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31 Oct 2011: H. Ahmad, M. Liu, T. Javadi, Q. Zhao and B. Krishnamachari, “Op-timality of Myopic Sensing in Multi-Channel Opportunistic Access,”IEEE Trans.

15 Sep 2011: In this paper welook at a number of models, making different assumptionsabout the parameters that can be measured, and obtain op-timal policies for each model. ... Thus, a sharing policy which simply op-timizes the efficiency of the system for a given

15 Sep 2011: Appendix I contains a derivation of the op-timization problem of maximizing expected social welfare,and Appendix II justifies the fact that it can be solve usingLagrangian methods. ... APPENDIX IIJUSTIFICATION FOR USE OF LAGRANGIAN METHODS. We prove that

15 Sep 2011: to test whether the system can op- erated in a manner that keeps expected inventory levels uniformly bounded through time.

15 Sep 2011: However,in the following section we discuss variations of the problem in which the op-timal policy does indeed lie within the class of partition policies.

15 Sep 2011: The network op-erator posts taris that have been computed for the current operating point ofthe link, which corresponds to some values of the parameters s;t.

15 Sep 2011: Optimal Call Routing in VoIPCostas Courcoubetis. Department of Computer ScienceAthens University. of Economics and Business47A Evelpidon StrAthens 11363, GR. Email: courcou@aueb.gr. Costas KalogirosDepartment of Computer Science. Athens Universityof

18 Sep 2011: Minimizing expected makespans on uniform processor systems 193. Remark. Clearly, the thresholds too= to, =0 and t1o = t(r)I define an op- timal threshold rule.

23 Apr 1997: From: Stephen Gale. Newsgroups: sci.op-research. Subject: Re: SIMPLEX code for PC.

24 Apr 2005: "! # $%& $. '(),.-/10325468739:-;=<4>/@?A+. BDCFEHGHI6JLKNM%OPGHQRQTSAUVSXWVJ6YZBDC@W[C]M_C],WVQba8WdcbGVe]W[C]GVe_fg J6ThiSjekMklCmf GVnoOpWVq c6ekRYUHS. r Y6RMsM_SjesC@W[C]GHJtMkuc5qvTCsCkS,YwnxGVepC]ISYSjUHesSjSGVn.yzG{1C]GVe|GVn}I6RQGHMsGV5IDf! "

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.

9 Jun 2016: Journal of Machine Learning Research? (?)? -? Submitted 11/13; Revised 3/16; Published? /? Modelling Interactions in High-dimensional Data withBacktracking. Rajen D. Shah r.shah@statslab.cam.ac.ukStatistical Laboratory. University of Cambridge.

8 Apr 2017: Goodness of fit tests for high-dimensional linear models. Rajen D. Shah. University of CambridgePeter BühlmannETH Zürich. April 8, 2017. Abstract. In this work we propose a framework for constructing goodness of fit tests in both lowand

29 Apr 2024: Lecture Notes on Statistical Modelling. Qingyuan Zhao. December 2, 2021. Website for this course: http://www.statslab.cam.ac.uk/qz280/teaching/modelling-2021/. Copyright c2021 Dr Qingyuan Zhao (qyzhao@statslab.cam.ac.uk). This document should be

29 Apr 2024: where R(Pn,P) = oP(1/n) is a negligible remainder term. See blackboard:.

29 Apr 2024: 1. cov(Ai, g(Zi)). R3. =1pn. nX. i=1. (Zi, Ai, Yi) op(1). ... This implies. that:pn(̂ ) = 1p. n. nX. i=1. (xi) op(1) (14).

29 Apr 2024: Lecture Notes on Causal Inference(with corrections). Qingyuan Zhao. May 30, 2022. Website for this course: http://www.statslab.cam.ac.uk/qz280/teaching/causal-2020/. Please contact me if you find any mistakes or have any comments. Copyright c2022 Dr

29 Apr 2024: Assumption. I ‖µ̂t µt‖2 = op(n1/4);I ‖µ̂y µy‖2 = op(1);I ‖µ̂t µt‖2 ‖µ̂y µy‖2 = op(n1/2).

29 Apr 2024: RemarksBy assuming f0 and f are differentiable at τ. λ and (f0/f ). ′(τλ) > 0, we show in the paperthat τ̂λ,n,m τλ = Op((n m)1/3).

29 Apr 2024: difference is op(1). The actual proof is much more technical (mainly becauseestimation error complicates the selection event). ... References. 26/28. Assumptions in the paper II. Assumption. (Accuracy of treatment model) ‖µ̂t µt‖ = op(n1/4).

11 Sep 2008: n sup. f F. f (x)pn(x)d x. f (x)p0(x)d x. = OP(1), (3). ... supf F. |(Pn P)(µ̄n f f )| = oP(1/. n). The last two estimates prove (9) since F is P-Donsker.

9 Apr 2007: P. A similar remark appliesto the symbols oP , OP, and oP.]. ... 16). for every real k > 1/2. Furthermore,. β(P̂n, P) = OP(n1/2).

30 Apr 2009: n(pYn pY. ) (pZn pZ). p,λ= oP(1) (8). for p = (or p = 2). ... OP(n2t/(2t1). ) = oP(n1/2. ). since t > 1/2, and we have, for example, the following:.

22 May 2023: We also use the standard OP , oP , O, o notation to estimate the orderof magnitude of sequences of random variables and real numbers, respectively. ... logpf0+"h. pf0(Y ) = hDGf0 [h], WiL2. 12kDGf0 [h]k2L2 oP Yf0 (1) as "! 0,. and the LAN-norm is given by

26 Feb 2010: o(n1/2H(n)2tK(n)ts) oP(K(n)(sk)). If s t, then. ... OP (n1/2(tk)/(2t1)) OP(n1/2H(n)(tk)) o(H(n)2t).

11 Sep 2008: 420) and has convergence rateβ(Pn, P ) = OP (n1/2). Note however that Pn is not consistent in ‖ ‖T V -loss, since ‖Pn P‖T V = 2for every n and absolutely ... pKn (ĥn) p0‖1 = oP (1). (7)If, in addition, p0 Wt1(R) for some 0 < t T , we have.

25 Feb 2020: Mathematical Foundations of Infinite-DimensionalStatistical Models. In nonparametric and high-dimensional statistical models, the classical Gauss–Fisher–Le Cam theory of the optimality of maximum likelihood and Bayesianposterior inference does

16 Jan 2024: Theusual stochastic OP ;oP notation will be used throughout for P D PN or equivalentlyP N. –

19 Dec 2020: p.602, last display of Corollary 7.3.24 should read. = OP. ... n/ log n)γ/(2γ1)un. ), instead of OP. ((n/ log n)γ/(2γ1)un. )p.609, in the 3rd display in Theorem 8.1.1, the exponents should be ‘ 14r1 ’

6 Nov 2017: Kekkonen, H., Lassas, M. and Samuli Siltanen.(2016). Posterior consistency and convergencerates for Bayesian inversion with hypoelliptic op-erators.

19 Nov 2010: Proof. Given ε > 0, apply Proposition 4 below with λ = ε so that ‖F Sn Fn‖ = oP (1/.

17 Feb 2011: The Annals of Statistics2011, Vol. 39, No. 1, 201–231DOI: 10.1214/10-AOS836 Institute of Mathematical Statistics, 2011. GLOBAL UNIFORM RISK BOUNDS FOR WAVELETDECONVOLUTION ESTIMATORS. BY KARIM LOUNICI AND RICHARD NICKL. University of Cambridge. We

19 Feb 2010: The Annals of Statistics2010, Vol. 38, No. 2, 1122–1170DOI: 10.1214/09-AOS738 Institute of Mathematical Statistics, 2010. CONFIDENCE BANDS IN DENSITY ESTIMATION. BY EVARIST GINÉ AND RICHARD NICKL. University of Connecticut and University of

28 Oct 2013: Then, as n ,P nf0 (f0 Cn) 1 α and Rn = OP (1). ... n(f : ‖f f0‖22 > rn. ) = oP (1).Let μn, νn satisfy (21).

22 Jul 2009: Donsker classes F. Our proofs will in fact show ‖P Wn Pn‖F = oP (1/.

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2 Oct 2001: GI?:&6OP-/W.W.-4w+":e&D{B/RS7:W&IiNJ,& J);?:&nJj),9;-/":ef@>B/9,C3-<M7N9,-37& ... p),?N&69 Ba"=-/R),.RS& J Z OP-39ThµBa9;&fJF);-/7:7N+":ey);RS& JBa"N=UcE5);?:&pJj),9;-/":e5@>B/9,C3-<y7N9,-37& 9j)FE.

10 Dec 2004: O 6gfh 7jikU?B]Z>l<VOQX SmOQ;no@p<VKmSeR]SL;> FVEfG7:qrU?ZtsKL;DRT;DOQ;D>T>lU?Mvu)wx<VOQXYU?B]RTyQU8d?U?Op<VK2sBCUVzA;DPDRTSeU?O ... WSeO#;no@p<VKmSeRTSe;>D7uNU<?><VMWSeKmI; BTR>Asp<?P;V7XW BTRTy#U8d8U?Op<JK s#BCUJzA;PDR]SLU?O2BC;DKL<VRTSeU?OY8

22 Jan 2024: Probability. J.R. Norris. January 22, 2024. 1. Contents. 1 Mathematical models for randomness 61.1 A general definition. 61.2 Equally likely outcomes. 61.3 Throwing a die. 61.4 Balls from a bag. 71.5 A well-shuffled pack of cards. 71.6 Distribution

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