89
Views
3
CrossRef citations to date
0
Altmetric
Original Articles

Nonparametric Density Estimation under Unimodality and Monotonicity Constraints

, &
Pages 1-21 | Received 01 May 1997, Published online: 21 Feb 2012

References

  • Bickel , P. J. and Fan , J. 1996 . “Some Problems on the Estimation of Unimodal Densities,” . Statistica Sinica , 6 : 23 – 45 .
  • Cox , D. R. 1966 . “Notes on the Analysis of Mixed Frequency Distributions,” . British Journal of Mathematical and Statistical Psychology , 19 : 39 – 47 .
  • Fraser , D. A.S. and Massam , H. 1989 . “A Mixed Primal-Dual Bases Algorithm for Regression Under Inequality Constraints. Application to Convex Regression,” . Scandinavian Journal of Statistics , 16 : 65 – 74 .
  • Grenander , U. 1956 . “On the Theory of Mortality Measurement, II,” . Skandinavisk Aktuarietidskrift , 39 : 125 – 153 .
  • Hartigan , J. A. and Hartigan , P. M. 1985 . “The DIP Test of Unimodality,” . The Annals of Statistics , 13 : 70 – 84 .
  • Loader , C. R. 1996 . “Local Likelihood Density Estimation,” . The Annals of Statistics , 24 : 1602 – 1618 .
  • Hjort , N. L. and Jones , M. C. 1996 . “Locally Parametric Nonparametric Density Estimation,” . The Annals of Statistics , 24 : 1619 – 1647 .
  • Mammen , E. , Marron , J. S. and Fisher , N. I. 1992 . “Some Asymptotics for Multimodality Tests Based on Kernel Density Estimates,” . Probability Theory and Related Fields , 91 : 115 – 132 .
  • Meyer , M. C. 1997 . “An Extension of the Mixed Primal-Dual Bases Algorithm to the Case of More Constraints than Dimensions,” unpublished manuscript
  • Müller , D. W. and Sawitzki , G. 1991 . “Excess Mass estimates and Tests for Multimodality,” . Journal of the American Statistical Association , 86 : 738 – 746 .
  • Qian , S. 1994 . “Generalization of Least-Square Isotonic Regression,” . Journal of Statistical Planning and Inference , 38 : 389 – 397 .
  • Robertson , T. , Wright , F. and Dykstra , R. 1988 . Order Restricted Inference , New York : Wiley .
  • Scott , D. W. 1992 . Multivariate Density Estimation—Theory, Practice and Visualization , New York : Wiley .
  • Shi , N.-Z. 1995 . “The Minimal L 1 Isotonic Regression,” . Communications in Statistics , 24 : 175 – 189 . Series A
  • Silverman , B. W. 1981 . “Using Kernel Density Estimates to Investigate Multimodality,” . Journal of the Royal Statistical Society , 43 : 97 – 99 . Ser. B
  • Simonoff , J. S. 1996 . Smoothing Methods in Statistics , New York : Springer .
  • Sun , J. and Woodroofe , M. 1996 . “Adaptive Smoothing for a Penalized NPMLE of a Non-increasing Density,” . Journal of Statistical Planning and Inference , 52 : 143 – 159 .
  • Tantiyaswasdikul , C. and Woodroofe , M. 1994 . “Isotonic Smoothing Splines Under Sequential Designs,” . Journal of Statistical Planning and Inference , 38 : 75 – 87 .
  • Wand , M. P. and Jones , M. C. 1995 . Kernel Smoothing , London : Chapman & Hall .
  • Wang , Y. 1995 . “The L1 Theory of Estimation of Monotone and Unimodal Densities,” . Journal of Nonparametric Statistics , 4 : 249 – 261 .
  • Woodroofe , M. and Sun , J. 1993 . “A Penalized Maximum Likelihood Estimator of f(0+) When f is Non-increasing,” . Statistica Sinica , 3 : 501 – 515 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.