380 research outputs found
A Convex Approach to Frisch-Kalman Problem
This paper proposes a convex approach to the Frisch-Kalman problem that
identifies the linear relations among variables from noisy observations. The
problem was proposed by Ragnar Frisch in 1930s, and was promoted and further
developed by Rudolf Kalman later in 1980s. It is essentially a rank
minimization problem with convex constraints. Regarding this problem,
analytical results and heuristic methods have been pursued over a half century.
The proposed convex method in this paper is shown to be accurate and
demonstrated to outperform several commonly adopted heuristics when the noise
components are relatively small compared with the underlying data
Factor Models with Real Data: a Robust Estimation of the Number of Factors
Factor models are a very efficient way to describe high dimensional vectors
of data in terms of a small number of common relevant factors. This problem,
which is of fundamental importance in many disciplines, is usually reformulated
in mathematical terms as follows. We are given the covariance matrix Sigma of
the available data. Sigma must be additively decomposed as the sum of two
positive semidefinite matrices D and L: D | that accounts for the idiosyncratic
noise affecting the knowledge of each component of the available vector of data
| must be diagonal and L must have the smallest possible rank in order to
describe the available data in terms of the smallest possible number of
independent factors.
In practice, however, the matrix Sigma is never known and therefore it must
be estimated from the data so that only an approximation of Sigma is actually
available. This paper discusses the issues that arise from this uncertainty and
provides a strategy to deal with the problem of robustly estimating the number
of factors.Comment: arXiv admin note: text overlap with arXiv:1708.0040
Towards a new theory of economic policy: Continuity and innovation
This paper outlines the evolution of the theory of economic policy from the classical contributions of Frisch, Hansen, Tinbergen and Theil to situations of strategic interaction. Andrew Hughes Hallett has taken an active and relevant part in this evolution, having contributed to both the development and recent rediscovery of the classical theory, with possible relevant applications for model building.policy games, policy effectiveness, controllability, equilibrium existence
Towards a new theory of economic policy: Continuity and innovation
This paper outlines the evolution of the theory of economic policy from the classical contributions of Frisch, Hansen, Tinbergen and Theil to situations of strategic interaction. Andrew Hughes Hallett has taken an active and relevant part in this evolution, having contributed to both the development and recent rediscovery of the classical theory, with possible relevant applications for model building.policy games; policy effectiveness; controllability; equilibrium existence
Diagonal and Low-Rank Matrix Decompositions, Correlation Matrices, and Ellipsoid Fitting
In this paper we establish links between, and new results for, three problems
that are not usually considered together. The first is a matrix decomposition
problem that arises in areas such as statistical modeling and signal
processing: given a matrix formed as the sum of an unknown diagonal matrix
and an unknown low rank positive semidefinite matrix, decompose into these
constituents. The second problem we consider is to determine the facial
structure of the set of correlation matrices, a convex set also known as the
elliptope. This convex body, and particularly its facial structure, plays a
role in applications from combinatorial optimization to mathematical finance.
The third problem is a basic geometric question: given points
(where ) determine whether there is a centered
ellipsoid passing \emph{exactly} through all of the points.
We show that in a precise sense these three problems are equivalent.
Furthermore we establish a simple sufficient condition on a subspace that
ensures any positive semidefinite matrix with column space can be
recovered from for any diagonal matrix using a convex
optimization-based heuristic known as minimum trace factor analysis. This
result leads to a new understanding of the structure of rank-deficient
correlation matrices and a simple condition on a set of points that ensures
there is a centered ellipsoid passing through them.Comment: 20 page
Errors-In-Variables-Based Approach for the Identification of AR Time-Varying Fading Channels
This letter deals with the identification of time-varying
Rayleigh fading channels using a training sequence-based
approach. When the fading channel is approximated by an
autoregressive (AR) process, it can be estimated by means of
Kalman filtering, for instance. However, this method requires the
estimations of both the AR parameters and the noise variances in
the state–space representation of the system. For this purpose, the
existing noise compensated approaches could be considered, but
they usually require a long observation window and do not necessarily
provide reliable estimates when the signal-to-noise ratio is
low. Therefore, we propose to view the channel identification as an
errors-in-variables (EIV) issue. The method consists in searching
the noise variances that enable specific noise compensated autocorrelation
matrices of observations to be positive semidefinite. In
addition, the AR parameters can be estimated from the null spaces
of these matrices. Simulation results confirm the effectiveness of
this approach, especially in presence of a high amount of noise
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