68,747 research outputs found
Estimating the Null and the Proportion of non-Null effects in Large-scale Multiple Comparisons
An important issue raised by Efron in the context of large-scale multiple
comparisons is that in many applications the usual assumption that the null
distribution is known is incorrect, and seemingly negligible differences in the
null may result in large differences in subsequent studies. This suggests that
a careful study of estimation of the null is indispensable.
In this paper, we consider the problem of estimating a null normal
distribution, and a closely related problem, estimation of the proportion of
non-null effects. We develop an approach based on the empirical characteristic
function and Fourier analysis. The estimators are shown to be uniformly
consistent over a wide class of parameters. Numerical performance of the
estimators is investigated using both simulated and real data. In particular,
we apply our procedure to the analysis of breast cancer and HIV microarray data
sets. The estimators perform favorably in comparison to existing methods.Comment: 42 pages, 6 figure
Optimal rates of convergence for estimating the null density and proportion of nonnull effects in large-scale multiple testing
An important estimation problem that is closely related to large-scale
multiple testing is that of estimating the null density and the proportion of
nonnull effects. A few estimators have been introduced in the literature;
however, several important problems, including the evaluation of the minimax
rate of convergence and the construction of rate-optimal estimators, remain
open. In this paper, we consider optimal estimation of the null density and the
proportion of nonnull effects. Both minimax lower and upper bounds are derived.
The lower bound is established by a two-point testing argument, where at the
core is the novel construction of two least favorable marginal densities
and . The density is heavy tailed both in the spatial and frequency
domains and is a perturbation of such that the characteristic
functions associated with and match each other in low frequencies.
The minimax upper bound is obtained by constructing estimators which rely on
the empirical characteristic function and Fourier analysis. The estimator is
shown to be minimax rate optimal. Compared to existing methods in the
literature, the proposed procedure not only provides more precise estimates of
the null density and the proportion of the nonnull effects, but also yields
more accurate results when used inside some multiple testing procedures which
aim at controlling the False Discovery Rate (FDR). The procedure is easy to
implement and numerical results are given.Comment: Published in at http://dx.doi.org/10.1214/09-AOS696 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Nonlinear microwave response of MgB2
We calculate the intrinsic nonlinear microwave response of the two gap
superconductor MgB2 in the clean and dirty limits. Due to the small value of
the pi band gap, the nonlinear response at low temperatures is larger than for
a single gap Bardeen-Cooper-Schrieffer (BCS) s-wave superconductor with a
transition temperature of 40 K. Comparing this result with the intrinsic
nonlinear d-wave response of YBa2Cu3O7 (YBCO) we find a comparable response at
temperatures around 20 K. Due to its two gap nature, impurity scattering in
MgB2 can be used to reduce the nonlinear response if the scattering rate in the
pi band is made larger than the one in the sigma band.Comment: 4 pages, 4 figure
Effect and Compensation of Timing Jitter in Through-Wall Human Indication via Impulse Through-Wall Radar
Impulse through-wall radar (TWR) is considered as one of preferred choices for through-wall human indication due to its good penetration and high range resolution. Large bandwidth available for impulse TWR results in high range resolution, but also brings an atypical adversity issue not substantial in narrowband radars — high timing jitter effect, caused by the non-ideal sampling clock at the receiver. The fact that impulse TWR employs very narrow pulses makes little jitter inaccuracy large enough to destroy the signal correlation property and then degrade clutter suppression performance. In this paper, we focus on the timing jitter impact on clutter suppression in through-wall human indication via impulse TWR. We setup a simple timing jitter model and propose a criterion namely average range profile (ARP) contrast is to evaluate the jitter level. To combat timing jitter, we also develop an effective compensation method based on local ARP contrast maximization. The proposed method can be implemented pulse by pulse followed by exponential average background subtraction algorithm to mitigate clutters. Through-wall experiments demonstrate that the proposed method can dramatically improve through-wall human indication performance
Estimation and confidence sets for sparse normal mixtures
For high dimensional statistical models, researchers have begun to focus on
situations which can be described as having relatively few moderately large
coefficients. Such situations lead to some very subtle statistical problems. In
particular, Ingster and Donoho and Jin have considered a sparse normal means
testing problem, in which they described the precise demarcation or detection
boundary. Meinshausen and Rice have shown that it is even possible to estimate
consistently the fraction of nonzero coordinates on a subset of the detectable
region, but leave unanswered the question of exactly in which parts of the
detectable region consistent estimation is possible. In the present paper we
develop a new approach for estimating the fraction of nonzero means for
problems where the nonzero means are moderately large. We show that the
detection region described by Ingster and Donoho and Jin turns out to be the
region where it is possible to consistently estimate the expected fraction of
nonzero coordinates. This theory is developed further and minimax rates of
convergence are derived. A procedure is constructed which attains the optimal
rate of convergence in this setting. Furthermore, the procedure also provides
an honest lower bound for confidence intervals while minimizing the expected
length of such an interval. Simulations are used to enable comparison with the
work of Meinshausen and Rice, where a procedure is given but where rates of
convergence have not been discussed. Extensions to more general Gaussian
mixture models are also given.Comment: Published in at http://dx.doi.org/10.1214/009053607000000334 the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Chiral rings and GSO projection in Orbifolds
The GSO projection in the twisted sector of orbifold background is sometimes
subtle and incompatible descriptions are found in literatures. Here, from the
equivalence of partition functions in NSR and GS formalisms, we give a simple
rule of GSO projection for the chiral rings of string theory in \C^r/\Z_n,
. Necessary constructions of chiral rings are given by explicit mode
analysis.Comment: 24 page
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