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29 Nov 2018: We mention that in thecase d = 1, Doss and Wellner (2016b) proved thatd2H(f̂n, f0) = Op(n4/5) for each fixed f0 F1, andindeed showed that the same rate holds for ... Then. supx0I. f̂n(x0) f0(x0) = Op((. log n. n. )β/(2β1)). Here the log-concave MLE

10 Oct 2011: The previous result shows that minb=1,.,B ‖Z0 cZb‖ is of order Op(B1/q) as B. ... nj=1. (W (2)nj 1)2 = Op(n1). by (W.1-2), so V̄n p 1.Case 3: Vni = W 2ni.

21 Apr 2010: x2jx2j 1. f̂h(x) f (x) dx}. (A.8). Op(. log(1/ h). nh2+ h. ... 2r. Thus B̂1,j = B1,j Op(n2/7), B̂2,j = B2,j Op(n.

24 Apr 2005: HJI8IL]MPOnak3Oy]RTM[?Y[REuPH(cREL] LdB) #KR X OP" RTMM[H3gfk2ak3U] ak3OnY[RTM. ... Rl[]giYkiXiL_SY[RNQePvP]ltutuLGVYSU[RNL_lVY[]tQVUceSVYXZL:kiSYccemcTm bXi[RNX[]dVUXiL1QTzMVUXiceSZS Wcbgxw EHG;G I 4CTA)C O[M[cRam UZ|LZYy<32O)C8yRTMeMcIk3OY[REgfUZoaopb_M

16 Aug 2005: 9x W.k oW op Z-5B21s34'!7&% W[5%21s3=5B-21C9 407!".K&!"24PLNy6%5B21.B50"!78/!;& 46GI21H/3@4>>-2TaE!"8/ &!7#d&%U3!4g524--B5B-(4Y.

28 Aug 2007: From these. properties, (A.8) and (A.11) it can be proved that φ(Z(k)) 1 = qk Qk 1 =. Op(k/T). This property suggests, although of course does not ... enables us to convert the in-probability bound (qk Qk 1) PPois(z,Z(k)) = Op(k/T).

24 Apr 2005: 9999 m "2@ op@ ) }. "¤£ ) "6@ ¢ "¤£ )) 9999 m£ 9999 == =. "¤£ ) } "¤£ ) "6@ ¢ "¤£ )) m£ 9999. ... ØcËÝ m "2@ op@ )@ ¢ " ¢ ) F }. ò " } ) l F. }ò # F 1 " ) ¢ l F } m.

24 Mar 2010: I. Stewart. this has resulted in algorithms, e.g. Chiu (1992), that achieve the optimal rate of convergence of therelative error, namely Op(n1/2), where n is the sample size,

23 Oct 2016: s. Then. ‖ sin (V̂ , V )‖F 2 min(d1/2‖̂ ‖op, ‖̂ ‖F). ... is in themin(d 1/2‖̂ ‖op, ‖̂ ‖F) term in the numerator of the bounds.

12 Mar 2024: Y ), which determines the op-timal h, will be unknown.