8,028 research outputs found
A pseudo empirical likelihood approach for stratified samples with nonresponse
Nonresponse is common in surveys. When the response probability of a survey
variable depends on through an observed auxiliary categorical variable
(i.e., the response probability of is conditionally independent of
given ), a simple method often used in practice is to use categories as
imputation cells and construct estimators by imputing nonrespondents or
reweighting respondents within each imputation cell. This simple method,
however, is inefficient when some categories have small sizes and ad hoc
methods are often applied to collapse small imputation cells. Assuming a
parametric model on the conditional probability of given and a
nonparametric model on the distribution of , we develop a pseudo empirical
likelihood method to provide more efficient survey estimators. Our method
avoids any ad hoc collapsing small categories, since reweighting or
imputation is done across categories. Asymptotic distributions for
estimators of population means based on the pseudo empirical likelihood method
are derived. For variance estimation, we consider a bootstrap procedure and its
consistency is established. Some simulation results are provided to assess the
finite sample performance of the proposed estimators.Comment: Published in at http://dx.doi.org/10.1214/07-AOS578 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Semidefinite approximation for mixed binary quadratically constrained quadratic programs
Motivated by applications in wireless communications, this paper develops
semidefinite programming (SDP) relaxation techniques for some mixed binary
quadratically constrained quadratic programs (MBQCQP) and analyzes their
approximation performance. We consider both a minimization and a maximization
model of this problem. For the minimization model, the objective is to find a
minimum norm vector in -dimensional real or complex Euclidean space, such
that concave quadratic constraints and a cardinality constraint are
satisfied with both binary and continuous variables. {\color{blue}By employing
a special randomized rounding procedure, we show that the ratio between the
norm of the optimal solution of the minimization model and its SDP relaxation
is upper bounded by \cO(Q^2(M-Q+1)+M^2) in the real case and by
\cO(M(M-Q+1)) in the complex case.} For the maximization model, the goal is
to find a maximum norm vector subject to a set of quadratic constraints and a
cardinality constraint with both binary and continuous variables. We show that
in this case the approximation ratio is bounded from below by
\cO(\epsilon/\ln(M)) for both the real and the complex cases. Moreover, this
ratio is tight up to a constant factor
Joint Downlink Base Station Association and Power Control for Max-Min Fairness: Computation and Complexity
In a heterogeneous network (HetNet) with a large number of low power base
stations (BSs), proper user-BS association and power control is crucial to
achieving desirable system performance. In this paper, we systematically study
the joint BS association and power allocation problem for a downlink cellular
network under the max-min fairness criterion. First, we show that this problem
is NP-hard. Second, we show that the upper bound of the optimal value can be
easily computed, and propose a two-stage algorithm to find a high-quality
suboptimal solution. Simulation results show that the proposed algorithm is
near-optimal in the high-SNR regime. Third, we show that the problem under some
additional mild assumptions can be solved to global optima in polynomial time
by a semi-distributed algorithm. This result is based on a transformation of
the original problem to an assignment problem with gains , where
are the channel gains.Comment: 24 pages, 7 figures, a shorter version submitted to IEEE JSA
Drawing Big Graphs using Spectral Sparsification
Spectral sparsification is a general technique developed by Spielman et al.
to reduce the number of edges in a graph while retaining its structural
properties. We investigate the use of spectral sparsification to produce good
visual representations of big graphs. We evaluate spectral sparsification
approaches on real-world and synthetic graphs. We show that spectral
sparsifiers are more effective than random edge sampling. Our results lead to
guidelines for using spectral sparsification in big graph visualization.Comment: Appears in the Proceedings of the 25th International Symposium on
Graph Drawing and Network Visualization (GD 2017
Iteration Complexity Analysis of Block Coordinate Descent Methods
In this paper, we provide a unified iteration complexity analysis for a
family of general block coordinate descent (BCD) methods, covering popular
methods such as the block coordinate gradient descent (BCGD) and the block
coordinate proximal gradient (BCPG), under various different coordinate update
rules. We unify these algorithms under the so-called Block Successive
Upper-bound Minimization (BSUM) framework, and show that for a broad class of
multi-block nonsmooth convex problems, all algorithms covered by the BSUM
framework achieve a global sublinear iteration complexity of , where r
is the iteration index. Moreover, for the case of block coordinate minimization
(BCM) where each block is minimized exactly, we establish the sublinear
convergence rate of without per block strong convexity assumption.
Further, we show that when there are only two blocks of variables, a special
BSUM algorithm with Gauss-Seidel rule can be accelerated to achieve an improved
rate of
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