Variance-covariance Matrix Research Articles

A New Variance-Covariance Matrix for Improving Positioning Accuracy in High-Speed GPS Receivers.

One of the main challenges in using GPS is reducing the positioning accuracy in high-speed conditions. In this contribution, by considering the effect of spatial correlation between observations in estimating the covariances, we propose a model for determining the variance–covariance matrix (VCM) that improves the positioning accuracy without increasing the computational load. In addition, we compare the performance of the extended Kalman filter (EKF) and unscented Kalman filter (UKF) combined with different dynamic models, along with the proposed VCM in GPS positioning at high speeds. To review and test the methods, we used six motion scenarios with different speeds from medium to high and examined the positioning accuracy of the methods and some of their statistical characteristics. The simulation results demonstrate that the EKF algorithm based on the Gauss–Markov model, along with the proposed VCM (based on the sinusoidal function and considering spatial correlations), performs better and provides at least 30% improvement in the positioning, compared to the other methods.

Environmental effects on the genetic architecture of fitness components in a simultaneous hermaphrodite.

Understanding how environmental change affects genetic variances and covariances of reproductive traits is key to formulate firm predictions on evolutionary responses. This is particularly true for sex-specific variance in reproductive success, which has been argued to affect how populations can adapt to environmental change. Our current knowledge on the impact of environmental stress on sex-specific genetic architecture of fitness components is still limited and restricted to separate-sexed organisms. However, hermaphroditism is widespread across animals and may entail interesting peculiarities with respect to genetic constraints imposed on the evolution of male and female reproduction. We explored how food restriction affects the genetic variance-covariance (G) matrix of body size and reproductive success of the simultaneously hermaphroditic freshwater snail Physa acuta. Our results provide strong evidence that the imposed environmental stress elevated the opportunity for selection in both sex functions. However, the G-matrix remained largely stable across the tested food treatments. Importantly, our results provide no support for cross-sex genetic correlations suggesting no strong evolutionary coupling of male and female reproductive traits. We discuss potential implications for the adaptation to changing environments and highlight the need for more quantitative genetic studies on male and female fitness components in simultaneous hermaphrodites.

Hybrid robust/stochastic transmission expansion planning considering uncertainties in generators’ offer prices: A second-order cone program approach

The aim of this paper is to propose a hybrid robust/stochastic model for transmission expansion planning (TEP) problem. The uncertainties related to demand and wind are modelled via stochastic programming (SP), while the uncertainties associated with the generators’ offer prices are modelled via robust optimization (RO). In this sense, an ellipsoidal uncertainty set is considered which the offer price values are known to lie in these given ellipsoids. The model presented is then divided into a master problem and several independent subproblems using a tailored implementation of Bender's decomposition (BD) method. Robust linear constraints of the lower level problems are then transformed into a convex second-order cone programming (SOCP) problem. We will apply the proposed model to IEEE-118 bus power system showing that generators’ offer price and their correlation can considerably affect the optimal plan of the transmission planning. It is observed that considering correlation among generators’ offer prices would not necessarily yield more expensive expansion plan in comparison with the case where correlation is ignored. Indeed, increase or decrease in investment cost depends on the entries of the variance-covariance matrix, network topology and the location of generators. Moreover, the results show the computational efficiency of the robust convex model.

Weighted least-squares regression with competing risks data.

The semiparametric accelerated failure time (AFT) model linearly relates the logarithm of the failure time to a set of covariates, while leaving the error distribution unspecified. This model has been widely investigated in survival literature due to its simple interpretation and relationship with linear models. However, there has been much less focus on developing AFT-type linear regression methods for analyzing competing risks data, in which patients can potentially experience one of multiple failure causes. In this article, we propose a simple least-squares (LS) linear regression model for a cause-specific subdistribution function, where the conventional LS equation is modified to account for data incompleteness under competing risks. The proposed estimators are shown to be consistent and asymptotically normal with consistent estimation of the variance-covariance matrix. We further extend the proposed methodology to risk prediction and analysis under clustered competing risks scenario. Simulation studies suggest that the proposed method provides rapid and valid statistical inferences and predictions. Application of our method to two oncology datasets demonstrate its utility in routine clinical data analysis.

Integrating genomics and multivariate evolutionary quantitative genetics: a case study of constraints on sexual selection in Drosophila serrata.

In evolutionary quantitative genetics, the genetic variance-covariance matrix, G, and the vector of directional selection gradients, β, are key parameters for predicting multivariate selection responses and genetic constraints. Historically, investigations of G and β have not overlapped with those dissecting the genetic basis of quantitative traits. Thus, it remains unknown whether these parameters reflect pleiotropic effects at individual loci. Here, we integrate multivariate genome-wide association study (GWAS) with G and β estimation in a well-studied system of multivariate constraint: sexual selection on male cuticular hydrocarbons (CHCs) in Drosophila serrata. In a panel of wild-derived re-sequenced lines, we augment genome-based restricted maximum likelihood to estimate G alongside multivariate single nucleotide polymorphism (SNP) effects, detecting 532 significant associations from 1 652 276 SNPs. Constraint was evident, with β lying in a direction of G with low evolvability. Interestingly, minor frequency alleles typically increased male CHC-attractiveness suggesting opposing natural selection on β. SNP effects were significantly misaligned with the major eigenvector of G, gmax, but well aligned to the second and third eigenvectors g2 and g3. We discuss potential factors leading to these varied results including multivariate stabilizing selection and mutational bias. Our framework may be useful as researchers increasingly access genomic methods to study multivariate selection responses in wild populations.

Morphometric variance, evolutionary constraints and their change through time in Late Devonian Palmatolepis conodonts.

Phenotypic variation is the raw material of evolution. Standing variation can facilitate response to selection along "lines of least evolutionary resistance", but selection itself might alter the structure of the variance. Shape was quantified using 2D geometric morphometrics in Palmatolepis conodonts through the Late Devonian period. Patterns of variance were characterized along the record by the variance-covariance matrix (P-matrix) and its first axis (Pmax). The Late Frasnian was marked by environmental oscillations culminating with the Frasnian/Famennian mass extinction. A shape response was associated with these fluctuations, together with a deflection of the Pmax and the P-matrix. Thereafter, along the Famennian, Palmatolepis mean shape shifted from broad elements with a large platform to slender elements devoid of platform. This shift in shape was associated with a reorientation of Pmax and the P-matrix, due to profound changes in the functioning of the elements selecting for new types of variants. Both cases provide empirical evidences that moving adaptive optimum can reorient phenotypic variation, boosting response to environmental changes. On such time scales, the question seems thus not to be whether the P-matrix is stable, but how it is varying in response to changes in selection regimes and shifts in adaptive optimum.

Data-driven sensitivity analysis in surface structure determination using total-reflection high-energy positron diffraction (TRHEPD)

The present article proposes a data analysis method for experimentally-derived measurements, which consists of an auto-optimization procedure and a sensitivity analysis. The method was applied to the results of a total-reflection high-energy positron diffraction (TRHEPD) experiment, a novel technique of determining surface structures or the position of the atoms near the material surface. This method solves numerically the partial differential equation in the fully-dynamical quantum diffraction theory with many trial surface structures. In the sensitivity analysis, we focused on the experimental uncertainties and the variation over individual fitting parameters, which was analyzed by solving the eigenvalue problem of the variance-covariance matrix. A modern massively parallel supercomputer was used to complete the analysis within a moderate computational time. The sensitivity analysis provides a basis for the choice of variables in the data analysis for practical reliability. The effectiveness of the present analysis method was demonstrated in the structure determination of a Si4O5N3 / 6H-SiC(0001)-(3×3) R30∘ surface. Furthermore, this analysis method is applicable to many experiments other than TRHEPD.

Two-phase sample selection strategies for design and analysis in post-genome-wide association fine-mapping studies.

Post‐GWAS analysis, in many cases, focuses on fine‐mapping targeted genetic regions discovered at GWAS‐stage; that is, the aim is to pinpoint potential causal variants and susceptibility genes for complex traits and disease outcomes using next‐generation sequencing (NGS) technologies. Large‐scale GWAS cohorts are necessary to identify target regions given the typically modest genetic effect sizes. In this context, two‐phase sampling design and analysis is a cost‐reduction technique that utilizes data collected during phase 1 GWAS to select an informative subsample for phase 2 sequencing. The main goal is to make inference for genetic variants measured via NGS by efficiently combining data from phases 1 and 2. We propose two approaches for selecting a phase 2 design under a budget constraint. The first method identifies sampling fractions that select a phase 2 design yielding an asymptotic variance covariance matrix with certain optimal characteristics, for example, smallest trace, via Lagrange multipliers (LM). The second relies on a genetic algorithm (GA) with a defined fitness function to identify exactly a phase 2 subsample. We perform comprehensive simulation studies to evaluate the empirical properties of the proposed designs for a genetic association study of a quantitative trait. We compare our methods against two ranked designs: residual‐dependent sampling and a recently identified optimal design. Our findings demonstrate that the proposed designs, GA in particular, can render competitive power in combined phase 1 and 2 analysis compared with alternative designs while preserving type 1 error control. These results are especially evident under the more practical scenario where design values need to be defined a priori and are subject to misspecification. We illustrate the proposed methods in a study of triglyceride levels in the North Finland Birth Cohort of 1966. R code to reproduce our results is available at github.com/egosv/TwoPhase_postGWAS.

Learning Target Class Feature Subspace (LTC-FS) Using Eigenspace Analysis and N-ary Search-Based Autonomous Hyperparameter Tuning for OCSVM

Existing dimensionality reduction (DR) techniques such as principal component analysis (PCA) and its variants are not suitable for target class mining due to the negligence of unique statistical properties of class-of-interest (CoI) samples. Conventionally, these approaches utilize higher or lower eigenvalued principal components (PCs) for data transformation; but the higher eigenvalued PCs may split the target class, whereas lower eigenvalued PCs do not contribute significant information and wrong selection of PCs leads to performance degradation. Considering these facts, the present research offers a novel target class-guided feature extraction method. In this approach, initially, the eigendecomposition is performed on variance–covariance matrix of only the target class samples, where the higher- and lower-valued eigenvectors are rejected via statistical analysis, and the selected eigenvectors are utilized to extract the most promising feature subspace. The extracted feature-subset gives a more tighter description of the CoI with enhanced associativity among target class samples and ensures the strong separation from nontarget class samples. One-class support vector machine (OCSVM) is evaluated to validate the performance of learned features. To obtain optimized values of hyperparameters of OCSVM a novel [Formula: see text]-ary search-based autonomous method is also proposed. Exhaustive experiments with a wide variety of datasets are performed in feature-space (original and reduced) and eigenspace (obtained from original and reduced features) to validate the performance of the proposed approach in terms of accuracy, precision, specificity and sensitivity.

A New Generalized t Distribution Based on a Distribution Construction Method

In this paper, a new generalized t (new Gt) distribution based on a distribution construction approach is proposed and proved to be suitable for fitting both the data with high kurtosis and heavy tail. The main innovation of this article consists of four parts. First of all, the main characteristics and properties of this new distribution are outined. Secondly, we derive the explicit expression for the moments of order statistics as well as its corresponding variance–covariance matrix. Thirdly, we focus on the parameter estimation of this new Gt distribution and introduce several estimation methods, such as a modified method of moments (MMOM), a maximum likelihood estimation (MLE) using the EM algorithm, a novel iterative algorithm to acquire MLE, and improved probability weighted moments (IPWM). Through simulation studies, it can be concluded that the IPWM estimation performs better than the MLE using the EM algorithm and the MMOM in general. The newly-proposed iterative algorithm has better performance than the EM algorithm when the sample kurtosis is greater than 2.7. For four parameters of the new Gt distribution, a profile maximum likelihood approach using the EM algorithm is developed to deal with the estimation problem and obtain acceptable.

Maximum Likelihood Estimation using the EM Algorithm

This paper yields with the Maximum likelihood estimation using the EM algorithm. This algorithm is very used to solve nonlinear equations with missing data. We estimated the linear mixed model parameters and those of the variance-covariance matrix. The considered structure of this matrix is not necessarily linear. Keywords: Algorithm EM; Maximum likelihood; Mixed linear model.

CONTINUOUSLY UPDATED INDIRECT INFERENCE IN HETEROSKEDASTIC SPATIAL MODELS

Spatial units typically vary over many of their characteristics, introducing potential unobserved heterogeneity which invalidates commonly used homoskedasticity conditions. In the presence of unobserved heteroskedasticity, methods based on the quasi-likelihood function generally produce inconsistent estimates of both the spatial parameter and the coefficients of the exogenous regressors. A robust generalized method of moments estimator as well as a modified likelihood method have been proposed in the literature to address this issue. The present paper constructs an alternative indirect inference (II) approach which relies on a simple ordinary least squares procedure as its starting point. Heteroskedasticity is accommodated by utilizing a new version of continuous updating that is applied within the II procedure to take account of the parameterization of the variance–covariance matrix of the disturbances. Finite-sample performance of the new estimator is assessed in a Monte Carlo study. The approach is implemented in an empirical application to house price data in the Boston area, where it is found that spatial effects in house price determination are much more significant under robustification to heterogeneity in the equation errors.

Structural reliability under uncertainty in moments: distributionally-robust reliability-based design optimization

This study considers structural optimization under a reliability constraint, in which the input distribution is only partially known. Specifically, when it is only known that the expected value vector and the variance-covariance matrix of the input distribution belong to a given convex set, it is required that the failure probability of a structure should be no greater than a specified target value for any realization of the input distribution. We demonstrate that this distributionally-robust reliability constraint can be reduced equivalently to deterministic constraints. By using this reduction, we can handle a reliability-based design optimization problem under the distributionally-robust reliability constraint within the framework of deterministic optimization; in particular, nonlinear semidefinite programming. Two numerical examples are solved to demonstrate the relation between the optimal value and either the target reliability or the uncertainty magnitude.

Covariance matrices of S robust regression estimators

Asymptotic properties of robust regression estimators are well known. However, it is not always clear what is the best strategy for confidence intervals and hypothesis testing when the sample size is not very large, since the distribution of residuals coming from robust estimates has unknown properties for small samples. In the present work we propose an analysis of various strategies for estimating the variance-covariance matrix of the S estimators at the variation of n and p, considering different ρ functions. An adaptive correction strategy is proposed. In addition to the simulation study, an example on a benchmark dataset is shown.

Subgraph Network Random Effects Error Components Models: Specification and Testing

Abstract This paper develops a subgraph random effects error components model for network data linear regression where the unit of observation is the node. In particular, it allows for link and triangle specific components, which serve as a basal model for modeling network effects. It then evaluates the potential effects of ignoring network effects in the estimation of the coefficients’ variance-covariance matrix. It also proposes consistent estimators of the variance components using quadratic forms and Lagrange Multiplier tests for evaluating the appropriate model of random components in networks. Monte Carlo simulations show that the tests have good performance in finite samples. It applies the proposed tests to the Call interbank market in Argentina.

Topological features of multivariate distributions: Dependency on the covariance matrix

Topological data analysis provides a new perspective on many problems in the domain of complex systems. Here, we establish the dependency of mean values of functional p-norms of ’persistence landscapes’ on a uniform scaling of the underlying multivariate distribution. Furthermore, we demonstrate that average values of p-norms are decreasing, when the covariance in a system is increasing. To illustrate the complex dependency of these topological features on changes in the variance-covariance matrix, we conduct numerical experiments utilizing bi-variate distributions with known statistical properties. Our results help to explain the puzzling behavior of p-norms derived from daily log-returns of major equity indices on European and US markets at the inception phase of the global financial meltdown caused by the COVID-19 pandemic.

Real-time GNSS attitude determination by a direct approach with efficiency and robustness

Estimating attitude directly from multi-antenna carrier phase measurements is known as the direct approach of global navigation satellite system attitude determination. Without the process of resolving baseline vectors in advance, this approach makes full use of raw observations. However, the known baseline constraints would be missing when the least squares method is used in the direct approach, of which the corresponding model contains no baseline parameter. The constraint information is important for real-time ambiguity resolution. Therefore, we propose using an adaptively robust Kalman filter for the direct approach, in which the predicted attitude plays the role of an attitude constraint. An observation model parameterized by the multiplicative quaternion error vector and the integer ambiguities is derived, accompanied with a state model consisting of the quaternion error vector, the ambiguities and the angular rate. Since the state vector contains three different types of parameters, the filter uses an adaptive matrix consisting of different adaptive factors instead of a single factor. The factor of the quaternion error vector is determined by a three-section function containing the ratio value from the ratio-test of ambiguity resolution. The factors of the ambiguities are calculated by the detected cycle slip. The equivalent weight matrix of the filtering can resist the influence of outliers in harsh environment. By the direct approach with the proposed adaptively robust filtering, the accuracy of the float solution and the variance-covariance matrix are significantly improved, and the ambiguity can be efficiently searched and fixed using the standard least-squares ambiguity decorrelation adjustment method. The proposed algorithm is suitable for real-time applications since no time-consuming and complex searching of ambiguity resolution is required. Finally, the efficiency and robustness of the algorithm is validated by a field test.

Early-pregnancy maternal body mass index is associated with common DNA methylation markers in cord blood and placenta: a paired-tissue epigenome-wide association study

ABSTRACT Women entering pregnancy with elevated body mass index (BMI) face greater risk of adverse outcomes during pregnancy, delivery, and for their offspring later in life, potentially via epigenetics. If epigenetic programming occurs early during in utero development, the differential marks should be detectable in multiple tissues despite the known unique epigenetic profile in each. We used early-pregnancy BMI as reflection of maternal metabolic milieu exposure in peri-conception and early-pregnancy period. We analysed DNA methylation in paired cord blood and placenta samples among 437 newborns from Gen3G, a pre-birth prospective cohort of primarily European descent. We measured DNA methylation in both tissues across the genome in >720,000 CpG sites using the Illumina MethylationEPIC array. At each site, we used linear mixed models (LMMs) with an unstructured variance-covariance matrix to test for an association between maternal early-pregnancy BMI and DNA methylation in both tissues (modelled as M-values). We adjusted for tissue-specific covariates, offspring sex, gestational age at delivery, and maternal smoking and age. Women had a mean (SD) BMI of 25.4 (5.7) kg/m2 measured at first trimester visit (mean=9.9 weeks). Early-pregnancy BMI was associated with differential DNA methylation levels in paired-tissue analyses at two sites: cg10593758 (β=0.0126, SE=0.0025; P=4.07e-7), annotated to CRHBP, and cg0762168 (β=−0.0094, SE=0.0018; P=2.78e-7), annotated to CCDC97. Application of LMMs in DNA methylation data from distinct fetal-origin tissues allowed us to identify CpG sites at which early-pregnancy BMI may have an epigenetic ‘programming’ effect on overall fetus development. One site (CRHBP) may play a role in hypothalamic-pituitary-adrenal axis regulation.

A New Procedure of Clustering Based on Multivariate Outlier Detection

Clustering is an extremely important task in a wide variety of ap plication domains especially in management and social science research. In this paper, an iterative procedure of clustering method based on multivariate outlier detection was proposed by using the famous Mahalanobis distance. At first, Mahalanobis distance should be calculated for the entire sample, then using T 2 -statistic fix a UCL. Above the UCL are treated as outliers which are grouped as outlier cluster and repeat the same procedure for the remaining inliers, until the variance-covariance matrix for the variables in the last cluster achieved singularity. At each iteration, multivariate test of mean used to check the discrimination between the outlier clusters and the inliers. Moreover, multivariate control charts also used to graphically visual izes the iterations and outlier clustering process. Finally multivariate test of means helps to firmly establish the cluster discrimination and validity. This paper employed this procedure for clustering 275 customers of a famous two wheeler in India based on 19 different attributes of the two wheeler and its company. The result of the proposed technique confirms there exist 5 and 7 outlier clusters of customers in the entire sample at 5% and 1% significance level respectively.

D-optimal joint best linear unbiased prediction of order statistics

In life-testing experiments, it is often of interest to predict unobserved future failure times based on observed early failure times. A point best linear unbiased predictor (BLUP) has been developed in this context by Kaminsky and Nelson (J Am Stat Assoc 70:145–150, 1975). In this article, we develop joint BLUPs of two future failure times based on early failure times by minimizing the determinant of the variance–covariance matrix of the predictors. The advantage of applying joint prediction is demonstrated by using two real data sets. The non-existence of joint BLUPs in certain setups is also discussed.