58,043 research outputs found
Spectrum Estimation: A Unified Framework for Covariance Matrix Estimation and PCA in Large Dimensions
Covariance matrix estimation and principal component analysis (PCA) are two
cornerstones of multivariate analysis. Classic textbook solutions perform
poorly when the dimension of the data is of a magnitude similar to the sample
size, or even larger. In such settings, there is a common remedy for both
statistical problems: nonlinear shrinkage of the eigenvalues of the sample
covariance matrix. The optimal nonlinear shrinkage formula depends on unknown
population quantities and is thus not available. It is, however, possible to
consistently estimate an oracle nonlinear shrinkage, which is motivated on
asymptotic grounds. A key tool to this end is consistent estimation of the set
of eigenvalues of the population covariance matrix (also known as the
spectrum), an interesting and challenging problem in its own right. Extensive
Monte Carlo simulations demonstrate that our methods have desirable
finite-sample properties and outperform previous proposals.Comment: 40 pages, 8 figures, 5 tables, University of Zurich, Department of
Economics, Working Paper No. 105, Revised version, July 201
Robust Pilot Decontamination Based on Joint Angle and Power Domain Discrimination
We address the problem of noise and interference corrupted channel estimation
in massive MIMO systems. Interference, which originates from pilot reuse (or
contamination), can in principle be discriminated on the basis of the
distributions of path angles and amplitudes. In this paper we propose novel
robust channel estimation algorithms exploiting path diversity in both angle
and power domains, relying on a suitable combination of the spatial filtering
and amplitude based projection. The proposed approaches are able to cope with a
wide range of system and topology scenarios, including those where, unlike in
previous works, interference channel may overlap with desired channels in terms
of multipath angles of arrival or exceed them in terms of received power. In
particular we establish analytically the conditions under which the proposed
channel estimator is fully decontaminated. Simulation results confirm the
overall system gains when using the new methods.Comment: 14 pages, 5 figures, accepted for publication in IEEE Transactions on
Signal Processin
Signal Processing in Large Systems: a New Paradigm
For a long time, detection and parameter estimation methods for signal
processing have relied on asymptotic statistics as the number of
observations of a population grows large comparatively to the population size
, i.e. . Modern technological and societal advances now
demand the study of sometimes extremely large populations and simultaneously
require fast signal processing due to accelerated system dynamics. This results
in not-so-large practical ratios , sometimes even smaller than one. A
disruptive change in classical signal processing methods has therefore been
initiated in the past ten years, mostly spurred by the field of large
dimensional random matrix theory. The early works in random matrix theory for
signal processing applications are however scarce and highly technical. This
tutorial provides an accessible methodological introduction to the modern tools
of random matrix theory and to the signal processing methods derived from them,
with an emphasis on simple illustrative examples
When do improved covariance matrix estimators enhance portfolio optimization? An empirical comparative study of nine estimators
The use of improved covariance matrix estimators as an alternative to the
sample estimator is considered an important approach for enhancing portfolio
optimization. Here we empirically compare the performance of 9 improved
covariance estimation procedures by using daily returns of 90 highly
capitalized US stocks for the period 1997-2007. We find that the usefulness of
covariance matrix estimators strongly depends on the ratio between estimation
period T and number of stocks N, on the presence or absence of short selling,
and on the performance metric considered. When short selling is allowed,
several estimation methods achieve a realized risk that is significantly
smaller than the one obtained with the sample covariance method. This is
particularly true when T/N is close to one. Moreover many estimators reduce the
fraction of negative portfolio weights, while little improvement is achieved in
the degree of diversification. On the contrary when short selling is not
allowed and T>N, the considered methods are unable to outperform the sample
covariance in terms of realized risk but can give much more diversified
portfolios than the one obtained with the sample covariance. When T<N the use
of the sample covariance matrix and of the pseudoinverse gives portfolios with
very poor performance.Comment: 30 page
- …