Accurate Covariance Matrix Estimation Research Articles

An Improved DCC Model Based on Large-Dimensional Covariance Matrices Estimation and Its Applications

The covariance matrix estimation plays an important role in portfolio optimization and risk management. It is well-known that portfolio is essentially a convex quadratic programming problem, which is also a special case of symmetric cone optimization. Accurate covariance matrix estimation will lead to more reasonable asset weight allocation. However, some existing methods do not consider the influence of time-varying factor on the covariance matrix estimations. To remedy this, in this article, we propose an improved dynamic conditional correlation model (DCC) by using nonconvex optimization model under smoothly clipped absolute deviation and hard-threshold penalty functions. We first construct a nonconvex optimization model to obtain the optimal covariance matrix estimation, and then we use this covariance matrix estimation to replace the unconditional covariance matrix in the DCC model. The result shows that the loss of the proposed estimator is smaller than other variants of the DCC model in numerical experiments. Finally, we apply our proposed model to the classic Markowitz portfolio. The results show that the improved dynamic conditional correlation model performs better than the current DCC models.

Empirical Analysis of the Impact of High and New Technology on the Export of Traditional Cultural Industry Based on Random Matrix Theory

Accurate estimation of covariance matrix is the basis of effective development of high-dimensional optimal portfolio. Random matrix theory provides an effective means to improve the estimation of high-dimensional covariance matrix. Based on the empirical research on the export excess return rate of traditional cultural industry, the result is a combination with higher precision and lower risk. Based on relevant data, this paper constructs a stochastic matrix theoretical model to analyze the impact of human capital, new fixed asset investment, independent innovation and technology purchase, financing sources, and other factors on high-tech industry export. Based on the results of empirical analysis, some policy suggestions are put forward, such as increasing r&d investment, improving enterprises’ innovation ability, and introducing core scientific and technological talents to promote the export scale growth of high-tech industries. Model comparative analysis is made on the influence of traditional industries’ concentrated export, foreign trade environment, and cost advantage on the export of high-tech products. Through comparative analysis of the influencing factors of the export of high-tech products in the two periods before and after the export crisis of traditional culture, the new changes of the influencing factors of the export of high-tech products are analyzed. In addition, through the change of the internal and external environment of the current high-tech product export, the reasons for the new change of the influencing factors are discussed.

Covariance Matrix Estimation in Massive MIMO

Interference during the uplink training phase significantly deteriorates the performance of a massive MIMO system. The impact of the interference can be reduced by exploiting second order statistics of the channel vectors, e.g., to obtain minimum mean squared error estimates of the channel. In practice, the channel covariance matrices have to be estimated. The estimation of the covariance matrices is also impeded by the interference during the training phase. However, the coherence interval of the covariance matrices is larger than that of the channel vectors. This allows us to derive methods for accurate covariance matrix estimation by appropriate assignment of pilot sequences to users in consecutive channel coherence intervals.

Robust Beamforming for Speech Recognition Using DNN-Based Time-Frequency Masks Estimation

This paper addresses the robust beamforming problem for speech recognition using a novel time-frequency mask estimator. The beamformer first estimates the time-frequency mask using a deep neural network (DNN) based on which the covariance matrices of the target speech and noise are computed. Then, the beamformer coefficients are directly obtained via generalized eigenvector decomposition. To achieve accurate covariance matrix estimation for robust beamforming, we propose a DNN-based mask estimator which can exploit the spatial features of the multi-channel microphone signals. The proposed mask estimator leverages the spatial information of the microphone array by using multi-channel signals to estimate a speech-aware mask and a noise-aware mask simultaneously. Using the target-specified masks, accurate covariance matrices of the target speech and noise can be obtained from the observation independently. Experiments on CHiME4 data sets demonstrate that, compared with the baseline toolkit (BeamformIt) and the winner in the CHiME3 challenge, the proposed method achieves better results both in terms of perceptual speech quality and speech recognition error rate.

Optimising beamformer regions of interest analysis

Beamforming is a spatial filtering based source reconstruction method for EEG and MEG that allows the estimation of neuronal activity at a particular location within the brain. The computation of the location specific filter depends solely on an estimate of the data covariance matrix and on the forward model. Increasing the number of M/EEG sensors, increases the quantity of data required for accurate covariance matrix estimation. Often however we have a prior hypothesis about the site of, or the signal of interest. Here we show how this prior specification, in combination with optimal estimations of data dimensionality, can give enhanced beamformer performance for relatively short data segments. Specifically we show how temporal (Bayesian Principal Component Analysis) and spatial (lead field projection) methods can be combined to produce improvements in source estimation over and above employing the approaches individually.

Target Detection Using Nonsingular Approximations for a Singular Covariance Matrix

Accurate covariance matrix estimation for high‐dimensional data can be a difficult problem. A good approximation of the covariance matrix needs in most cases a prohibitively large number of pixels, that is, pixels from a stationary section of the image whose number is greater than several times the number of bands. Estimating the covariance matrix with a number of pixels that is on the order of the number of bands or less will cause not only a bad estimation of the covariance matrix but also a singular covariance matrix which cannot be inverted. In this paper we will investigate two methods to give a sufficient approximation for the covariance matrix while only using a small number of neighboring pixels. The first is the quasilocal covariance matrix (QLRX) that uses the variance of the global covariance instead of the variances that are too small and cause a singular covariance. The second method is sparse matrix transform (SMT) that performs a set of K‐givens rotations to estimate the covariance matrix. We will compare results from target acquisition that are based on both of these methods. An improvement for the SMT algorithm is suggested.

Contrast enhancement and robustness improvement of adaptive ultrasound imaging using forward-backward minimum variance beamforming

In adaptive ultrasound imaging, accurate estimation of the array covariance matrix is of great importance, and biases the performance of the adaptive beamformer. The more accurately the covariance matrix can be estimated, the better the resolution and contrast can be achieved in the ultrasound image. To this end, in this paper, we have used the forward-backward spatial averaging for array covariance matrix estimation, which is then employed in minimum variance (MV) weights calculation. The performance of the proposed forward-backward MV (FBMV) beamformer is tested on simulated data obtained using Field II. Data for two closely located point targets surrounded by speckle pattern are simulated showing the higher amplitude resolution of the FBMV beamformer in comparison to the forward-only (F-only) MV beamformers, without the need for diagonal loading. A circular cyst with a diameter of 6 mm and a phantom containing wire targets and two cysts with different diameters of 8 mm and 6 mm are also simulated. The simulations show that the FBMV beamformer, in contrast to the F-only MV, could estimate the background speckle statistics without the need for temporal smoothing, resulting in higher contrast for the FBMV-resulted image in comparison to the MV images. In addition, the effect of steering vector errors is investigated by applying an error of the sound speed estimate to the ultrasound data. The simulations show that the proposed FBMV beamformer presents a satisfactory robustness against data misalignment resulted from steering vector errors, outperforming the regularized F-only MV beamformer. These improvements are achieved without compromising the good resolution of the MV beamformer and resulted from more accurate estimation of the covariance matrix and consequently, the more accurate setting of the MV weights.

Adaptive support vector machine and Markov random field model for classifying hyperspectral imagery

Markov random field (MRF) provides a useful model for integrating contextual information into remote sensing image classification. However, there are two limitations when using the conventional MRF model in hyperspectral image classification. First, the maximum likelihood classifier used in MRF to estimate the spectral-based probability needs accurate estimation of covariance matrix for each class, which is often hard to obtain with a small number of training samples for hyperspectral imagery. Second, a fixed spatial neighboring impact parameter for all pixels causes overcorrection of spatially high variation areas and makes class boundaries blurred. This paper presents an improved method for integrating a support vector machine (SVM) and Markov random field to classify the hyperspectral imagery. An adaptive spatial neighboring impact parameter is assigned to each pixel according to its spatial contextualcorrelation.Experimentalresultsofahyperspectralimageshowthattheclassification accuracyfromtheproposedmethodhasbeenimprovedcomparedtothosefromtheconventional MRF model and pixel-wise classifiers including the maximum likelihood classifier and SVM

Single-trial analysis and classification of ERP components — A tutorial

Analyzing brain states that correspond to event related potentials (ERPs) on a single trial basis is a hard problem due to the high trial-to-trial variability and the unfavorable ratio between signal (ERP) and noise (artifacts and neural background activity). In this tutorial, we provide a comprehensive framework for decoding ERPs, elaborating on linear concepts, namely spatio-temporal patterns and filters as well as linear ERP classification. However, the bottleneck of these techniques is that they require an accurate covariance matrix estimation in high dimensional sensor spaces which is a highly intricate problem. As a remedy, we propose to use shrinkage estimators and show that appropriate regularization of linear discriminant analysis (LDA) by shrinkage yields excellent results for single-trial ERP classification that are far superior to classical LDA classification. Furthermore, we give practical hints on the interpretation of what classifiers learned from the data and demonstrate in particular that the trade-off between goodness-of-fit and model complexity in regularized LDA relates to a morphing between a difference pattern of ERPs and a spatial filter which cancels non task-related brain activity.