398,289 research outputs found
Properties of higher criticism under strong dependence
The problem of signal detection using sparse, faint information is closely
related to a variety of contemporary statistical problems, including the
control of false-discovery rate, and classification using very high-dimensional
data. Each problem can be solved by conducting a large number of simultaneous
hypothesis tests, the properties of which are readily accessed under the
assumption of independence. In this paper we address the case of dependent
data, in the context of higher criticism methods for signal detection.
Short-range dependence has no first-order impact on performance, but the
situation changes dramatically under strong dependence. There, although higher
criticism can continue to perform well, it can be bettered using methods based
on differences of signal values or on the maximum of the data. The relatively
inferior performance of higher criticism in such cases can be explained in
terms of the fact that, under strong dependence, the higher criticism statistic
behaves as though the data were partitioned into very large blocks, with all
but a single representative of each block being eliminated from the dataset.Comment: Published in at http://dx.doi.org/10.1214/009053607000000767 the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Finding the chiral gravitational wave background of an axion-SU(2) inflationary model using CMB observations and laser interferometers
A detection of B-mode polarization of the Cosmic Microwave Background (CMB)
anisotropies would confirm the presence of a primordial gravitational wave
background (GWB). In the inflation paradigm this would be an unprecedented
probe of the energy scale of inflation as it is directly proportional to the
power spectrum of the GWB. However, similar tensor perturbations can be
produced by the matter fields present during inflation, breaking this simple
relationship. It is therefore important to be able to distinguish between
different generation mechanisms of the GWB. In this paper, we analyse the
detectability of a new axion-SU(2) gauge field model using its chiral,
scale-dependent tensor spectrum. We forecast the detectability of the resulting
CMB TB and EB cross-correlations by the LiteBIRD satellite, considering the
effects of residual foregrounds, gravitational lensing, and for the first time
assess the ability of such an experiment to jointly detect primordial TB and EB
spectra and self-calibrate its polarimeter. We find that LiteBIRD will be able
to detect the chiral signal for with denoting the
tensor-to-scalar ratio at the peak scale, and that the maximum signal-to-noise
for is . We go on to consider an advanced stage of a
LISA-like mission, and find that such experiments would complement CMB
observations by providing sensitivity to GWB chirality on scales inaccessible
to the CMB. We conclude that in order to use the CMB to distinguish this model
from a conventional vacuum fluctuation model two-point statistics provide some
power, but to achieve high statistical significance we would require higher
order statistics which take advantage of the model's non-Gaussianity. On the
other hand, in the case of a spectrum peaked at very small scales, inaccessible
to the CMB, a highly significant detection could be made using space-based
laser interferometers.Comment: 24 pages, 12 figures, accepted by PhysRev
Direction Finding Estimators of Cyclostationary Signals in Array Processing for Microwave Power Transmission
A solar power satellite is paid attention to as a clean, inexhaustible large- scale base-load power supply. The following technology related to beam control is used: A pilot signal is sent from the power receiving site and after direction of arrival estimation the beam is directed back to the earth by same direction. A novel direction-finding algorithm based on linear prediction technique for exploiting cyclostationary statistical information (spatial and temporal) is explored. Many modulated communication signals exhibit a cyclostationarity (or periodic correlation) property, corresponding to the underlying periodicity arising from carrier frequencies or baud rates. The problem was solved by using both cyclic second-order statistics and cyclic higher-order statistics. By evaluating the corresponding cyclic statistics of the received data at certain cycle frequencies, we can extract the cyclic correlations of only signals with the same cycle frequency and null out the cyclic correlations of stationary additive noise and all other co-channel interferences with different cycle frequencies. Thus, the signal detection capability can be significantly improved. The proposed algorithms employ cyclic higher-order statistics of the array output and suppress additive Gaussian noise of unknown spectral content, even when the noise shares common cycle frequencies with the non-Gaussian signals of interest. The proposed method completely exploits temporal information (multiple lag ), and also can correctly estimate direction of arrival of desired signals by suppressing undesired signals. Our approach was generalized over direction of arrival estimation of cyclostationary coherent signals. In this paper, we propose a new approach for exploiting cyclostationarity that seems to be more advanced in comparison with the other existing direction finding algorithms
A Joint Optimization Criterion for Blind DS-CDMA Detection
This paper addresses the problem of the blind detection of a desired user in an asynchronous DS-CDMA communications system
with multipath propagation channels. Starting from the inverse filter criterion introduced by Tugnait and Li in 2001, we propose
to tackle the problem in the context of the blind signal extraction methods for ICA. In order to improve the performance of the
detector, we present a criterion based on the joint optimization of several higher-order statistics of the outputs. An algorithm that
optimizes the proposed criterion is described, and its improved performance and robustness with respect to the near-far problem
are corroborated through simulations. Additionally, a simulation using measurements on a real software-radio platform at 5 GHz
has also been performed.Ministerio de Ciencia y tecnologĂa TEC2004-06451-C05-0
On the (In)Efficiency of the Cross-Correlation Statistic for Gravitational Wave Stochastic Background Signals with Non-Gaussian Noise and Heterogeneous Detector Sensitivities
Under standard assumptions including stationary and serially uncorrelated
Gaussian gravitational wave stochastic background signal and noise
distributions, as well as homogenous detector sensitivities, the standard
cross-correlation detection statistic is known to be optimal in the sense of
minimizing the probability of a false dismissal at a fixed value of the
probability of a false alarm. The focus of this paper is to analyze the
comparative efficiency of this statistic, versus a simple alternative statistic
obtained by cross-correlating the \textit{squared} measurements, in situations
that deviate from such standard assumptions. We find that differences in
detector sensitivities have a large impact on the comparative efficiency of the
cross-correlation detection statistic, which is dominated by the alternative
statistic when these differences reach one order of magnitude. This effect
holds even when both the signal and noise distributions are Gaussian. While the
presence of non-Gaussian signals has no material impact for reasonable
parameter values, the relative inefficiency of the cross-correlation statistic
is less prominent for fat-tailed noise distributions but it is magnified in
case noise distributions have skewness parameters of opposite signs. Our
results suggest that introducing an alternative detection statistic can lead to
noticeable sensitivity gains when noise distributions are possibly non-Gaussian
and/or when detector sensitivities exhibit substantial differences, a situation
that is expected to hold in joint detections from Advanced LIGO and Advanced
Virgo, in particular in the early phases of development of the detectors, or in
joint detections from Advanced LIGO and Einstein Telescope.Comment: 36 pages, 5 figures and 1 table, accepted for publication in Physical
Review
Detection of multiplicative noise in stationary random processes using second- and higher order statistics
This paper addresses the problem of detecting the presence of colored multiplicative noise, when the information process can be modeled as a parametric ARMA process. For the case of zero-mean multiplicative noise, a cumulant based suboptimal detector is studied. This detector tests the nullity of a specific cumulant slice. A second detector is developed when the multiplicative noise is nonzero mean. This detector consists of filtering the data by an estimated AR filter. Cumulants of the residual data are then shown to be well suited to the detection problem. Theoretical expressions for the asymptotic probability of
detection are given. Simulation-derived finite-sample ROC curves are shown for different sets of model parameters
Detecting a stochastic background of gravitational waves in the presence of non-Gaussian noise: A performance of generalized cross-correlation statistic
We discuss a robust data analysis method to detect a stochastic background of
gravitational waves in the presence of non-Gaussian noise. In contrast to the
standard cross-correlation (SCC) statistic frequently used in the stochastic
background searches, we consider a {\it generalized cross-correlation} (GCC)
statistic, which is nearly optimal even in the presence of non-Gaussian noise.
The detection efficiency of the GCC statistic is investigated analytically,
particularly focusing on the statistical relation between the false-alarm and
the false-dismissal probabilities, and the minimum detectable amplitude of
gravitational-wave signals. We derive simple analytic formulae for these
statistical quantities. The robustness of the GCC statistic is clarified based
on these formulae, and one finds that the detection efficiency of the GCC
statistic roughly corresponds to the one of the SCC statistic neglecting the
contribution of non-Gaussian tails. This remarkable property is checked by
performing the Monte Carlo simulations and successful agreement between
analytic and simulation results was found.Comment: 15 pages, 8 figures, presentation and some figures modified, final
version to be published in PR
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