An introduction to nonparametric multimodal regression

  1. Alonso-Pena, M. 1
  1. 1 Universidade de Santiago de Compostela
    info

    Universidade de Santiago de Compostela

    Santiago de Compostela, España

    ROR https://ror.org/030eybx10

Revista:
BEIO, Boletín de Estadística e Investigación Operativa

ISSN: 1889-3805

Ano de publicación: 2020

Volume: 36

Número: 1

Páxinas: 5-23

Tipo: Artigo

DIALNET GOOGLE SCHOLAR lock_openAcceso aberto editor

Outras publicacións en: BEIO, Boletín de Estadística e Investigación Operativa

Resumo

The mean, the median and the mode are the classical location measures introduced in any elementary course in statistics. Although mean and median based statistical methods are the usual approaches in different contexts, the mode seems to be somehow neglected. This paper gives a review on nonparametric multimodal regression, an approach for regression where, instead of seeking the mean of the conditional density, as in classical regression models, the conditional local modes are targeted. In addition to revising the existing literature on multimodal regression, the finite sample performance of the multimodal regression estimator is explored with both simulated and real data examples. © 2020 SEIO

€ Ver financiamento

Información de financiamento

The author acknowledges the financial support from the Xunta de Galicia grant ED481A-2019/139 through Programa de axudas á etapa predoutoral da Xunta de Galicia (Consellería de Educación, Universidade e Formación Pro-fesional). This research has been partially supported by Project MTM2016-76969-P from the AEI co-funded by the European Regional Development Fund (ERDF), the Competitive Reference Groups 2017-2020 (ED431C 2017/38) from the Xunta de Galicia through the ERDF.

Financiadores

Referencias bibliográficas

  • [1] Bashtannyk, D. M. and Hyndman, R. J. (2001). Bandwidth selection forkernel conditional density estimation.Computational Statistics and DataAnalysis,36(1), 279-298.
  • [2] Chen, Y-C. and Genovese, C.R. and Tibshirani, R.J. and Wasserman, L.(2016). Nonparametric modal regression.The Annals of Statistics,44(2),489-514.
  • [3] Chen, Y-C. (2018). Modal regression using kernel density estimation: Areview.WIREs Computational Statistics,10, e1431.
  • [4] Cheng, Y. (1995).Mean shift, mode seeking, and clustering.IEEE Transac-tions on Pattern Analysis and Machine Intelligence,17(8), 790-799.
  • [5] Comaniciu, D. and Meer, P. (2002). Mean shift: a robust approach towardfeature space analysis.IEEE Transactions on Pattern Analysis and MachineIntelligence,24(5), 603-619.
  • [6] Einbeck, J. and Tutz, G. (2006). Modelling beyond regression functions: Anapplication of multimodal regression to speedflow data.Journal of the RoyalStatistical Society. Series C (Applied Statistics),55(4), 461-475.
  • [7] Fan, J. and Yim , T.H. (2004). A crossvalidation method for estimatingconditional densities.Biometrika,91(4), 819–834.
  • [8] Fukunaga, K. and Hostetler, L. (1974). The estimation of the gradient ofa density function, with applications in pattern recognition.IEEE Transac-tions on Information Theory,22(1), 32-40.
  • [9] Hall, P.J. and Racine, J. and Li, Q. (2004). Cross-validation and the estima-tion of conditional probability densities.Journal of the American StatisticalAssociation,99(468), 1015-1026.
  • [10] Hyndman, R.J., and Bashtannyk, D.M., and Grunwald,G. K. (1996). Esti-mating and visualizing conditional densities.Journal of Computational andGraphical Statistics,5(1), 315-336.
  • [11] Kemp, G.C.R. and Santos-Silva, J.M.C (2012). Regression towards themode.Journal of Econometrics,170(1), 92-101.
  • [12] Koenker, R. and Bassett, G. (1978). Regression quantiles.Econometrica,46(1), 33-50.
  • [13] Lee, M.J. (1989). Mode regression.Journal of Econometrics,42(3), 337-349.
  • [14] R Core Team (2016). R: A language and environment for statisticalcomputing. R Foundation for Statistical Computing, Vienna, Austria.http://www.R-project.org/.
  • [15] Sager, T. W. and Thisted, R. A. (1982). Maximum likelihood estimationof isotonic modal regression.The Annals of Statistics,10(3), 690-707.
  • [16] Scott, D.W. (1992).Multivariate Density Estimation, Wiley, New York(USA).
  • [17] Yao, W. and Li, L. (2014). A new regression model: modal linear regression.Scandinavian Journal of Statistics,41(3), 656-671.
  • [18] Yao, W., and Lindsay, B.G. and Li, R. (2012). Local modal regression.Journal of Nonparametric Statistics,24(3), 647-663.
  • [19] Young, S. and Bowman, A.W. (1995) Nonparametric analysis of covariance.Biometrics,51(1), 920-931.
  • [20] Zhou, H. and Huang, X. (2019). Bandwidth selection for nonparametricmodal regression.Communications in Statistics - Simulation and Computa-tion,48(4), 968-98
Fonte de datos: Dialnet