  Modal linear regression (MLR) is a method for obtaining a conditional mode
predictor as a linear model. We study kernel selection for MLR from two
perspectives: "which kernel achieves smaller error?" and "which kernel is
computationally efficient?". First, we show that a Biweight kernel is optimal
in the sense of minimizing an asymptotic mean squared error of a resulting MLR
parameter. This result is derived from our refined analysis of an asymptotic
statistical behavior of MLR. Secondly, we provide a kernel class for which
iteratively reweighted least-squares algorithm (IRLS) is guaranteed to
converge, and especially prove that IRLS with an Epanechnikov kernel terminates
in a finite number of iterations. Simulation studies empirically verified that
using a Biweight kernel provides good estimation accuracy and that using an
Epanechnikov kernel is computationally efficient. Our results improve MLR of
which existing studies often stick to a Gaussian kernel and modal EM algorithm
specialized for it, by providing guidelines of kernel selection.
