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Asymptotics and optimal bandwidth selection for highest density…
www.statslab.cam.ac.uk/~rjs57/Samworth10.pdf21 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. -
IMS CollectionsHigh Dimensional Probability V: The Luminy VolumeVol.…
www.statslab.cam.ac.uk/~nickl/Site/__files/IMSCOLL522.pdf26 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). -
Confidence bands in density estimation
www.statslab.cam.ac.uk/~nickl/Site/__files/AOS738.pdf19 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 -
Maximum likelihood estimation of a multidimensional log-concave…
www.statslab.cam.ac.uk/~rjs57/CSSFinalLV.pdf24 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, -
Adaptive estimation of a distribution function and its density in…
www.statslab.cam.ac.uk/~nickl/Site/__files/BEJ239.pdf19 Nov 2010: Proof. Given ε > 0, apply Proposition 4 below with λ = ε so that ‖F Sn Fn‖ = oP (1/.
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