  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.
