15,283 research outputs found
Robust Multiple Signal Classification via Probability Measure Transformation
In this paper, we introduce a new framework for robust multiple signal
classification (MUSIC). The proposed framework, called robust
measure-transformed (MT) MUSIC, is based on applying a transform to the
probability distribution of the received signals, i.e., transformation of the
probability measure defined on the observation space. In robust MT-MUSIC, the
sample covariance is replaced by the empirical MT-covariance. By judicious
choice of the transform we show that: 1) the resulting empirical MT-covariance
is B-robust, with bounded influence function that takes negligible values for
large norm outliers, and 2) under the assumption of spherically contoured noise
distribution, the noise subspace can be determined from the eigendecomposition
of the MT-covariance. Furthermore, we derive a new robust measure-transformed
minimum description length (MDL) criterion for estimating the number of
signals, and extend the MT-MUSIC framework to the case of coherent signals. The
proposed approach is illustrated in simulation examples that show its
advantages as compared to other robust MUSIC and MDL generalizations
Semiparametric Inference and Lower Bounds for Real Elliptically Symmetric Distributions
This paper has a twofold goal. The first aim is to provide a deeper
understanding of the family of the Real Elliptically Symmetric (RES)
distributions by investigating their intrinsic semiparametric nature. The
second aim is to derive a semiparametric lower bound for the estimation of the
parametric component of the model. The RES distributions represent a
semiparametric model where the parametric part is given by the mean vector and
by the scatter matrix while the non-parametric, infinite-dimensional, part is
represented by the density generator. Since, in practical applications, we are
often interested only in the estimation of the parametric component, the
density generator can be considered as nuisance. The first part of the paper is
dedicated to conveniently place the RES distributions in the framework of the
semiparametric group models. The second part of the paper, building on the
mathematical tools previously introduced, the Constrained Semiparametric
Cram\'{e}r-Rao Bound (CSCRB) for the estimation of the mean vector and of the
constrained scatter matrix of a RES distributed random vector is introduced.
The CSCRB provides a lower bound on the Mean Squared Error (MSE) of any robust
-estimator of mean vector and scatter matrix when no a-priori information on
the density generator is available. A closed form expression for the CSCRB is
derived. Finally, in simulations, we assess the statistical efficiency of the
Tyler's and Huber's scatter matrix -estimators with respect to the CSCRB.Comment: This paper has been accepted for publication in IEEE Transactions on
Signal Processin
Semiparametric CRB and Slepian-Bangs formulas for Complex Elliptically Symmetric Distributions
The main aim of this paper is to extend the semiparametric inference
methodology, recently investigated for Real Elliptically Symmetric (RES)
distributions, to Complex Elliptically Symmetric (CES) distributions. The
generalization to the complex field is of fundamental importance in all
practical applications that exploit the complex representation of the acquired
data. Moreover, the CES distributions has been widely recognized as a valuable
and general model to statistically describe the non-Gaussian behaviour of
datasets originated from a wide variety of physical measurement processes. The
paper is divided in two parts. In the first part, a closed form expression of
the constrained Semiparametric Cram\'{e}r-Rao Bound (CSCRB) for the joint
estimation of complex mean vector and complex scatter matrix of a set of
CES-distributed random vectors is obtained by exploiting the so-called
\textit{Wirtinger} or -\textit{calculus}. The second part
deals with the derivation of the semiparametric version of the Slepian-Bangs
formula in the context of the CES model. Specifically, the proposed
Semiparametric Slepian-Bangs (SSB) formula provides us with a useful and
ready-to-use expression of the Semiparametric Fisher Information Matrix (SFIM)
for the estimation of a parameter vector parametrizing the complex mean and the
complex scatter matrix of a CES-distributed vector in the presence of unknown,
nuisance, density generator. Furthermore, we show how to exploit the derived
SSB formula to obtain the semiparametric counterpart of the Stochastic CRB for
Direction of Arrival (DOA) estimation under a random signal model assumption.
Simulation results are also provided to clarify the theoretical findings and to
demonstrate their usefulness in common array processing applications.Comment: Submitted to IEEE Transactions on Signal Processing. arXiv admin
note: substantial text overlap with arXiv:1807.08505, arXiv:1807.0893
An Estimation and Analysis Framework for the Rasch Model
The Rasch model is widely used for item response analysis in applications
ranging from recommender systems to psychology, education, and finance. While a
number of estimators have been proposed for the Rasch model over the last
decades, the available analytical performance guarantees are mostly asymptotic.
This paper provides a framework that relies on a novel linear minimum
mean-squared error (L-MMSE) estimator which enables an exact, nonasymptotic,
and closed-form analysis of the parameter estimation error under the Rasch
model. The proposed framework provides guidelines on the number of items and
responses required to attain low estimation errors in tests or surveys. We
furthermore demonstrate its efficacy on a number of real-world collaborative
filtering datasets, which reveals that the proposed L-MMSE estimator performs
on par with state-of-the-art nonlinear estimators in terms of predictive
performance.Comment: To be presented at ICML 201
Performance analysis and optimal selection of large mean-variance portfolios under estimation risk
We study the consistency of sample mean-variance portfolios of arbitrarily
high dimension that are based on Bayesian or shrinkage estimation of the input
parameters as well as weighted sampling. In an asymptotic setting where the
number of assets remains comparable in magnitude to the sample size, we provide
a characterization of the estimation risk by providing deterministic
equivalents of the portfolio out-of-sample performance in terms of the
underlying investment scenario. The previous estimates represent a means of
quantifying the amount of risk underestimation and return overestimation of
improved portfolio constructions beyond standard ones. Well-known for the
latter, if not corrected, these deviations lead to inaccurate and overly
optimistic Sharpe-based investment decisions. Our results are based on recent
contributions in the field of random matrix theory. Along with the asymptotic
analysis, the analytical framework allows us to find bias corrections improving
on the achieved out-of-sample performance of typical portfolio constructions.
Some numerical simulations validate our theoretical findings
- …