Quantile-slicing estimation for dimension reduction in regression

Sufficient dimension reduction (SDR) has recently received much attention due to its promising performance under less stringent model assumptions. We propose a new class of SDR approaches based on slicing conditional quantiles: quantile-slicing mean estimation (QUME) and quantile-slicing variance estimation (QUVE). Quantile-slicing is particularly useful when the quantile function is more efficient to capture underlying model structure than the response itself, for example, when heteroscedasticity exists in a regression context. Both simulated and real data analysis results demonstrate promising performance of the proposed quantile-slicing SDR estimation methods.