Incorporate expectiles and M-quantiles into AdapDISCOM for inference beyond the mean

Integrate expectile and M-quantile loss formulations into AdapDISCOM to enable inference beyond mean regression, thereby capturing distributional aspects of the response while maintaining its multimodal covariance-based sparse estimation under missingness and measurement error.

Background

The current AdapDISCOM framework optimizes an LASSO-type objective based on mean squared loss. Extending it to alternative loss functions could broaden its inferential scope beyond the conditional mean.

The authors explicitly identify incorporating expectiles and M-quantiles as an open and promising direction to capture more nuanced features of the response distribution.