136 research outputs found
Auditor Malpractice: Identifying High-Risk Engagements by the Use of Multivariate Analysis
Auditor Malpractice: Identifying high-risk engagements by the use of multivariate analysi
The forensic analysis of soil by FTIR with multivariate analysis
Over the past few years more and more studies have been carried out in an attempt to utilize chemical profiles
of soil using a wide variety of analytical methods. The value of soil as evidence rests with its prevalence at
crime scenes and its transferability between the scene and the criminal. This can be of value for comparison if
the scene of crime is known, but could also be so in the identification of a scene. The main basis for the
comparison of sites to determine provenance is that soils vary from one place to another. The aim of this work
is to find simple methods to identify soil provenance based on FTIR and multivariate analysi
On Identity Tests for High Dimensional Data Using RMT
In this work, we redefined two important statistics, the CLRT test (Bai
et.al., Ann. Stat. 37 (2009) 3822-3840) and the LW test (Ledoit and Wolf, Ann.
Stat. 30 (2002) 1081-1102) on identity tests for high dimensional data using
random matrix theories. Compared with existing CLRT and LW tests, the new tests
can accommodate data which has unknown means and non-Gaussian distributions.
Simulations demonstrate that the new tests have good properties in terms of
size and power. What is more, even for Gaussian data, our new tests perform
favorably in comparison to existing tests. Finally, we find the CLRT is more
sensitive to eigenvalues less than 1 while the LW test has more advantages in
relation to detecting eigenvalues larger than 1.Comment: 16 pages, 2 figures, 3 tables, To be published in the Journal of
Multivariate Analysi
Large Dimensional Analysis and Optimization of Robust Shrinkage Covariance Matrix Estimators
This article studies two regularized robust estimators of scatter matrices
proposed (and proved to be well defined) in parallel in (Chen et al., 2011) and
(Pascal et al., 2013), based on Tyler's robust M-estimator (Tyler, 1987) and on
Ledoit and Wolf's shrinkage covariance matrix estimator (Ledoit and Wolf,
2004). These hybrid estimators have the advantage of conveying (i) robustness
to outliers or impulsive samples and (ii) small sample size adequacy to the
classical sample covariance matrix estimator. We consider here the case of
i.i.d. elliptical zero mean samples in the regime where both sample and
population sizes are large. We demonstrate that, under this setting, the
estimators under study asymptotically behave similar to well-understood random
matrix models. This characterization allows us to derive optimal shrinkage
strategies to estimate the population scatter matrix, improving significantly
upon the empirical shrinkage method proposed in (Chen et al., 2011).Comment: Journal of Multivariate Analysi
Extreme Eigenvalue Distributions of Some Complex Correlated Non-Central Wishart and Gamma-Wishart Random Matrices
Let be a correlated complex non-central Wishart matrix defined
through , where is complex Gaussian with non-zero mean and
non-trivial covariance . We derive exact expressions for
the cumulative distribution functions (c.d.f.s) of the extreme eigenvalues
(i.e., maximum and minimum) of for some particular cases. These
results are quite simple, involving rapidly converging infinite series, and
apply for the practically important case where has rank
one. We also derive analogous results for a certain class of gamma-Wishart
random matrices, for which
follows a matrix-variate gamma distribution. The eigenvalue distributions in
this paper have various applications to wireless communication systems, and
arise in other fields such as econometrics, statistical physics, and
multivariate statistics.Comment: Accepted for publication in Journal of Multivariate Analysi
The multivariate Piecing-Together approach revisited
The univariate Piecing-Together approach (PT) fits a univariate generalized
Pareto distribution (GPD) to the upper tail of a given distribution function in
a continuous manner. A multivariate extension was established by Aulbach et al.
(2012a): The upper tail of a given copula C is cut off and replaced by a
multivariate GPD-copula in a continuous manner, yielding a new copula called a
PT-copula. Then each margin of this PT-copula is transformed by a given
univariate distribution function. This provides a multivariate distribution
function with prescribed margins, whose copula is a GPD-copula that coincides
in its central part with C. In addition to Aulbach et al. (2012a), we achieve
in the present paper an exact representation of the PT-copula's upper tail,
giving further insight into the multivariate PT approach. A variant based on
the empirical copula is also added. Furthermore our findings enable us to
establish a functional PT version as well.Comment: 12 pages, 1 figure. To appear in the Journal of Multivariate Analysi
Densities for random balanced sampling
A random balanced sample (RBS) is a multivariate distribution with n
components X_1,...,X_n, each uniformly distributed on [-1, 1], such that the
sum of these components is precisely 0. The corresponding vectors X lie in an
(n-1)-dimensional polytope M(n). We present new methods for the construction of
such RBS via densities over M(n) and these apply for arbitrary n. While simple
densities had been known previously for small values of n (namely 2,3 and 4),
for larger n the known distributions with large support were fractal
distributions (with fractal dimension asymptotic to n as n approaches
infinity). Applications of RBS distributions include sampling with antithetic
coupling to reduce variance, and the isolation of nonlinearities. We also show
that the previously known densities (for n<5) are in fact the only solutions in
a natural and very large class of potential RBS densities. This finding
clarifies the need for new methods, such as those presented here.Comment: 20 pages, 6 figures, to appear in Journal of Multivariate Analysi
Parametric estimation of the driving L\'evy process of multivariate CARMA processes from discrete observations
We consider the parametric estimation of the driving L\'evy process of a
multivariate continuous-time autoregressive moving average (MCARMA) process,
which is observed on the discrete time grid . Beginning with a
new state space representation, we develop a method to recover the driving
L\'evy process exactly from a continuous record of the observed MCARMA process.
We use tools from numerical analysis and the theory of infinitely divisible
distributions to extend this result to allow for the approximate recovery of
unit increments of the driving L\'evy process from discrete-time observations
of the MCARMA process. We show that, if the sampling interval is chosen
dependent on , the length of the observation horizon, such that
converges to zero as tends to infinity, then any suitable generalized
method of moments estimator based on this reconstructed sample of unit
increments has the same asymptotic distribution as the one based on the true
increments, and is, in particular, asymptotically normally distributed.Comment: 38 pages, four figures; to appear in Journal of Multivariate Analysi
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