On Estimation of Conditional Modes Using Multiple Quantile Regressions
This work addresses a specific statistical estimation problem for researchers and practitioners dealing with high-dimensional data, but it appears incremental as it builds on existing quantile regression techniques.
The authors tackled the problem of estimating conditional modes in high-dimensional settings by proposing a method that first estimates the conditional density through multiple quantile regressions and then finds its maximum. Their method showed better performance in synthetic and real-world experiments compared to existing approaches, with advantages in computational stability and statistical efficiency.
We propose an estimation method for the conditional mode when the conditioning variable is high-dimensional. In the proposed method, we first estimate the conditional density by solving quantile regressions multiple times. We then estimate the conditional mode by finding the maximum of the estimated conditional density. The proposed method has two advantages in that it is computationally stable because it has no initial parameter dependencies, and it is statistically efficient with a fast convergence rate. Synthetic and real-world data experiments demonstrate the better performance of the proposed method compared to other existing ones.