23,074 research outputs found
Adaptive covariance matrix estimation through block thresholding
Estimation of large covariance matrices has drawn considerable recent
attention, and the theoretical focus so far has mainly been on developing a
minimax theory over a fixed parameter space. In this paper, we consider
adaptive covariance matrix estimation where the goal is to construct a single
procedure which is minimax rate optimal simultaneously over each parameter
space in a large collection. A fully data-driven block thresholding estimator
is proposed. The estimator is constructed by carefully dividing the sample
covariance matrix into blocks and then simultaneously estimating the entries in
a block by thresholding. The estimator is shown to be optimally rate adaptive
over a wide range of bandable covariance matrices. A simulation study is
carried out and shows that the block thresholding estimator performs well
numerically. Some of the technical tools developed in this paper can also be of
independent interest.Comment: Published in at http://dx.doi.org/10.1214/12-AOS999 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Discussion: "A significance test for the lasso"
Discussion of "A significance test for the lasso" by Richard Lockhart,
Jonathan Taylor, Ryan J. Tibshirani, Robert Tibshirani [arXiv:1301.7161].Comment: Published in at http://dx.doi.org/10.1214/13-AOS1175B the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Optimal estimation of the mean function based on discretely sampled functional data: Phase transition
The problem of estimating the mean of random functions based on discretely
sampled data arises naturally in functional data analysis. In this paper, we
study optimal estimation of the mean function under both common and independent
designs. Minimax rates of convergence are established and easily implementable
rate-optimal estimators are introduced. The analysis reveals interesting and
different phase transition phenomena in the two cases. Under the common design,
the sampling frequency solely determines the optimal rate of convergence when
it is relatively small and the sampling frequency has no effect on the optimal
rate when it is large. On the other hand, under the independent design, the
optimal rate of convergence is determined jointly by the sampling frequency and
the number of curves when the sampling frequency is relatively small. When it
is large, the sampling frequency has no effect on the optimal rate. Another
interesting contrast between the two settings is that smoothing is necessary
under the independent design, while, somewhat surprisingly, it is not essential
under the common design.Comment: Published in at http://dx.doi.org/10.1214/11-AOS898 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Sediment and Hydrologic Budgets for the Lake of the Woods Watershed, Champaign County, Illinois
published or submitted for publicationis peer reviewedOpe
Influence of boundary conditions and geometric imperfections on lateralātorsional buckling resistance of a pultruded FRP I-beam by FEA
Presented are results from geometric non-linear finite element analyses to examine the lateral torsional buckling (LTB) resistance of a Pultruded fibre reinforced polymer (FRP) I-beam when initial geometric imperfections associated with the LTB mode shape are introduced. A data reduction method is proposed to define the limiting buckling load and the method is used to present strength results for a range of beam slendernesses and geometric imperfections. Prior to reporting on these non-linear analyses, Eigenvalue FE analyses are used to establish the influence on resistance of changing load height or displacement boundary conditions. By comparing predictions for the beam with either FRP or steel elastic constants it is found that the former has a relatively larger effect on buckling strength with changes in load height and end warping fixity. The developed finite element modelling methodology will enable parametric studies to be performed for the development of closed form formulae that will be reliable for the design of FRP beams against LTB failure
Bipairing and the Stripe Phase in 4-Leg Ladders
Density Matrix Renormalization Group (DMRG) calculations on 4-leg t-J and
Hubbard ladders have found a phase exhibiting "stripes" at intermediate doping.
Such behavior can be viewed as generalized Friedel oscillations, with
wavelength equal to the inverse hole density, induced by the open boundary
conditions. So far, this phase has not been understood using the conventional
weak coupling bosonization approach. Based on studies from a general
bosonization proof, finite size spectrum, an improved analysis of weak coupling
renormalization group equations and the decoupled 2-leg ladders limit, we here
find new types of phases of 4-leg ladders which exhibit "stripes". They also
inevitably exhibit "bipairing", meaning that there is a gap to add 1 or 2
electrons (but not 4) and that both single electron and electron pair
correlation functions decay exponentially while correlation functions of charge
4 operators exhibit power-law decay. Whether or not bipairing occurs in the
stripe phase found in DMRG is an important open question.Comment: 33 pages, 4 figure
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