Covariance Averaging for Improved Estimation and Portfolio Allocation

We propose a new method for estimating the covariance matrix of a multivariate time series of nancial returns. The method is based on estimating sample covariances from overlapping windows of observations which are then appropriately weighted to obtain the nal covariance estimate. We extend the idea of (model) covariance averaging o ered in the covariance shrinkage approach by means of greater ease of use, exibility and robustness in averaging information over different data segments. The suggested approach does not su er from the curse of dimensionality and can be used without problems of either approximation or any demand for numerical optimization.

Improved reliability in diagnosing faults using multivariate statistics

This paper analyses multivariate statistical techniques for identifying and isolating abnormal process behaviour. These techniques include contribution charts and variable reconstructions that relate to the application of principal component analysis (PCA). The analysis reveals firstly that contribution charts produce variable contributions which are linearly dependent and may lead to an incorrect diagnosis, if the number of principal components retained is close to the number of recorded process variables. The analysis secondly yields that variable reconstruction affects the geometry of the PCA decomposition. The paper further introduces an improved variable reconstruction method for identifying multiple sensor and process faults and for isolating their influence upon the recorded process variables. It is shown that this can accommodate the effect of reconstruction, i.e. changes in the covariance matrix of the sensor readings and correctly re-defining the PCA-based monitoring statistics and their confidence limits. (c) 2006 Elsevier Ltd. All rights reserved.

Passing quantum correlations to qubits using any two-mode state

We draw an explicit connection between the statistical properties of an entangled two-mode continuous variable (CV) resource and the amount of entanglement that can be dynamically transferred to a pair of noninteracting two-level systems. More specifically, we rigorously reformulate entanglement-transfer process by making use of covariance matrix formalism. When the resource state is Gaussian, our method makes the approach to the transfer of quantum correlations much more flexible than in previously considered schemes and allows the straightforward inclusion of the effects of noise affecting the CV system. Moreover, the proposed method reveals that the use of de-Gaussified two-mode states is almost never advantageous for transferring entanglement with respect to the full Gaussian picture, despite the entanglement in the non-Gaussian resource can be much larger than in its Gaussian counterpart. We can thus conclude that the entanglement-transfer map overthrows the

A fast multi-output RBF neural network construction method

This paper investigates the center selection of multi-output radial basis function (RBF) networks, and a multi-output fast recursive algorithm (MFRA) is proposed. This method can not only reveal the significance of each candidate center based on the reduction in the trace of the error covariance matrix, but also can estimate the network weights simultaneously using a back substitution approach. The main contribution is that the center selection procedure and the weight estimation are performed within a well-defined regression context, leading to a significantly reduced computational complexity. The efficiency of the algorithm is confirmed by a computational complexity analysis, and simulation results demonstrate its effectiveness. (C) 2010 Elsevier B.V. All rights reserved.

Moving window kernel PCA for adaptive monitoring of nonlinear processes

This paper discusses the monitoring of complex nonlinear and time-varying processes. Kernel principal component analysis (KPCA) has gained significant attention as a monitoring tool for nonlinear systems in recent years but relies on a fixed model that cannot be employed for time-varying systems. The contribution of this article is the development of a numerically efficient and memory saving moving window KPCA (MWKPCA) monitoring approach. The proposed technique incorporates an up- and downdating procedure to adapt (i) the data mean and covariance matrix in the feature space and (ii) approximates the eigenvalues and eigenvectors of the Gram matrix. The article shows that the proposed MWKPCA algorithm has a computation complexity of O(N2), whilst batch techniques, e.g. the Lanczos method, are of O(N3). Including the adaptation of the number of retained components and an l-step ahead application of the MWKPCA monitoring model, the paper finally demonstrates the utility of the proposed technique using a simulated nonlinear time-varying system and recorded data from an industrial distillation column.

On MIMO Radar Subarrayed Transmit Beamforming

Multiple-input-multiple-output (MIMO) radar schemes whereby the transmit array is partitioned into subarrays have recently been proposed in the literature to combine advantages of phased array and MIMO radar technology. In this work, we utilize this architecture to significantly simplify a transmit procedure in which the covariance matrix across the MIMO radar array is optimized to improve the Cramer-Rao bound (CRB) on target parameter estimation. The MIMO effective array for regular subarrayed transmit apertures is studied, and necessary conditions to obtain a filled effective aperture are presented, which is important for maintaining nonambiguous, low sidelobe beampatterns. The performance of the subarrayed transmit approach is evaluated in terms of the CRB on target parameter estimation, and the optimisation of the beamformer applied to the subarrays to minimize the CRB is considered. The subarrayed transmit scheme is found to have a CRB which is suboptimal to the full diversity transmission, as expected, but is solvable in a small fraction of the time using an iterative beamspace algorithm developed here.

Harnessing the complexity of gene expression data from cancer: from single gene to structural pathway methods

High-dimensional gene expression data provide a rich source of information because they capture the expression level of genes in dynamic states that reflect the biological functioning of a cell. For this reason, such data are suitable to reveal systems related properties inside a cell, e.g., in order to elucidate molecular mechanisms of complex diseases like breast or prostate cancer. However, this is not only strongly dependent on the sample size and the correlation structure of a data set, but also on the statistical hypotheses tested. Many different approaches have been developed over the years to analyze gene expression data to (I) identify changes in single genes, (II) identify changes in gene sets or pathways, and (III) identify changes in the correlation structure in pathways. In this paper, we review statistical methods for all three types of approaches, including subtypes, in the context of cancer data and provide links to software implementations and tools and address also the general problem of multiple hypotheses testing. Further, we provide recommendations for the selection of such analysis methods.

Semi batch learning with store management using enhanced conjugate gradient

This paper explores the performance of sliding-window based training, termed as semi batch, using multilayer perceptron (MLP) neural network in the presence of correlated data. The sliding window training is a form of higher order instantaneous learning strategy without the need of covariance matrix, usually employed for modeling and tracking purposes. Sliding-window framework is implemented to combine the robustness of offline learning algorithms with the ability to track online the underlying process of a function. This paper adopted sliding window training with recent advances in conjugate gradient direction with application of data store management e.g. simple distance measure, angle evaluation and the novel prediction error test. The simulation results show the best convergence performance is gained by using store management techniques. © 2012 Springer-Verlag.

Geostatistical Fisher discriminant analysis

A geostatistical version of the classical Fisher rule (linear discriminant analysis) is presented.This method is applicable when a large dataset of multivariate observations is available within a domain split in several known subdomains, and it assumes that the variograms (or covariance functions) are comparable between subdomains, which only differ in the mean values of the available variables. The method consists on finding the eigen-decomposition of the matrix W-1B, where W is the matrix of sills of all direct- and cross-variograms, and B is the covariance matrix of the vectors of weighted means within each subdomain, obtained by generalized least squares. The method is used to map peat blanket occurrence in Northern Ireland, with data from the Tellus
survey, which requires a minimal change to the general recipe: to use compositionally-compliant variogram tools and models, and work with log-ratio transformed data.

Exploring the joint compositional variability of major components and trace elements in the Tellus soil geochemistry survey (Northern Ireland)

The complexity of modern geochemical data sets is increasing in several aspects (number of available samples, number of elements measured, number of matrices analysed, geological-environmental variability covered, etc), hence it is becoming increasingly necessary to apply statistical methods to elucidate their structure. This paper presents an exploratory analysis of one such complex data set, the Tellus geochemical soil survey of Northern Ireland (NI). This exploratory analysis is based on one of the most fundamental exploratory tools, principal component analysis (PCA) and its graphical representation as a biplot, albeit in several variations: the set of elements included (only major oxides vs. all observed elements), the prior transformation applied to the data (none, a standardization or a logratio transformation) and the way the covariance matrix between components is estimated (classical estimation vs. robust estimation). Results show that a log-ratio PCA (robust or classical) of all available elements is the most powerful exploratory setting, providing the following insights: the first two processes controlling the whole geochemical variation in NI soils are peat coverage and a contrast between “mafic” and “felsic” background lithologies; peat covered areas are detected as outliers by a robust analysis, and can be then filtered out if required for further modelling; and peat coverage intensity can be quantified with the %Br in the subcomposition (Br, Rb, Ni).

In vitro release of nonoxynol-9 from silicone matrix intravaginal rings

The controlled-release characteristics of matrix silicone intravaginal rings loaded with between 100 and 971 mg of nonoxynol-9 have been investigated with a view to developing a ring that may offer a new female-controlled method for the prevention of transmission of sexually transmitted diseases, particularly HIV. Intravaginal rings containing 253, 487 and 971 mg of nonoxynol-9 provided a daily release of 2 mg or more over the 8-day release period, the minimal amount of nonoxynol-9 considered to provide an effective vaginal concentration for the prevention of HIV. Furthermore, the maximum daily release of N9 was about 6 mg, an amount significantly smaller than that observed for other nonoxynol-9 products whose large daily doses may in fact increase the occurrence of HIV by causing epithelial damage to the vaginal tissue. The release mechanism of the liquid nonoxynol-9 from the intravaginal rings has also been investigated and compared to models describing the release of solid drugs from the rings. It has been demonstrated through release studies and surface microscopy that a drug depletion zone is not established in such liquid-loaded intravaginal ring systems, with implications for the release kinetics. (C) 2003 Elsevier B.V. All rights reserved.

High speed DSC (hyper-DSC) as a tool to measure the solubility of a drug within a solid or semi-solid matrix

Conventional differential scanning calorimetry (DSC) techniques are commonly used to quantify the solubility of drugs within polymeric-controlled delivery systems. However, the nature of the DSC experiment, and in particular the relatively slow heating rates employed, limit its use to the measurement of drug solubility at the drug's melting temperature. Here, we describe the application of hyper-DSC (HDSC), a variant of DSC involving extremely rapid heating rates, to the calculation of the solubility of a model drug, metronidazole, in silicone elastomer, and demonstrate that the faster heating rates permit the solubility to be calculated under non-equilibrium conditions such that the solubility better approximates that at the temperature of use. At a heating rate of 400 degrees C/min (HDSC), metronidazole solubility was calculated to be 2.16 mg/g compared with 6.16 mg/g at 20 degrees C/min. (C) 2005 Elsevier B.V. All rights reserved.