WLS Estimator Research Articles

An NCS-Based WLS Estimator for Airborne Microwave Photonic SAR Autofocus

An NCS-Based WLS Estimator for Airborne Microwave Photonic SAR Autofocus

Heywood Cases in Unidimensional Factor Models and Item Response Models for Binary Data.

Heywood cases are known from linear factor analysis literature as variables with communalities larger than 1.00, and in present day factor models, the problem also shows in negative residual variances. For binary data, factor models for ordinal data can be applied with either delta parameterization or theta parametrization. The former is more common than the latter and can yield Heywood cases when limited information estimation is used. The same problem shows up as non convergence cases in theta parameterized factor models and as extremely large discriminations in item response theory (IRT) models. In this study, we explain why the same problem appears in different forms depending on the method of analysis. We first discuss this issue using equations and then illustrate our conclusions using a small simulation study, where all three methods, delta and theta parameterized ordinal factor models (with estimation based on polychoric correlations and thresholds) and an IRT model (with full information estimation), are used to analyze the same datasets. The results generalize across WLS, WLSMV, and ULS estimators for the factor models for ordinal data. Finally, we analyze real data with the same three approaches. The results of the simulation study and the analysis of real data confirm the theoretical conclusions.

The Comparison of WLS and DWLS Estimation Methods in SEM to Construct Health Behavior Model

It is unknown how reliable various point estimates, standard errors, and standard several test statistics are for standardized SEM parameters when categorical data used or misspecified models are present. This paper discusses the comparison between WLS and DWLS for examining hypothesized relations among ordinal variables. In SEM, the polychoric correlation is employed either in WLS or DWLS. This study constructs the Health behavior model as an endogenous latent variable in which exogenous latent variables are Perceived susceptibility and Health motivation. All indicators are in categorical types. Thus, data are not multivariate normal, or the model could be misspecified. This study compares the values of standard deviation and coefficient determination to determine a better model. The criteria for the goodness of fit for the overall model are based on RMSEA, CFI, and TLI values. This present study found that the WLS estimator method resulted in better values than DWLS’s.

A Robust TSWLS Localization of Moving Target in Widely Separated MIMO Radars

In this paper, we investigate the target localization problem in a Multiple-Input Multiple-Output (MIMO) radar systems with Widely Separated Antennas (WSA). We derive an accurate and robust closed-form estimator for the target's location and velocity by using the well-known Two-Stage Weighted Least Squares (TSWLS) technique. We define the nuisance variables in the first stage to obtain a set of pseudo-linear equations and solve them by the WLS estimator. We then approximate the nuisance variables with the first-order Taylor series around the estimates from the previous stage in order to reformulate a set of linear equations which is solved again using the WLS estimator. Unlike the state-of-the-art methods, the proposed method is robust against the presence of incorrect Doppler Shift (DS) measurements and perturbations errors imposed by the linear approximations. Simulation results demonstrate that our method outperforms the state-of-the-art methods not only in performance and complexity but also in robustness.

A partitioning strategy for improved state estimation performance in ill-conditioned power systems with hybrid measurement set

Considering the increase in power system size and the number of PMUs, the utilization of a computationally efficient yet accurate static state estimator is crucial. The fast-decoupled WLS estimator (FD-WLS) is the most common method employed in industrial applications, thanks to its computational efficiency and ease of implementation. However, it is known that FD-WLS fails in the presence of an ill-conditioned power system, e.g., a power system with high R/X ratio and large difference between measurement error variances. This paper proposes a partitioning strategy for ill-conditioned power systems. The proposed method forms two types of sub-systems, such that one can apply FD-WLS in the type-1 sub-systems, and conventional formulation of WLS should be applied in the type-2 sub-systems. The utilization of the proposed method enables a computational performance comparable to that of FD-WLS and an accuracy comparable to that of the centralized solution.

A multivariate HAR-RV model with heteroscedastic errors and its WLS estimation

This work considers a multivariate heterogeneous autoregressive-realized volatility (HAR-RV) model in the presence of heteroscedasticity and aims to analyze realized volatilities of multiple assets that possess non-standard features, such as non-Gaussianity, time varying volatility and long-memory dependence. For capturing the long-memory, a HAR-RV model is employed, while for a heavy-tailed distribution, a GARCH process is adopted on the noise term. To estimate coefficients of the HAR-RV-GARCH model, we suggest weighted least squares estimator (WLSE) based on an observed weighting scheme and prove its asymptotic normality. Simulation results show a good performance on the WLSE. The multivariate HAR-RV-GARCH model fitted by the WLSE is illustrated with an application to realized volatilities of multiple financial data.

A photovoltaics-aided interlaced extended Kalman filter for distribution systems state estimation

Distribution system state estimation (DSSE) is essential for smart grid monitoring and control. Bus voltage phasors and, consequently, DSSE uncertainty can be significantly affected by photovoltaic (PV) penetration, even when suitable hosting capacity strategies are adopted to keep voltage levels within given limits. In this paper, it is shown that the state estimation uncertainty achievable with algorithms exploiting PV information can be significantly lower than using classic techniques, such as the Weighted Least Squares approach that is still widely adopted at the distribution level. The proposed analysis is based on on an Interlaced Extended Kalman Filter (IEKF) that, in the prediction step, relies on the available information on active and reactive power injections. The use of an interlaced implementation makes the estimator more robust to zero-power injections, which otherwise could make the Kalman innovation matrix ill-conditioned. In the update step, the PV power data measured on the field, possibly supported by Phasor Measurement Units (PMUs), complement the virtual measurements, the traditional pseudo-measurements, and those obtained by aggregating smart meter data. The results of one-year-long simulations confirm the benefits of including the available information on PV generation on state estimation uncertainty. • The PV-IEKF system state estimator relies on PV generation and smart meters data. • Higher numerical robustness results from an interlaced Kalman filter implementation. • PV-IEKF is about 30% faster and is usually more accurate than a classic WLS estimator. • Accurate results can be achieved by using a small number of PMUs, too.

Corrective Measures in Linear Regression Model Plagued with Heteroscedasticity: A Monte Carlo

Cet article se focalise sur le modele lineaire multivarie des moindres carres ou ordinaire (MLMO) en presence d'heteroscedasticite. Dans un tel cas, les estimateurs sont sans biais certes mais ils sont non-efficacces. Quatre tests d'heteroscedasticite ont ete appliques. Le test de Goldfeld-Quandt est plus performant pour de petites tailles alors que le test Glejser est meilleur pour de grandes tailles. Les results HC3 sont meilleurs que ceux relatifs a HCCM pour de petites tailles mais leur sont equivalent pour de grandes tailles au niveau de la qualite de l'inference. Les performances comparees des modeles MLMO, WLS et HC3 montrent que les estimateurs WLS sont preferables par rapport a l'estimation des parametres en presence d'heteroscedasticite lorsque les formes fonctionelles ne sont pas connues.

Asymptotic Properties of the Restricted GMM and WLS Estimators in the Localization Framework

We consider the implications of choosing weighting matrix (projection) on the asymptotic risk of the restricted GMM and WLS estimators. Decomposing expected square error risk into variance part and squared bias part, we show that for both GMM and WLS its variance part is minimized by choosing classical optimal weighting matrix, whereas the squared bias part is minimized using the weighting matrix chosen for the asymptotic risk function.

Iterative reconstruction with segmentation penalty for PET.

Segmentation technique is widely accepted to reduce noise propagation from transmission scanning for positron emission tomography. The conventional routine is to sequentially perform reconstruction and segmentation. A smoothness penalty is also usually used to reduce noise, which can be imposed to both the ML and WLS estimators. In this paper we replace the smoothness penalty by a segmentation penalty that biases the object toward piecewise-homogeneous reconstruction. Two updating algorithms are developed to solve the penalized ML and WLS estimates, which monotonically decrease the cost functions. Experimental results on simulated phantom and real clinical data were both given to demonstrate the effectiveness and efficiency of the algorithms which were proposed.

Sample Size Requirements of the Robust Weighted Least Squares Estimator

The present study investigated sample size requirements of maximum likelihood (ML) and robust weighted least squares (robust WLS) estimation for ordinal data with confirmatory factor analysis (CFA) models with 3–10 indicators per factor, primary loadings between .4 and .9, and four different levels of categorization (2, 3, 5, and 7). Additionally, the utility of the H-measure of construct reliability (an index combining the number of indicators and the magnitude of loadings) in predicting sample size requirements was examined. Results indicated that a higher number of indicators per factors and higher factor loadings increased the rates of proper convergence and solution propriety. However, the H-measure could only partly account for the results. Moreover, it was demonstrated that robust WLS was mostly superior to ML, suggesting that there is little reason to prefer ML over robust WLS when the data are ordinal. Sample size recommendations for the robust WLS estimator are provided.

Relative Performance of Categorical Diagonally Weighted Least Squares and Robust Maximum Likelihood Estimation

Robust maximum likelihood (ML) and categorical diagonally weighted least squares (cat-DWLS) estimation have both been proposed for use with categorized and nonnormally distributed data. This study compares results from the 2 methods in terms of parameter estimate and standard error bias, power, and Type I error control, with unadjusted ML and WLS estimation methods included for purposes of comparison. Conditions manipulated include model misspecification, level of asymmetry, level and categorization, sample size, and type and size of the model. Results indicate that cat-DWLS estimation method results in the least parameter estimate and standard error bias under the majority of conditions studied. Cat-DWLS parameter estimates and standard errors were generally the least affected by model misspecification of the estimation methods studied. Robust ML also performed well, yielding relatively unbiased parameter estimates and standard errors. However, both cat-DWLS and robust ML resulted in low power under conditions of high data asymmetry, small sample sizes, and mild model misspecification. For more optimal conditions, power for these estimators was adequate.

A Geometrical View for Multiple Gross Errors Detection, Identification, and Correction in Power System State Estimation

In this paper a geometrical approach is described to detect, identify, and recover multiple gross errors in power system state estimation. Using the classical WLS estimator, the measurement residuals is computed, and then the error is composed. For the detection and identification of the measurements with gross errors, the composed measurement error in the normalized form (CMEN) is used. The measurement magnitude corrections otherwise are performed using the composed normalized measurement error (CNE). To give support to the detection and identification of the measurements containing gross errors, a generalization of the classical largest normalized residual test is provided.

Robust WLS estimator using reweighting techniques for electric energy systems

The state estimator is a key tool in the operation of any real-world electric energy system. In this paper, a state estimator based on a weighted least squares model is proposed which is robust against outliers. This algorithm presents two relevant features: robustness that is achieved by readjusting measurement weights, and accuracy that is attained by considering measurement dependencies. The proposed method is tested in the IEEE 57-bus and 118-bus systems and the obtained results are analyzed using Design of Experiments and ANOVA techniques.

Modeling FACTS Devices in Power System State Estimation

In this paper is modeled different types of control devices including various kinds of FACTS devices based on power system states. Also, the impact of each device on the amount of injection active or reactive powers as well as active and reactive power flow will be investigated. Based on the type of these devices which can be in parallel, in series or in series–shunt in power systems, proposed models is considered differently. Accordingly, case studies will be performed for three different types of control devices installed in series, in shunt and in series-shunt fashions. State estimation results based on Weighted Least Square not only confirm the proposed models’ effectiveness in accurately state estimating of the system and measurement values but also shows that the estimated values can be obtained from the states of the control devices. Keywords: State Estimation; FACTS Devises; Measurement Function; WLS Estimator DOI: http://dx.doi.org/10.11591/ijece.v2i1.132

Bias-Correction in Vector Autoregressive Models: A Simulation Study

We analyze and compare the properties of various methods for bias-correcting parameter estimates in vector autoregressions. First, we show that two analytical bias formulas from the existing literature are in fact identical. Next, based on a detailed simulation study, we show that this simple and easy-to-use analytical bias formula compares very favorably to the more standard but also more computer intensive bootstrap bias-correction method, both in terms of bias and mean squared error. Both methods yield a notable improvement over both OLS and a recently proposed WLS estimator. We also investigate the properties of an iterative scheme when applying the analytical bias formula, and we find that this can imply slightly better finite-sample properties for very small sample sizes while for larger sample sizes there is no gain by iterating. Finally, we also pay special attention to the risk of pushing an otherwise stationary model into the non-stationary region of the parameter space during the process of correcting for bias.

Tie-line constrained distributed state estimation

This paper presents an implementable distributed state estimation method for online analysis of power systems having multiple, geographically separated areas. Distributed state estimation apart from giving a faster solution, also improves the condition number of the resultant gain matrices. The method proposed here uses the conventional WLS estimator (Gauss–Newton method) with equality constraints forcing the tie line flows as calculated by the adjacent areas to be equal. Based on the topology of the network, the system is partitioned into multiple areas and a processor is assigned to each of these areas for solving the local state estimation problem. Simulations carried out on the IEEE 14, 30 and 118 bus systems show good convergence properties and improvement on the condition number of the gain matrices when compared with centralized algorithms.

Sustainability of marine fishing: a case study of West Bengal

The marine fishery sector in India is important not only for domestic demand for protein food requirements but also from the imperatives of exports. An increased investment in this sector has taken place during the last few years and the fishing fleet has expanded at a very rapid rate. Presently, however, marine fishers are facing difficulties in fish capture in spite of exerting the same and sometimes more effort. Thus the question of the sustainability of marine fishing arises. The sustainability of marine fishing in the Digha-Shankarpur coastal region has been studied through estimation of the maximum sustainable yield based on a simple bioeconomic model. WLS estimation has been done to remove heteroscedastic disturbances. Estimated results show that actual yields of all varieties are still below maximum sustainable yield (MSY) except prawn, which has reached near optimal levels.

The Performance of ML, GLS, and WLS Estimation in Structural Equation Modeling Under Conditions of Misspecification and Nonnormality

This simulation study demonstrates how the choice of estimation method affects indexes of fit and parameter bias for different sample sizes when nested models vary in terms of specification error and the data demonstrate different levels of kurtosis. Using a fully crossed design, data were generated for 11 conditions of peakedness, 3 conditions of misspecification, and 5 different sample sizes. Three estimation methods (maximum likelihood [ML], generalized least squares [GLS], and weighted least squares [WLS]) were compared in terms of overall fit and the discrepancy between estimated parameter values and the true parameter values used to generate the data. Consistent with earlier findings, the results show that ML compared to GLS under conditions of misspecification provides more realistic indexes of overall fit and less biased parameter values for paths that overlap with the true model. However, despite recommendations found in the literature that WLS should be used when data are not normally distributed, we find that WLS under no conditions was preferable to the 2 other estimation procedures in terms of parameter bias and fit. In fact, only for large sample sizes (N = 1,000 and 2,000) and mildly misspecified models did WLS provide estimates and fit indexes close to the ones obtained for ML and GLS. For wrongly specified models WLS tended to give unreliable estimates and over-optimistic values of fit.

Rent controls and homeless rates

This paper extends the earlier analysis of Tucker [1987] and Quigley [1990] regarding the relationship between a city's homeless rate and the existence of rent controls. Performing WLS estimation on the logit of the homeless rate, this paper concludes that rent controls have the effect of lowering, not increasing, the homeless rate.