On Estimation of Conditional Modes Using Multiple Quantile Regressions

The estimation of the conditional mode, or modal regression [24, 11, 5, 22], is an important topic in statistics [21, 25, 24], econometrics [16, 17, 8, 15, 11], and machine learning [7, 22]. Compared to ordinary regression, modal regression is particularly useful when the data distribution is highly skewed and has fat tails. 1 In such a situation, ordinary regression, which estimates the conditional mean of the distribution, fails to capture the major trend underlying the data. This is because the conditional mean is not necessarily the point where the data points distribute densely, i.e., it can be far away from the majority of the data. Conditional mode is a convenient alternative to the conditional mean in this situation as it can capture the majority of the data. Hence, with modal regression, we can find a major trend underlying the data.