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.
Gromov-Hausdorff stable signatures for shapes using persistence.Computer Graphics Forum, 28(5):1393–1403, 2009
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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.