Robust Covariance Matrix Estimation Research Articles

Robust speckle covariance matrix estimation of sea clutter based on spectral symmetry

Speckle covariance matrix estimation plays an important role in adaptive target detection of maritime radars. Spatial heterogeneity of sea clutter incurs insufficient secondary data in estimation, which degrades detection performance. It is an effective way of estimation improvement to exploit the Doppler spectrum knowledge of sea clutter for structural dimension reduction of the speckle covariance matrix. This paper proposes a speckle covariance matrix estimation method based on the spectral symmetry knowledge of sea clutter, indicating that the spectrum of sea clutter is symmetric with respect to the Doppler offset. First of all, the spectral symmetry of sea clutter is analyzed by using the measured data from several opened databases and the results show that most of the data excluding sea spikes have symmetric Doppler spectra. Secondly, the spectral symmetry constrains the speckle covariance matrix into the Hadamard product of a special rank-one Toeplitz matrix and a real positive definite symmetric matrix. The degrees of freedom are reduced to almost half of that of a Hermitian matrix and thus fewer secondary data are required. Thirdly, a robust iterative maximum likelihood estimator is proposed to estimate the speckle covariance matrix with structural constraint and is free of the clutter texture distribution. The performance of the estimator is verified by the measured data and the results show that it is superior to traditional estimators, particularly in fewer secondary data.

Sexual pleasure and HIV-related worry in female sex workers on oral pre-exposure prophylaxis in south-western Uganda.

Female sex workers (FSWs) contribute disproportionately to HIV transmission in Uganda, and pre-exposure prophylaxis (PrEP) is effective in preventing HIV among cisgender women. Psychological factors are important for PrEP uptake, but few studies have examined psychosocial changes due to PrEP use in Uganda. In 2021, we recruited 524 FSWs in three Trans-African Highway towns and four fishing communities in south-western Uganda. We conducted structured interviews among women who were attending routine PrEP follow-up visits in six health units. Bivariable and multivariable modified regression using a robust covariance matrix estimator were used to identify factors associated with experiencing increased sexual pleasure and less worry about HIV because of PrEP. Overall, 80.9% participants reported that sex was more pleasurable because of taking PrEP. There were statistical trends for sex being more pleasurable when taking PrEP or when having condomless sex with casual paying partners (aPR=1.19, 95% CI=1.07-1.32, P=0.001). Almost three-quarters of the participants (76.3%) were less worried about getting HIV because of PrEP. Condomless sex with casual paying partners (aPR=1.17, 95% CI=1.05-1.31, P=0.032, P=0.003) and being On PrEP for the past 1-2years (aPR=1.18, 95% CI=1.00-1.38, P=0.032) was significantly associated with HIV-related worry (aPR=1.17, 95% CI=1.05-1.31, P=0.032, P=0.003)Conclusions:We found a positive impact of PrEP in Ugandan FSWs on two key psychosocial dimensions: (1) more pleasurable sex; and (2) less worry about acquiring HIV. Interventions aiming to increase PrEP uptake may find it useful to focus on psychosocial dimensions.

The stock market reaction to COVID-19 vaccination in ASEAN.

Previous studies have shown that the confirmed cases drive investor sentiment, reflecting the stock's return. Based on this, the vaccination growth is also expected to drive the investor's sentiment, which can be reflected in the return of the stock market in ASEAN. Therefore, this study explores the vaccination impact on stock returns in ASEAN countries. This study contributes to the gap of taking the COVID-19 vaccination impact to the stock return into account by using the panel regression model with HC and Driscoll and Kraay robust covariance matrix estimator, which addresses the cross-dependency and heterogeneity problems. This study is one of the early studies of the topic, especially in ASEAN. The panel regression model with HC and Driscoll and Kraay robust covariance matrix estimator uses three variables: the daily stocks return, vaccine growth, and cases growth. It is a balanced panel data that includes six countries and 117 daily series data, making 702 observations used in the study. The results show conflicting results where daily vaccination growth negatively affects the stock return. This problem can arise for several reasons, such as the uncertainty in the financial market and cross-dependency and heterogeneity detected in the model. We can see that the investors still have a negative sentiment because COVID-19 has resulted in uncertainty on the financial market in ASEAN. This gives us practical implications that the ASEAN country members' government needs to push vaccination policy more aggressively.

Overdispersion Models for Clustered Toxicological Data in a Bioassay of Entomopathogenic Fungus

We consider discrete mortality data for groups of individuals observed over time. The fitting of cumulative mortality curves as a function of time involves the longitudinal modelling of the multinomial response. Typically such data exhibit overdispersion, that is greater variation than predicted by the multinomial distribution. To model the extra-multinomial variation (overdispersion) we consider a Dirichlet-multinomial model, a random intercept model and a random intercept and slope model. We construct asymptotic and robust covariance matrix estimators for the regression parameter standard errors. Applying this model to a specific insect bioassay of the fungus Beauveria bassiana, we note some simple relationships in the results and explore why these are simply a consequence of the data structure. Fitted models are used to make inferences on the effectiveness and consistency of different isolates of the fungus to provide recommendations for its use as a biological control in the field.

A concentration of measure and random matrix approach to large-dimensional robust statistics

This article studies the robust covariance matrix estimation of a data collection X=(x1,…,xn) with xi=τ izi+m, where zi∈Rp is a concentrated vector (e.g., an elliptical random vector), m∈Rp a deterministic signal and τi∈R a scalar perturbation of possibly large amplitude, under the assumption where both n and p are large. This estimator is defined as the fixed point of a function which we show is contracting for a so-called stable semi-metric. We exploit this semi-metric along with concentration of measure arguments to prove the existence and uniqueness of the robust estimator as well as evaluate its limiting spectral distribution.

Robust Covariance Matrix Estimation for High-Dimensional Compositional Data with Application to Sales Data Analysis

Compositional data arises in a wide variety of research areas when some form of standardization and composition is necessary. Estimating covariance matrices is of fundamental importance for high-dimensional compositional data analysis. However, existing methods require the restrictive Gaussian or sub-Gaussian assumption, which may not hold in practice. We propose a robust composition adjusted thresholding covariance procedure based on Huber-type M-estimation to estimate the sparse covariance structure of high-dimensional compositional data. We introduce a cross-validation procedure to choose the tuning parameters of the proposed method. Theoretically, by assuming a bounded fourth moment condition, we obtain the rates of convergence and signal recovery property for the proposed method and provide the theoretical guarantees for the cross-validation procedure under the high-dimensional setting. Numerically, we demonstrate the effectiveness of the proposed method in simulation studies and also a real application to sales data analysis.

The stock market reaction to COVID-19 vaccination in ASEAN

Previous studies have shown that the confirmed cases drive investor sentiment, reflecting the stock's return. Based on this, the vaccination growth is also expected to drive the investor’s sentiment, which can be reflected in the return of the stock market in ASEAN. Therefore, this study explores the vaccination impact on stock returns in ASEAN countries. This study contributes to the gap of taking the COVID-19 vaccination impact to the stock return into account by using the panel regression model with HC and Driscoll and Kraay robust covariance matrix estimator, which addresses the cross-dependency and heterogeneity problems. This study is one of the early studies of the topic, especially in ASEAN. The panel regression model with HC and Driscoll and Kraay robust covariance matrix estimator uses three variables: the daily stocks return, vaccine growth, and cases growth. It is a balanced panel data that includes six countries and 117 daily series data, making 702 observations used in the study. The results show conflicting results where daily vaccination growth negatively affects the stock return. This problem can arise for several reasons, such as the uncertainty in the financial market and cross-dependency and heterogeneity detected in the model. We can see that the investors still have a negative sentiment because COVID-19 has resulted in uncertainty on the financial market in ASEAN. This gives us practical implications that the ASEAN country members’ government needs to push vaccination policy more aggressively.

A new data covariance matrix estimation for improving minimum variance brain source localization

Data with finite samples results in accuracy and robustness reduction of data covariance matrix estimation, which in turn results in performance reduction of minimum variance beamformer (MVB) for brain source localization (BSL). General linear combination (GLC) and convex combination (CC) are methods of interest for data covariance matrix estimation and increasing its accuracy and robustness because their scalar coefficients are obtained automatically and adaptively. However, based on our best knowledge, the applicability of GLC and CC algorithms has not been investigated for BSL to inform us about their performance. In this paper, we have two goals: 1) Investigation of GLC and CC covariance matrices applications for BSL is carried out using various simulated MEG scenarios and real MEG and clinical epilepsy data; 2) Modified GLC and CC are developed for more accurate and robust estimation of data covariance matrix when data with finite samples is available. In the modified versions, the scalar coefficients are replaced by diagonal matrix form coefficients. These matrix form coefficients are computed using the Hadamard product and mean square error concept. The evaluations show that the CC and modified CC based MVBs are not robust for BSL due to very small values of coefficients. Based on the simulated, real, and clinical data results, it can be stated that the modified GLC is significantly superior to conventional GLC in terms of localization error, spatial resolution (all z < -2; all p-values < 0.001), and offering reliable results. Also, the proposed GLC offers fewer missed sources and less sensitivity to the depth biasing problem, particularly in a high signal-to-noise ratio. In conclusion, it can be said that the covariance matrix of modified GLC which is user-free and robust against the finite data samples can improve the MVB performance for BSL in terms of localization error and spatial resolution.

Associations Between Residential Segregation and Incident Hypertension: The Multi-Ethnic Study of Atherosclerosis.

BackgroundResidential segregation, a geospatial manifestation of structural racism, is a fundamental driver of racial and ethnic health inequities, and longitudinal studies examining segregation’s influence on cardiovascular health are limited. This study investigates the impact of segregation on hypertension in a multiracial and multiethnic cohort and explores whether neighborhood environment modifies this association.Methods and ResultsLeveraging data from a diverse cohort of adults recruited from 6 sites in the United States with 2 decades of follow‐up, we used race‐ and ethnicity‐stratified Cox models to examine the association between time‐varying segregation with incident hypertension in 1937 adults free of hypertension at baseline. Participants were categorized as residing in segregated and nonsegregated neighborhoods using a spatial‐weighted measure. We used a robust covariance matrix estimator to account for clustering within neighborhoods and assessed effect measure modification by neighborhood social or physical environment. Over an average follow‐up of 7.35 years, 65.5% non‐Hispanic Black, 48.1% Chinese, and 53.7% Hispanic participants developed hypertension. Net of confounders, Black and Hispanic residents in segregated neighborhoods were more likely to develop hypertension relative to residents in nonsegregated neighborhoods (Black residents: hazard ratio [HR], 1.33; 95% CI, 1.09–1.62; Hispanic residents: HR, 1.33; 95% CI, 1.04–1.70). Results were similar but not significant among Chinese residents (HR, 1.20; 95% CI, 0.83–1.73). Among Black residents, neighborhood social environment significantly modified this association such that better social environment was associated with less pronounced impact of segregation on hypertension.ConclusionsThis study underscores the importance of continued investigations of groups affected by the health consequences of racial residential segregation while taking contextual neighborhood factors, such as social environment, into account.

Robust low-rank covariance matrix estimation with a general pattern of missing values

This paper tackles the problem of robust covariance matrix estimation when the data is incomplete. Classical statistical estimation methodologies are usually built upon the Gaussian assumption, whereas existing robust estimation ones assume unstructured signal models. The former can be inaccurate in real-world data sets in which heterogeneity causes heavy-tail distributions, while the latter does not profit from the usual low-rank structure of the signal. Taking advantage of both worlds, a covariance matrix estimation procedure is designed on a robust (mixture of scaled Gaussian) low-rank model by leveraging the observed-data likelihood function within an expectation-maximization algorithm. It is also designed to handle general pattern of missing values. The proposed procedure is first validated on simulated data sets. Then, its interest for classification and clustering applications is assessed on two real data sets with missing values, which include multispectral and hyperspectral time series.

A Compact Noise Covariance Matrix Model for MVDR Beamforming

Acoustic beamforming is routinely used to improve the SNR of the received signal in applications such as hearing aids, robot audition, augmented reality, teleconferencing, source localisation and source tracking. The beamformer can be made adaptive by using an estimate of the time-varying noise covariance matrix in the spectral domain to determine an optimised beam pattern in each frequency bin that is specific to the acoustic environment and that can respond to temporal changes in it. However, robust estimation of the noise covariance matrix remains a challenging task especially in non-stationary acoustic environments. This paper presents a compact model of the signal covariance matrix that is defined by a small number of parameters whose values can be reliably estimated. The model leads to a robust estimate of the noise covariance matrix which can, in turn, be used to construct a beamformer. The performance of beamformers designed using this approach is evaluated for a spherical microphone array under a range of conditions using both simulated and measured room impulse responses. The proposed approach demonstrates consistent gains in intelligibility and perceptual quality metrics compared to the static and adaptive beamformers used as baselines.

Bias Adjusted Sign Covariance Matrix

The spatial sign covariance matrix (SSCM), also known as the normalized sample covariance matrix (NSCM), has been widely used in signal processing as a robust alternative to the sample covariance matrix (SCM). It is well-known that the SSCM does not provide consistent estimates of the eigenvalues of the shape matrix (normalized scatter matrix). To alleviate this problem, we propose BASIC (Bias Adjusted SIgn Covariance), which performs an approximate bias correction to the eigenvalues of the SSCM under the assumption that the samples are generated from zero mean unspecified complex elliptically symmetric distributions (the real-valued case is also addressed). We then use the bias correction in order to develop a robust regularized SSCM based estimator, BASIC Shrinkage estimator (BASICS), which is suitable for high dimensional problems, where the dimension can be larger than the sample size. We assess the proposed estimator with several numerical examples as well as in a linear discriminant analysis (LDA) classification problem with real data sets. The simulations show that the proposed estimator compares well to competing robust covariance matrix estimators but has the advantage of being significantly faster to compute.

Robust covariance estimation for distributed principal component analysis

Fan et al. (Ann Stat 47(6):3009–3031, 2019) constructed a distributed principal component analysis (PCA) algorithm to reduce the communication cost between multiple servers significantly. However, their algorithm’s guarantee is only for sub-Gaussian data. Spurred by this deficiency, this paper enhances the effectiveness of their distributed PCA algorithm by utilizing robust covariance matrix estimators of Minsker (Ann Stat 46(6A):2871–2903, 2018) and Ke et al. (Stat Sci 34(3):454–471, 2019) to tame heavy-tailed data. The theoretical results demonstrate that when the sampling distribution is symmetric innovation with the bounded fourth moment or asymmetric with the finite 6th moment, the statistical error rate of the final estimator produced by the robust algorithm is similar to that of sub-Gaussian tails. Extensive numerical trials support the theoretical analysis and indicate that our algorithm is robust to heavy-tailed data and outliers.

ROBUST PARAMETER ESTIMATION FOR RANDOM EFFECT PANEL DATA MODEL IN THE PRESENCE OF HETEROSCEDASTICITY AND INFLUENTIAL OBSERVATIONS

Panel data estimators can strongly be biased and inconsistent in the presence of heteroscedasticity and anomalous observations called influential observations (IOs) in Random effect (RE) panel data model. The existing methods (LWS, WLSF, WLSDRGP) address only the problem of IO but fail to remedy the combine problem of heteroscedasticity and IOs. Therefore, in this research we develop a method that will remedy the combine problem of heteroscedasticity and IOs based on robust heteroscedasticity consistent covariance matrix (RHCCM) estimator and fast improvised influential distance (FIID) weighting method denoted by WLSFIID. The simulation and numerical evidences show that our proposed estimation method is more efficient than the existing methods by providing smallest bias, and smallest standard error of HC4 and HC5

Treatment Persistence in Patients Cycling on Subcutaneous Tumor Necrosis Factor-Alpha Inhibitors in Inflammatory Arthritis: A Retrospective Study.

Biologic treatments including subcutaneous tumor necrosis factor-alpha inhibitors (SC-TNFis) have greatly improved disease management of rheumatoid arthritis (RA), psoriatic arthritis (PsA) and ankylosing spondylitis (AS) (collectively inflammatory arthritis, IA). Nevertheless, some patients discontinue their first-line treatment; for them, one option may be a subsequent line of the same treatment class (i.e., cycling). The aim of this study was to assess treatment persistence between first- and second-line therapy in Swedish IA patients cycling on SC-TNFis. Using data from the Swedish Health Data Registers, adult IA patients filling prescriptions between May 1, 2010, and October 31, 2016, for a SC-TNFi (adalimumab, etanercept, certolizumab and golimumab) were included. Treatment persistence was derived based on information from filled prescriptions and a 60-day grace period. Unadjusted and adjusted marginal Cox proportional hazards models were fitted to estimate the relative risk of discontinuation across treatment lines, using robust sandwich covariance matrix estimates to account for intrapatient dependence (i.e., multiple treatment lines per patient). The analysis was restricted to the first two lines of treatment. Of the eligible patients, 3181 were identified as cyclers. Among these, most were female (68%), and 46%, 28% and 26% were diagnosed with RA, AS and PsA, respectively. Both the unadjusted and adjusted analyses showed that the relative risk of discontinuing SC-TNFi treatment was significantly lower in second compared to first line (hazard ratio; 0.60 [0.57, 0.63] and HR; 0.59 [0.56, 0.62]). This finding was also consistent across IA indications. In this study of patients cycling on SC-TNFis in IA, persistence was greater in second- compared to first-line treatment. The finding was consistent across all IA indications. Hence, patients who discontinue their first-line treatment may still benefit from treatment with an alternative SC-TNFi as a second-line therapy in IA.

ROBUST PARAMETER ESTIMATION FOR RANDOM EFFECT PANEL DATA MODEL IN THE PRESENCE OF HETEROSCEDASTICITY AND INFLUENTIAL OBSERVATIONS

Panel data estimators can strongly be biased and inconsistent in the presence of heteroscedasticity and anomalous observations called influential observations (IOs) in Random effect (RE) panel data model. The existing methods (LWS, WLSF, WLSDRGP) address only the problem of IO but fail to remedy the combine problem of heteroscedasticity and IOs. Therefore, in this research we develop a method that will remedy the combine problem of heteroscedasticity and IOs based on robust heteroscedasticity consistent covariance matrix (RHCCM) estimator and fast improvised influential distance (FIID) weighting method denoted by WLSFIID. The simulation and numerical evidences show that our proposed estimation method is more efficient than the existing methods by providing smallest bias, and smallest standard error of HC4 and HC5.

A Panel Data Approach for Identification of Determinants of Income Inequality: The Role of Macroeconomic, Human Capital and Environmental Variables

Previous studies under the theme of income inequality have majorly focused upon the macroeconomic and human capital-based determinants. This paper attempts to identify and elaborate upon the effects of environmental variables, including pollution and climate change, in addition to the macroeconomic and human capital variables. The study analyses panel data from 49 countries for the period from 2010 to 2016. Amongst the methods of static analysis, a Fixed Effects Model is found to be most suitable. After controlling for heteroscedasticity and serial correlation using robust covariance matrix estimation, it is found that macroeconomic variables including foreign direct investment inflows, the proportion of elderly, inflation, and Gross Domestic Product per capita are significant. Air pollution is found to be a significant determinant of income inequality as well. A major objective of this study is to add to the limited literature on the impacts of environmental variables on income inequality.

Inference of Breakpoints in High-dimensional Time Series

For multiple change-points detection of high-dimensional time series, we provide asymptotic theory concerning the consistency and the asymptotic distribution of the breakpoint statistics and estimated break sizes. The theory backs up a simple two-step procedure for detecting and estimating multiple change-points. The proposed two-step procedure involves the maximum of a MOSUM (moving sum) type statistics in the first step and a CUSUM (cumulative sum) refinement step on an aggregated time series in the second step. Thus, for a fixed time-point, we can capture both the biggest break across different coordinates and aggregating simultaneous breaks over multiple coordinates. Extending the existing high-dimensional Gaussian approximation theorem to dependent data with jumps, the theory allows us to characterize the size and power of our multiple change-point test asymptotically. Moreover, we can make inferences on the breakpoints estimates when the break sizes are small. Our theoretical setup incorporates both weak temporal and strong or weak cross-sectional dependence and is suitable for heavy-tailed innovations. A robust long-run covariance matrix estimation is proposed, which can be of independent interest. An application on detecting structural changes of the U.S. unemployment rate is considered to illustrate the usefulness of our method.

Robust mean and covariance matrix estimation under heterogeneous mixed-effects model with missing values

In this paper, robust mean and covariance matrix estimation are considered in the context of mixed-effects models. Such models are widely used to analyze repeated measures data which arise in several signal processing applications that need to incorporate possible individual variations within a common behavior of individuals. In this context, most algorithms are based on the assumption that the observations follow a Gaussian distribution. Nevertheless, in certain situations in which the data set contains outliers, such assumption is not valid and leads to a dramatic performance loss. To overcome this drawback, we design an expectation-conditional maximization either algorithm in which the heterogeneous component is considered as a part of the complete data. Then, the proposed algorithm is cast into a parallel scheme w.r.t. the individuals in order to mitigate the computational cost and a possible central processor overload. Finally, the proposed algorithm is extended to deal with missing data which refers to the situation where part of the individual responses are unobserved. Numerical simulations are conducted to assess the performance of the proposed algorithm regarding robust regression estimators, probabilistic principal component analysis and its recent robust version.

MIMO filters based on robust rank-constrained Kronecker covariance matrix estimation

In this paper, we propose a new estimator of the covariance matrix parameters when observations follow a mixture of a deterministic Compound-Gaussian (CG) and a white Gaussian noise. In particular, the covariance matrix of the CG contribution is assumed to be expressed as the Kronecker product of two low-rank matrices, which is a structure often involved in MIMO array processing. The proposed estimator is then obtained by maximizing the likelihood of the data with the use of a specifically tailored block Majorization-Minimization (MM) algorithm. Finally, the method is evaluated in terms of adaptive filtering on a MIMO-STAP radar setting, showing important improvements over standard processing.