To “ Nonparametric Estimation of Multivariate Convex - Transformed Densities
نویسندگان
چکیده
2. For any point x0 ∈ R+ and any subgradient a ∈ ∂g(x0) all coordinates of a are nonpositive. If in addition g(x0) > y0 then all coordinates of a are negative. 3. For any point x0 ∈ R+ such that g(x0) > y0 we have: h ◦ g(x0) ≤ Cd! ddV (x0) , where V (x) ≡ ∏d k=1 xk for x ∈ R+. 4. The function h reverses partial order on Rd+: if x1 < x2 then g(x1) ≥ g(x2) and the last inequality is strict if g(x1) > y0. 5. The supremum of g on Rd+ is attained at 0. ∗Research supported in part by NSF grant DMS-0804587 †Research supported in part by NSF grant DMS-0804587 and NI-AID grant 2R01 AI291968-04 AMS 2000 subject classifications: Primary 62G07, 62H12; secondary 62G05, 62G20
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تاریخ انتشار 2010