Moment-based detection of an epsilon-scale, mass-f distribution change requires polynomial degree at least log(1/f)/(2 epsilon), which yields a bandwidth rule for kernel shift tests.
Geometric inference for proba- bility measures.Foundations of Computational Mathematics, 11(6):733–751, 2011
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How fine a change can moments see? A scale law for detecting distribution shift, with a kernel calibration rule
Moment-based detection of an epsilon-scale, mass-f distribution change requires polynomial degree at least log(1/f)/(2 epsilon), which yields a bandwidth rule for kernel shift tests.