2 research outputs found
Scaled largest eigenvalue detection for stationary time-series
This paper studies the performance of the scaled largest eigenvalue (SLE) detector used for the detection of stationary time-series. We focus on a single-antenna setup and a blind detection scenario (neither the signal covariance, nor the noise variance are known). The SLE detector has received much attention in the context of cognitive radios (CR) due to its simplicity, good performance and robustness to noise level uncertainties. Specifically, our goal is to analyze the detector based on the statistic Γ = λ1∑i=1 p λi, where λ1 ≥ λ2 ≥ ⋯ ≥ λp represent the ordered eigenvalues of the sample covariance matrix. We derive a large-sample-size closed-form approximation for the test statistic which allows us to derive its statistical distribution and set up the detector to achieve the required probability of false-alarm (Pfa) and probability of detection (Pd). We also study the robustness of the detector in the presence of noise uncertainty and impulsive-noise and investigate the benefits of the spatial sign filter for such scenarios.SCOPUS: ar.jinfo:eu-repo/semantics/publishe
Extreme eigenvalues of sample covariance matrices under generalized elliptical models with applications
We consider the extreme eigenvalues of the sample covariance matrix
under the generalized elliptical model that Here
is a bounded positive definite deterministic matrix representing
the population covariance structure, is a random matrix
containing either independent columns sampled from the unit sphere in
or i.i.d. centered entries with variance and is a
diagonal random matrix containing i.i.d. entries and independent of Such a
model finds important applications in statistics and machine learning.
In this paper, assuming that and are comparably large, we prove that
the extreme edge eigenvalues of can have several types of distributions
depending on and asymptotically. These distributions include:
Gumbel, Fr\'echet, Weibull, Tracy-Widom, Gaussian and their mixtures. On the
one hand, when the random variables in have unbounded support, the edge
eigenvalues of can have either Gumbel or Fr\'echet distribution depending
on the tail decay property of On the other hand, when the random variables
in have bounded support, under some mild regularity assumptions on
the edge eigenvalues of can exhibit Weibull, Tracy-Widom,
Gaussian or their mixtures. Based on our theoretical results, we consider two
important applications. First, we propose some statistics and procedure to
detect and estimate the possible spikes for elliptically distributed data.
Second, in the context of a factor model, by using the multiplier bootstrap
procedure via selecting the weights in we propose a new algorithm to infer
and estimate the number of factors in the factor model. Numerical simulations
also confirm the accuracy and powerfulness of our proposed methods and
illustrate better performance compared to some existing methods in the
literature.Comment: 90 pages, 6 figures, some typos are correcte