Covariance Matrices Research Articles

An Adaptive Extended Kalman Filter With Passivity-Based Control for DC-DC Converter in DC Microgrids Supplying Constant Power Loads

This paper proposes an adaptive nonlinear control strategy to eliminate the instability problem of buck converters in DC microgrids (DCMG) considering constant power load (CPL). The strategy includes an Adaptive Passivity-Based Controller (PBC) and an Adaptive Extended Kalman Filter (AEKF). The proposed AEKF performs faster and more accurately than the conventional EKF and adjusts the covariance matrices adaptively. Furthermore, this AEKF directly estimates the unknown CPL power supplied by the converter and prevents the number of measurement sensors from increasing. Hence, PBC ensures system stability alongside AEKF. The controller guarantees Lyapunov stability and fast dynamic response in the presence of uncertainties and perturbations compared to other nonlinear methods. MATLAB simulations and laboratory implementation are provided to confirm the performance and robustness of the proposed control strategy and validate the analysis.

RESEARCH PAPER FOR USING MARKOWITZ MODEL AND INDEX MODEL UNDER REALISTIC ADDITIONAL CONSTRAINTS

The Markowitz and index models are widely used in portfolio optimization to achieve optimal asset allocation and maximize returns while controlling risk. However, in practical investment scenarios, additional constraints often need to be considered to ensure the feasibility and effectiveness of the portfolio strategy. This research focuses on incorporating realistic additional constraints into the Markowitz and index models for portfolio optimization. The study utilizes historical financial data and statistical techniques to estimate expected returns, variances, and covariance matrices. The Markowitz model is modified to incorporate the additional constraints, allowing for more realistic and accurate portfolio optimization outcomes. The index model is also adapted to consider the impact of these constraints on the construction and performance of passive investment portfolios.

Contribution of Surface Radiative Effects, Heat Fluxes and Their Interactions to Land Surface Temperature Variability

AbstractLand surface temperature anomalies can be linked to changes in local surface energy balance, although the relationship between surface temperature variability and individual radiative processes remains unclear. In this paper, we quantify the contributions of surface radiative effects and non‐radiative heat fluxes to the variance of monthly land surface temperature using European Centre for Medium‐Range Weather Forecasts Reanalysis v5 data and Coupled Model Intercomparison Project Phase 6 simulations. The surface energy budget equation is used to link changes in surface radiation, surface heat fluxes and land surface temperature. Subsequently, surface radiation is decomposed into the radiative effects of clouds, air temperature, surface albedo and relative humidity using radiative kernels. The contributions of these radiative processes, including their coupling effects, are quantified using covariance matrices. The results reveal the air temperature radiative effect to be the most significant contributor to the variability of land surface temperature. In addition, the covariance terms reveal important coupling effects. For example, the contribution from the cloud radiative effect is found to be substantially dampened by its coupling with surface heat fluxes. The air temperature radiative effect is further decomposed into a forcing component and a feedback component using different regression methods, in an attempt to separate the air temperature radiative effect as the driver of the surface temperature variability. The cloud radiative effect becomes the primary contributor to the variance of surface temperature after separating the air temperature feedback, while the contribution of the air temperature radiative forcing remains important.

Separable sample covariance matrices under elliptical populations with applications

This paper is to investigate the spectral properties of separable covariance matrices under elliptical populations. The separable covariance matrix model can handle both cross-row and cross-column correlations thus gain more popularity recently. Under the high-dimensional setting where the dimension p p and the sample size n n tend to infinity proportionally, we find the limit of the empirical spectral distribution and establish the central limit theorems (CLT) for linear spectral statistics of such kinds of sample covariance matrices. Some applications of our established CLT are also given.

Analytical Coherent Detection in High-Resolution Dual-Polarimetric Sea Clutter with Independent Inverse Gamma Textures

Polarization diversity has been widely used in maritime radars to improve target detection performance. Full utilization of the polarimetric characteristics of sea clutter is the key to designing effective polarimetric detectors. For high-resolution maritime radars, the HH-HV dual-polarization is an affordable and effective mode to monitor small targets, owing to the simple configuration of single-polarimetric transmit and dual-polarimetric reception and lower clutter powers at the HH and HV polarizations. Enlightened by the analytical coherent detector in compound-Gaussian clutter with inverse Gamma texture, this paper investigates dual-polarimetric coherent detection in dual-polarimetric compound-Gaussian clutter with independent inverse Gamma distributed textures. The analytical dual-polarimetric near-optimum coherent detector is derived, which is a fusion of the generalized likelihood ratio test linear threshold detectors (GLRT-LTDs) at the two polarizations. For short, it is referred to as the P-GLRT-LTD. It is proven that the P-GLRT-LTD is of constant false alarm rate with respect to the Doppler steering vector, scale parameters of textures, and speckle covariance matrices. Moreover, the thresholds of the P-GLRT-LTD are given analytically. Experiments using simulated sea clutter data with the estimated scale and shape parameters from the two measured intelligent pixel processing radar (IPIX) datasets and two measured IPIX datasets with test targets are made to compare P-GLRT-LTD with other existing dual-polarimetric coherent detectors. The results show that the P-GLRT-LTD attains the same detection performance as the existing best-performance detector. The P-GLRT-LTD has a lower computational cost than the existing best-performing one.

Sharp-SSL: Selective high-dimensional axis-aligned random projections for semi-supervised learning

We propose a new method for high-dimensional semi-supervised learning problems based on the careful aggregation of the results of a low-dimensional procedure applied to many axis-aligned random projections of the data. Our primary goal is to identify important variables for distinguishing between the classes; existing low-dimensional methods can then be applied for final class assignment. To this end, we score projections according to their class-distinguishing ability; for instance, motivated by a generalized Rayleigh quotient, we can compute the traces of estimated whitened between-class covariance matrices on the projected data. This enables us to assign an importance weight to each variable for a given projection, and to select our signal variables by aggregating these weights over high-scoring projections. Our theory shows that the resulting Sharp-SSL algorithm is able to recover the signal coordinates with high probability when we aggregate over sufficiently many random projections and when the base procedure estimates the diagonal entries of the whitened between-class covariance matrix sufficiently well. For the Gaussian EM base procedure, we provide a new analysis of its performance in semi-supervised settings that controls the parameter estimation error in terms of the proportion of labeled data in the sample. Numerical results on both simulated data and a real colon tumor dataset support the excellent empirical performance of the method.

Double verification for two‐sample covariance matrices test

This paper explores testing the equality of two covariance matrices under high‐dimensional settings. Existing test statistics are usually constructed based on the squared Frobenius norm or the elementwise maximum norm. However, the former may experience power loss when handling sparse alternatives, while the latter may have a poor performance against dense alternatives. In this paper, with a novel framework, we introduce a double verification test statistic designed to be powerful against both dense and sparse alternatives. Additionally, we propose an adaptive weight test statistic to enhance power. Furthermore, we present an analysis of the asymptotic size and power of the proposed test. Simulation results demonstrate the satisfactory performance of our proposed method.

Multivariate realized volatility: an analysis via shrinkage methods for Brazilian market data

IntroductionRealized volatility analysis of assets in the Brazilian market within a multivariate framework is the focus of this study. Despite the success of volatility models in univariate scenarios, challenges arise due to increasing dimensionality of covariance matrices and lower asset liquidity in emerging markets.MethodsIn this study, we utilize intraday stock trading data from the Brazilian Market to compute daily covariance matrices using various specifications. To mitigate dimensionality issues in covariance matrix estimation, we implement penalization restrictions on coefficients through regressions with shrinkage techniques using Ridge, LASSO, or Elastic Net estimators. These techniques are employed to capture the dynamics of covariance matrices.ResultsComparison of covariance construction models is performed using the Model Confidence Set (MCS) algorithm, which selects the best models based on their predictive performance. The findings indicate that the method used for estimating the covariance matrix significantly impacts the selection of the best models. Additionally, it is observed that more liquid sectors demonstrate greater intra-sectoral dynamics.DiscussionWhile the results benefit from shrinkage techniques, the high correlation between assets presents challenges in capturing stock or sector idiosyncrasies. This suggests the need for further exploration and refinement of methods to better capture the complexities of volatility dynamics in emerging markets like Brazil.

A comparison of channel selection for the assimilation of CrIS radiances for NWP

Abstract With hyperspectral instruments measuring radiation emitted by the earth and its atmosphere in the thermal infrared range in multiple channels, several studies were made to select a subset of channels in order to reduce the number of channels to be used in a data assimilation system. An optimal selection of channels based on information content depends on several factors related to observation and background error statistics and the assimilation system itself. An optimal channel selection for CrIS was obtained and then compared to selections made for different NWP systems. For instance, the channel selection of Carminati (2022) has 224 channels also present in to our optimal selection which includes 455 channels. However, in terms of analysis error variance, the difference between the two selections is small. Integrated over the whole profile, the relative difference is equal to 15.3 % and 4.5 % for temperature and humidity respectively. Also, different observation error covariance matrices were considered to evaluate the impact of this matrix on channel selection. Even though the channels selected optimally were different in terms of which channels were selected for the various R matrices.

The Kullback–Leibler Divergence and the Convergence Rate of Fast Covariance Matrix Estimators in Galaxy Clustering Analysis

We present a method to quantify the convergence rate of the fast estimators of the covariance matrices in the large-scale structure analysis. Our method is based on the Kullback–Leibler (KL) divergence, which describes the relative entropy of two probability distributions. As a case study, we analyze the delete-d jackknife estimator for the covariance matrix of the galaxy correlation function. We introduce the information factor or the normalized KL divergence with the help of a set of baseline covariance matrices to diagnose the information contained in the jackknife covariance matrix. Using a set of quick particle mesh mock catalogs designed for the Baryon Oscillation Spectroscopic Survey DR11 CMASS galaxy survey, we find that the jackknife resampling method succeeds in recovering the covariance matrix with 10 times fewer simulation mocks than that of the baseline method at small scales (s ≤ 40 h −1 Mpc). However, the ability to reduce the number of mock catalogs is degraded at larger scales due to the increasing bias on the jackknife covariance matrix. Note that the analysis in this paper can be applied to any fast estimator of the covariance matrix for galaxy clustering measurements.

Experimental Covariance Determination for Critical Integral Experiments

Integral benchmarks for criticality safety and nuclear data validation require expensive uncertainty quantification studies. In general, uncertainty quantification techniques ignore correlations between experiments and shared components. Experiments, such as the Thermal/Epithermal eXperiments (TEX) campaigns, consist of many shared components, such as the Jemima highly enriched uranium (HEU) fuel plates, which create a strong correlation in their uncertainties. While these correlations are known to exist, they are often not estimated because of the complexity of such calculations. This paper describes an intuitive method of determining the covariance for each of the experimental components, providing a correlation for each family of components across the multiple cases examined within a benchmark. A proof-of-principle study using the TEX-HEU experimental campaign was performed and verified that the covariance and correlation matrices can be calculated with information commonly found in the International Criticality Safety Benchmark Evaluation Project benchmarks. This study showed that the introduction of model and experimental covariances reduces the χ2 per degree of freedom from 2.203 to 1.179, indicating that the omission causes overly pessimistic bias quantifications. This technique can be seamlessly integrated to current benchmark evaluations as well as reevaluations of legacy benchmarks.

A Mixture of logistic skew-normal Multinomial Models

The logistic normal multinomial distribution is gaining interest in modelling microbiome data. It utilizes a hierarchical structure such that the observed counts conditional on the compositions are assumed to be multinomial random variables and the log-ratio transformed compositions are assumed to be from a Gaussian distribution. While multinomial distribution accounts for the compositional nature of the data, and a Gaussian prior offers flexibility in the structure of covariance matrices, the log-ratio transformed compositions of the microbiome data can be highly skewed, especially at a lower taxonomic level. Thus, a Gaussian distribution may not be an ideal prior for the log-ratio transformed compositions. A novel mixture of logistic skew-normal multinomial (LSNM) distribution is proposed in which a multivariate skew-normal distribution is utilized as a prior for the log-ratio transformed compositions. A variational Gaussian approximation in conjunction with the EM algorithm is utilized for parameter estimation.

JOINT INVERSION OF DIRECT WAVES, PRIMARIES AND MULTIPLES FOR VERTICAL CABLE SEISMIC DATA

By anchoring the vertical cable in seawater and receiving the data excited by the towing cable seismic source, the reflection data from subsurface structures with a high signal-to-noise ratio, wide frequency band, and wide azimuth angle can be obtained, thereby achieving high-quality imaging of the target area. However, due to drifting receivers driven by ocean currents and nonuniform coverage caused by the vertical orientation of the receivers, the traditional imaging method cannot be directly used in vertical cable seismic (VCS) data. Furthermore, crosstalk between primaries and multiples commonly contaminates the final imaging. A new inversion method, based on the Bayesian inference and the assumption that all errors are Gaussian distributed, is presented to address the above problems. The direct waves are used to invert source/receiver locations. The primary and multiple wavefields are accurately reconstructed based on the reconstructed direct wavefield, and the corresponding reflectivity updates are obtained. The model-domain Hessian matrices consisting of different data are approximated by their diagonal elements to mitigate the nonuniform coverage issue, and the related covariance matrices and data-domain Hessian matrices are defined and approximated, respectively, to alleviate the calculation problem. In addition, the zero-lag correlated wavefields in the gradient are consistent with the actual wavefield propagation process, e.g., a primary wave is generated when the direct wavefield encounters reflectivity, avoiding the crosstalk. Numerical examples for synthetic models and field data illustrate that the proposed method can accurately recover the source/receiver locations and provide high-resolution, balanced-amplitude imaging results without evident crosstalk.

Element Aggregation for Estimation of High-Dimensional Covariance Matrices

This study addresses the challenge of estimating high-dimensional covariance matrices in financial markets, where traditional sparsity assumptions often fail due to the interdependence of stock returns across sectors. We present an innovative element-aggregation method that aggregates matrix entries to estimate covariance matrices. This method is designed to be applicable to both sparse and non-sparse matrices, transcending the limitations of sparsity-based approaches. The computational simplicity of the method’s implementation ensures low complexity, making it a practical tool for real-world applications. Theoretical analysis then confirms the method’s consistency and effectiveness with its convergence rate in specific scenarios. Additionally, numerical experiments validate the method’s superior algorithmic performance compared to conventional methods, as well as the reduction in relative estimation errors. Furthermore, empirical studies in financial portfolio optimization demonstrate the method’s significant risk management benefits, particularly its ability to effectively mitigate portfolio risk even with limited sample sizes.

Covariance matrices of length power functionals of random geometric graphs – an asymptotic analysis

Asymptotic properties of a vector of length power functionals of random geometric graphs are investigated. Algebraic properties of the asymptotic covariance matrix are studied as the intensity of the underlying homogeneous Poisson point process increases. This includes a systematic discussion of matrix properties like rank, definiteness, determinant, eigenspaces or decompositions of interest. For the formulation of the results a case distinction is necessary. In the three possible regimes the respective covariance matrix is of quite different nature which leads to different statements. Stochastic consequences for random geometric graphs are derived.

Multilevel superposition for deciphering the conformational variability of protein ensembles.

The dynamics and variability of protein conformations are directly linked to their functions. Many comparative studies of X-ray protein structures have been conducted to elucidate the relevant conformational changes, dynamics and heterogeneity. The rapid increase in the number of experimentally determined structures has made comparison an effective tool for investigating protein structures. For example, it is now possible to compare structural ensembles formed by enzyme species, variants or the type of ligands bound to them. In this study, the author developed a multilevel model for estimating two covariance matrices that represent inter- and intra-ensemble variability in the Cartesian coordinate space. Principal component analysis using the two estimated covariance matrices identified the inter-/intra-enzyme variabilities, which seemed to be important for the enzyme functions, with the illustrative examples of cytochrome P450 family 2 enzymes and class A $\beta$-lactamases. In P450, in which each enzyme has its own active site of a distinct size, an active-site motion shared universally between the enzymes was captured as the first principal mode of the intra-enzyme covariance matrix. In this case, the method was useful for understanding the conformational variability after adjusting for the differences between enzyme sizes. The developed method is advantageous in small ensemble-size problems and hence promising for use in comparative studies on experimentally determined structures where ensemble sizes are smaller than those generated, for example, by molecular dynamics simulations.

Fusion-Based 2.5D Face Recognition System

Face recognition is the dominant biometrics system used to authenticate an individual’s identity in various applications. Most commercial face recognition systems rely on 2D face images, but the changes in the environment lighting and a person's posture affect the accuracy of the 2D face recognition systems. Hence, the 2.5D face recognition system arises as the solution to eliminate the drawbacks of the 2D face recognition system. The depth feature in the 2.5D data (depth image) provides additional information that can help to improve the accuracy and robustness of 2.5D face recognition systems, particularly in challenging scenarios. This paper proposes a fusion-based approach for the 2.5D face recognition system to enhance the system’s performance, where feature fusion involves the combination of features extracted from the depth image. Gabor-based Region Covariance Matrices (GRCMs) that serve as face identifiers combine the depth and texture images in the structure of a covariance matrix. Several experiments on different fusions have been conducted in the Face Recognition Grand Challenge version 2 (FRGC v2.0) database. This paper shows that the max-min fusion applied to the surface normal (y-direction) and the mean curvature has achieved the best accuracy rate of 93.66% among the other fusion approaches used.

To Be Long or To Be Wide: How Data Format Influences Convergence and Estimation Accuracy in Multilevel Structural Equation Modeling

A two-level data set can be structured in either long format (LF) or wide format (WF), and both have corresponding SEM approaches for estimating multilevel models. Intuitively, one might expect these approaches to perform similarly. However, the two data formats yield data matrices with different numbers of columns and rows, and their cols : rows is related to the magnitude of eigenvalue bias in sample covariance matrices. Previous studies have shown similar performance for both approaches, but they were limited to settings where cols ≪ rows in both data formats. We conducted a Monte Carlo study to investigate whether varying cols : rows result in differing performances. Specifically, we examined the p : N ( cols : rows ) effect on convergence and estimation accuracy in multilevel settings. Our findings suggest that (1) the LF approach is more likely to achieve convergence, but for the models that converged in both, (2) the LF and WF approach yield similar estimation accuracy, which is related to (3) differential cols : rows effects in both approaches, and (4) smaller ICC values lead to less accurate between-group parameter estimates.

ANALYSIS FOR MULTIPLE RESPONSES IN A COMPLETELY RANDOMIZED EXPERIMENTAL DESIGN

Multiple responses are often generated in agricultural and forestry research. For example, the moisture content, fatty acids, carbohydrates, size, diameter, length, shape and hardness, among other characteristics are measured to cottonseed. Of course, multiple responses are observed in many other areas of research. Multivariate analysis of variance (MANOVA) can be useful for multiple response analysis when differences in treatment effects are to be determined. However, the performance of current post hoc tests in this context is not satisfactory due to the limitations of the available methods, or because they are difficult to use for non-statistician researchers. Furthermore, this methodology requires the assumptions of multivariate normality and homogeneity of variance and covariance matrices, assumptions that are difficult to verify if the sample size is small. This research proposes an alternative analysis to test the hypothesis of equality of effects between treatments and post hoc tests in the case of multiple responses. An asymptotic result is demonstrated for the random variable generated in the proposal for the case of uncorrelated normal variables and the case for correlated normal random variables is left open. A simulation study shows that the performance of the proposal with small samples is satisfactory in terms of power and that it has advantages compared to MANOVA. Furthermore, the methodological approach allows for post hoc testing in the case of multiple responses in the completely randomized experimental design.

Improving model choice in classification: an approach based on clustering of covariance matrices

This work introduces a refinement of the Parsimonious Model for fitting a Gaussian Mixture. The improvement is based on the consideration of clusters of the involved covariance matrices according to a criterion, such as sharing Principal Directions. This and other similarity criteria that arise from the spectral decomposition of a matrix are the bases of the Parsimonious Model. We show that such groupings of covariance matrices can be achieved through simple modifications of the CEM (Classification Expectation Maximization) algorithm. Our approach leads to propose Gaussian Mixture Models for model-based clustering and discriminant analysis, in which covariance matrices are clustered according to a parsimonious criterion, creating intermediate steps between the fourteen widely known parsimonious models. The added versatility not only allows us to obtain models with fewer parameters for fitting the data, but also provides greater interpretability. We show its usefulness for model-based clustering and discriminant analysis, providing algorithms to find approximate solutions verifying suitable size, shape and orientation constraints, and applying them to both simulation and real data examples.