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Modal Regression using Kernel Density Estimation: a Review

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  • Yen-Chi Chen

Abstract

We review recent advances in modal regression studies using kernel density estimation. Modal regression is an alternative approach for investigating relationship between a response variable and its covariates. Specifically, modal regression summarizes the interactions between the response variable and covariates using the conditional mode or local modes. We first describe the underlying model of modal regression and its estimators based on kernel density estimation. We then review the asymptotic properties of the estimators and strategies for choosing the smoothing bandwidth. We also discuss useful algorithms and similar alternative approaches for modal regression, and propose future direction in this field.

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  • Yen-Chi Chen, 2017. "Modal Regression using Kernel Density Estimation: a Review," Papers 1710.07004, arXiv.org, revised Dec 2017.
  • Handle: RePEc:arx:papers:1710.07004
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    1. Lee, Myoung-jae, 1989. "Mode regression," Journal of Econometrics, Elsevier, vol. 42(3), pages 337-349, November.
    2. Jochen Einbeck & Gerhard Tutz, 2006. "Modelling beyond regression functions: an application of multimodal regression to speed-flow data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 55(4), pages 461-475.
    3. repec:taf:gnstxx:v:24:y:2012:i:3:p:647-663 is not listed on IDEAS
    4. Sophie Dabo-Niang & Ali Laksaci, 2010. "Note on conditional mode estimation for functional dependent data," Statistica, Department of Statistics, University of Bologna, vol. 70(1), pages 83-94.
    5. Kemp, Gordon C.R. & Santos Silva, J.M.C., 2012. "Regression towards the mode," Journal of Econometrics, Elsevier, vol. 170(1), pages 92-101.
    6. Burman, Prabir & Polonik, Wolfgang, 2009. "Multivariate mode hunting: Data analytic tools with measures of significance," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1198-1218, July.
    7. Robert Tibshirani & Guenther Walther & Trevor Hastie, 2001. "Estimating the number of clusters in a data set via the gap statistic," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 411-423.
    8. Weixin Yao & Longhai Li, 2014. "A New Regression Model: Modal Linear Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(3), pages 656-671, September.
    9. Lee, Myoung-jae, 1993. "Quadratic mode regression," Journal of Econometrics, Elsevier, vol. 57(1-3), pages 1-19.
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