Skewed Pivot-Adaptive Modeling with Applications to Semicontinuous Outcomes

Data skewness widely occurs in present-day statistical applications. Various distribution families have been recently proposed to model skewed data, many enforcing different scales in reference to the median or the mode. We argue that the pivotal point to incur unsymmetrical scales is not identical to a location shift parameter in the presence of skewness, and propose a framework of Skewed Pivot-adaptive Estimation with Unsymmetrical Scales (SPEUS). SPEUScan construct a skewed density family with continuity given any density function that may be nonsymmetric and nonunimodal, and includes many previously proposed skewed distributions as special cases. The framework allows us to simultaneously estimate the pivot, location, and scale parameters, and can be adapted to a skewed hurdle model with joint variable selection to cope with semicontinuous outcomes that contain with excessive zeros and skewed positive values, in addition to a large number of predictors. The computational issues brought by nonconvexity and nonsmoothness are tackled with a surrogate constructed by linearization and blockwise coordinate descent, the resulting algorithm having both implementation ease and guaranteed convergence. Moreover, we also perform finite-sample analysis to provide provable guarantees for the obtained estimators which, though not necessarily globally optimal, enjoy the desired order of statistical accuracy at the occurrence of skewness Experiments and real-life data applications to the medical expenditure panel survey data (MEPS) illustrate the excellent performance of the proposed method.