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Modal regression using kernel density estimation: A review

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We review recent advances in modal regression studies using kernel density estimation. Modal regression is an alternative approach for investigating the 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. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Bayesian Methods and Theory Statistical and Graphical Methods of Data Analysis > Nonparametric Methods Statistical and Graphical Methods of Data Analysis > Density Estimation
Unimodal regression (left; red curve) and multimodal regression (right; blue curves) on a simulation dataset with three components
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90% prediction regions constructed from unimodal regression (pink area in the left panel) and multimodal regression (light blue area in the right panel). Clearly, the prediction region is much smaller in the multimodal regression than in unimodal regression because multimodal regression detects all components whereas unimodal regression discovers only the main component
[ Normal View | Magnified View ]

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Statistical and Graphical Methods of Data Analysis > Nonparametric Methods
Statistical and Graphical Methods of Data Analysis > Density Estimation
Statistical and Graphical Methods of Data Analysis > Bayesian Methods and Theory

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