pour des observations dépendantes: méthodes du noyau et des k-points les plus proches. C. R. Acad. Sci. Paris Sér. I Math. 301 (1985) 653-656
    • (1985) C. R. Acad. Sci. Paris Sér. I Math. , vol.301 , pp. 653-656
    • Collomb, G.1    Hassani, S.2    Sarda, P.3    Vieu, P.4
  • 8
    • 0000289590 scopus 로고
    • A minimax optimal estimator for continuous monotone densities
    • Datta S. A minimax optimal estimator for continuous monotone densities. J. Statist. Plann. Inference 46 (1995) 183-193
    • (1995) J. Statist. Plann. Inference , vol.46 , pp. 183-193
    • Datta, S.1
  • 9
    • 33947162324 scopus 로고    scopus 로고
    • Dette, H., Pilz, K., 2007. On the estimation of a monotone conditional variance in nonparametric regression. Ann. Inst. Statist. Math., to appear.
  • 10
    • 33846090365 scopus 로고    scopus 로고
    • A simple nonparametric estimator of a strictly increasing regression function
    • Dette H., Neumeyer N., and Pilz K. A simple nonparametric estimator of a strictly increasing regression function. Bernoulli 12 (2006) 469-490
    • (2006) Bernoulli , vol.12 , pp. 469-490
    • Dette, H.1    Neumeyer, N.2    Pilz, K.3
  • 11
    • 0009911924 scopus 로고
    • The strong uniform consistency of nearest neighbor density estimates
    • Devroye L.P., and Wagner T.J. The strong uniform consistency of nearest neighbor density estimates. Ann. Statist. 5 (1977) 536-540
    • (1977) Ann. Statist. , vol.5 , pp. 536-540
    • Devroye, L.P.1    Wagner, T.J.2
  • 12
    • 33947165616 scopus 로고    scopus 로고
    • Devroye, L.P., Wagner, T.J., 1978. The strong uniform consistency of kernel density estimates. Multivariate Analysis, vol. V, Proceedings of the Fifth International Symposium, University of Pittsburgh, Pittsburgh, PA, 1978, North-Holland, Amsterdam-New York, 1980, pp. 59-77.
  • 13
    • 84945603474 scopus 로고
    • On the theory of mortality measurement II
    • Grenander U. On the theory of mortality measurement II. Skand. Aktuarietidskr. 39 (1956) 125-153
    • (1956) Skand. Aktuarietidskr. , vol.39 , pp. 125-153
    • Grenander, U.1
  • 14
    • 33947178775 scopus 로고    scopus 로고
    • Groeneboom, P., 1985. Estimating a monotone density. Proceedings of the Berkeley Conference in Honor of Jerzy Neyman and Jack Kiefer, vol. II, Berkeley, California, 1983, Wadsworth Statistics/Probability Series, pp. 539-555.
  • 15
    • 84995072178 scopus 로고
    • Isotonic estimators of monotone densities and distribution functions: basic facts
    • Groeneboom P., and Lopuhaä H.P. Isotonic estimators of monotone densities and distribution functions: basic facts. Statist. Neerlandica 47 (1993) 175-183
    • (1993) Statist. Neerlandica , vol.47 , pp. 175-183
    • Groeneboom, P.1    Lopuhaä, H.P.2
  • 16
    • 0001446881 scopus 로고    scopus 로고
    • On the strong universal consistency of a series type regression estimate
    • Györfi L., and Walk H. On the strong universal consistency of a series type regression estimate. Math. Methods Statist. 5 (1996) 332-342
    • (1996) Math. Methods Statist. , vol.5 , pp. 332-342
    • Györfi, L.1    Walk, H.2
  • 17
    • 0035539846 scopus 로고    scopus 로고
    • Nonparametric kernel regression subject to monotonicity constraints
    • Hall P., and Huang L.-S. Nonparametric kernel regression subject to monotonicity constraints. Ann. Statist. 29 (2001) 624-647
    • (2001) Ann. Statist. , vol.29 , pp. 624-647
    • Hall, P.1    Huang, L.-S.2
  • 18
    • 0035628555 scopus 로고    scopus 로고
    • Nonparametric estimation of hazard rate under the constraint of monotonicity
    • Hall P., Huang L.-S., Gifford J.A., and Gijbels I. Nonparametric estimation of hazard rate under the constraint of monotonicity. J. Comput. Graph. Statist. 10 (2001) 592-614
    • (2001) J. Comput. Graph. Statist. , vol.10 , pp. 592-614
    • Hall, P.1    Huang, L.-S.2    Gifford, J.A.3    Gijbels, I.4
  • 19
    • 0001919568 scopus 로고
    • Estimation of a monotone density or monotone hazard under random censoring
    • Huang J., and Wellner J.A. Estimation of a monotone density or monotone hazard under random censoring. Scand. J. Statist. 22 (1995) 3-33
    • (1995) Scand. J. Statist. , vol.22 , pp. 3-33
    • Huang, J.1    Wellner, J.A.2
  • 20
    • 21844483200 scopus 로고
    • Estimating a monotone density from censored observations
    • Huang Y., and Zhang C.-H. Estimating a monotone density from censored observations. Ann. Statist. 22 (1994) 1256-1274
    • (1994) Ann. Statist. , vol.22 , pp. 1256-1274
    • Huang, Y.1    Zhang, C.-H.2
  • 21
    • 26444555624 scopus 로고
    • Rate of strong uniform convergence of k-NN density estimates
    • Mack Y.P. Rate of strong uniform convergence of k-NN density estimates. J. Statist. Plann. Inference 8 (1983) 185-192
    • (1983) J. Statist. Plann. Inference , vol.8 , pp. 185-192
    • Mack, Y.P.1
  • 22
    • 0001194690 scopus 로고
    • Weak and strong uniform consistency of kernel regression estimates
    • Mack Y.P., and Silverman B.W. Weak and strong uniform consistency of kernel regression estimates. Z. Wahrsch. Verw. Gebiete 61 (1982) 405-415
    • (1982) Z. Wahrsch. Verw. Gebiete , vol.61 , pp. 405-415
    • Mack, Y.P.1    Silverman, B.W.2
  • 23
    • 0001354703 scopus 로고
    • Estimating a smooth monotone regression function
    • Mammen E. Estimating a smooth monotone regression function. Ann. Statist. 19 (1991) 724-740
    • (1991) Ann. Statist. , vol.19 , pp. 724-740
    • Mammen, E.1
  • 24
    • 0042205037 scopus 로고    scopus 로고
    • Vitesse de convergence uniforme presque sûre de l'estimateur linéaire par méthode d'ondelettes
    • Massiani A. Vitesse de convergence uniforme presque sûre de l'estimateur linéaire par méthode d'ondelettes. C. R. Math. Acad. Sci. Paris 337 (2003) 67-70
    • (2003) C. R. Math. Acad. Sci. Paris , vol.337 , pp. 67-70
    • Massiani, A.1
  • 25
    • 0031574858 scopus 로고    scopus 로고
    • Multivariate probability density estimation by wavelet methods: strong consistency and rates for stationary time series
    • Masry E. Multivariate probability density estimation by wavelet methods: strong consistency and rates for stationary time series. Stochastic Process. Appl. 67 (1997) 177-193
    • (1997) Stochastic Process. Appl. , vol.67 , pp. 177-193
    • Masry, E.1
  • 26
    • 0000290116 scopus 로고
    • Monotone nonparametric regression
    • Mukerjee H. Monotone nonparametric regression. Ann. Statist. 16 (1988) 741-750
    • (1988) Ann. Statist. , vol.16 , pp. 741-750
    • Mukerjee, H.1
  • 27
    • 0347281630 scopus 로고
    • Nonparametric maximum likelihood estimation of an increasing hazard rate for uncertain cause-of-death data
    • Mukerjee H., and Wang J.-L. Nonparametric maximum likelihood estimation of an increasing hazard rate for uncertain cause-of-death data. Scand. J. Statist. 20 (1993) 17-33
    • (1993) Scand. J. Statist. , vol.20 , pp. 17-33
    • Mukerjee, H.1    Wang, J.-L.2
  • 28
    • 0000105198 scopus 로고    scopus 로고
    • Convergence rates and asymptotic normality for series estimators
    • Newey W. Convergence rates and asymptotic normality for series estimators. J. Econometrics 79 (1997) 147-168
    • (1997) J. Econometrics , vol.79 , pp. 147-168
    • Newey, W.1
  • 29
    • 0002491164 scopus 로고
    • Density estimation under qualitative assumptions in higher dimensions
    • Polonik W. Density estimation under qualitative assumptions in higher dimensions. J. Multivariate Anal. 55 (1995) 61-81
    • (1995) J. Multivariate Anal. , vol.55 , pp. 61-81
    • Polonik, W.1
  • 30
    • 0032272797 scopus 로고    scopus 로고
    • The silhouette, concentration functions and ML-density estimation under order restrictions
    • Polonik W. The silhouette, concentration functions and ML-density estimation under order restrictions. Ann. Statist. 26 (1998) 1857-1877
    • (1998) Ann. Statist. , vol.26 , pp. 1857-1877
    • Polonik, W.1
  • 31
    • 84972507631 scopus 로고
    • Monotone regression splines in action (with discussion)
    • Ramsay J.O. Monotone regression splines in action (with discussion). Statist. Sci. 3 (1988) 425-441
    • (1988) Statist. Sci. , vol.3 , pp. 425-441
    • Ramsay, J.O.1
  • 32
    • 0003068254 scopus 로고
    • 1-functions under doubly stochastic transformations
    • 1-functions under doubly stochastic transformations. Trans. Amer. Math. Soc. 117 (1965) 92-100
    • (1965) Trans. Amer. Math. Soc. , vol.117 , pp. 92-100
    • Ryff, J.V.1
  • 33
    • 49849111521 scopus 로고
    • Measure preserving transformations and rearrangements
    • Ryff J.V. Measure preserving transformations and rearrangements. J. Math. Anal. Appl. 31 (1970) 449-458
    • (1970) J. Math. Anal. Appl. , vol.31 , pp. 449-458
    • Ryff, J.V.1
  • 34
    • 0001377295 scopus 로고
    • Weak and strong uniform consistency of the kernel estimate of a density and its derivatives
    • Silverman B.W. Weak and strong uniform consistency of the kernel estimate of a density and its derivatives. Ann. Statist. 6 (1978) 177-184
    • (1978) Ann. Statist. , vol.6 , pp. 177-184
    • Silverman, B.W.1
  • 35
    • 0001297207 scopus 로고
    • A law of the logarithm for kernel density estimators
    • Stute W. A law of the logarithm for kernel density estimators. Ann. Probab. 10 (1982) 414-422
    • (1982) Ann. Probab. , vol.10 , pp. 414-422
    • Stute, W.1
  • 36
    • 0031478562 scopus 로고    scopus 로고
    • On nonparametric estimation of density level sets
    • Tsybakov A.B. On nonparametric estimation of density level sets. Ann. Statist. 25 (1997) 948-969
    • (1997) Ann. Statist. , vol.25 , pp. 948-969
    • Tsybakov, A.B.1
  • 37
    • 0037562822 scopus 로고    scopus 로고
    • Smooth estimation of a monotone density
    • van der Vaart A.W., and van der Laan M.J. Smooth estimation of a monotone density. Statistics 37 (2003) 189-203
    • (2003) Statistics , vol.37 , pp. 189-203
    • van der Vaart, A.W.1    van der Laan, M.J.2
  • 38
    • 33947178774 scopus 로고    scopus 로고
    • Zhang, B., 1996. A Note on Strong Uniform Consistency of Kernel Estimators of Hazard Functions Under Random Censorship. Lifetime Data: Models in Reliability and Survival Analysis. Cambridge, MA, 1994, Kluwer Academic Publishers, Dordrecht, 1996, pp. 395-399.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.