Skewed Pivot-Blend Modeling with Applications to Semicontinuous Outcomes
arxiv(2024)
摘要
Skewness is a common occurrence in statistical applications. In recent years,
various distribution families have been proposed to model skewed data by
introducing unequal scales based on the median or mode. However, we argue that
the point at which unbalanced scales occur may be at any quantile and cannot be
reparametrized as an ordinary shift parameter in the presence of skewness. In
this paper, we introduce a novel skewed pivot-blend technique to create a
skewed density family based on any continuous density, even those that are
asymmetric and nonunimodal. Our framework enables the simultaneous estimation
of scales, the pivotal point, and other location parameters, along with various
extensions. We also introduce a skewed two-part model tailored for
semicontinuous outcomes, which identifies relevant variables across the entire
population and mitigates the additional skewness induced by commonly used
transformations. Our theoretical analysis reveals the influence of skewness
without assuming asymptotic conditions. Experiments on synthetic and real-life
data demonstrate the excellent performance of the proposed method.
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