Abstract
Motivated by problems in robust statistics we first give a simple proof of the following: Given a probability measure P and positive measures /spl mu/</spl nu/, the /spl gamma/-divergence from P of probability measures Q satisfying /spl mu//spl les/Q or /spl mu//spl les/Q/spl les//spl nu/ is minimized by an explicitly determined Q/sup */ not depending on (the convex function) /spl gamma/. Next we address /spl gamma/-divergence minimization under the above inequality constraint and additional moment constraints.
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