Mode regression

There exists a loss function whose expectation is minimized at mode (y{divides}x). Adding the assumption of mode(y{divides}x)=x′β, the mode regression estimator is derived. The mode regression finds its major application in the case of truncated dependent variable, particularly with asymmetric density under homogeneity. The identification of the population parameter β and the strong consistency of the mode regression estimator are proved. Since no distribution theory is available, a small-scale Monte Carlo study is given at the end.