Resiliency Improvement of an AC/DC Power Grid with Embedded LCC-HVDC Using Robust Power System State Estimation

The growth of renewable energy generation in the power grid brings attention to high-voltage direct current (HVDC) transmission as a valuable solution for stabilizing the system. Robust hybrid power system state estimation could enhance the resilience of the control of these systems. This paper proposes a two-stage, highly robust least-trimmed squares (LTS)-based estimator. The first step combines the supervisory control and data acquisition (SCADA) measurements using the robust LTS-based estimator. The second step merges the obtained state results with the available phasor measurement units (PMUs) measurements using a robust Huber M-estimator. The proposed robust LTS-based estimator shows good performance in the presence of Gaussian measurement noise. The proposed estimator is shown to resist and correct the effect of false data injection (FDI) attacks and random errors on the measurement vector and the Jacobian matrix. The state estimation (SE) is executed on a modified version of the CIGRE bipole LCC-HVDC benchmark model integrated into the IEEE 12-bus AC dynamic test system. The obtained simulation results confirm the effectiveness and robustness of the proposed two-stage LTS-based SE.

MUREN: a robust and multi-reference approach of RNA-seq transcript normalization

Background Normalization of RNA-seq data aims at identifying biological expression differentiation between samples by removing the effects of unwanted confounding factors. Explicitly or implicitly, the justification of normalization requires a set of housekeeping genes. However, the existence of housekeeping genes common for a very large collection of samples, especially under a wide range of conditions, is questionable. Results We propose to carry out pairwise normalization with respect to multiple references, selected from representative samples. Then the pairwise intermediates are integrated based on a linear model that adjusts the reference effects. Motivated by the notion of housekeeping genes and their statistical counterparts, we adopt the robust least trimmed squares regression in pairwise normalization. The proposed method (MUREN) is compared with other existing tools on some standard data sets. The goodness of normalization emphasizes on preserving possible asymmetric differentiation, whose biological significance is exemplified by a single cell data of cell cycle. MUREN is implemented as an R package. The code under license GPL-3 is available on the github platform: github.com/hippo-yf/MUREN and on the conda platform: anaconda.org/hippo-yf/r-muren. Conclusions MUREN performs the RNA-seq normalization using a two-step statistical regression induced from a general principle. We propose that the densities of pairwise differentiations are used to evaluate the goodness of normalization. MUREN adjusts the mode of differentiation toward zero while preserving the skewness due to biological asymmetric differentiation. Moreover, by robustly integrating pre-normalized counts with respect to multiple references, MUREN is immune to individual outlier samples.

Random Forests with Bagging and Genetic Algorithms Coupled with Least Trimmed Squares Regression for Soil Moisture Deficit Using SMOS Satellite Soil Moisture

Soil Moisture Deficit (SMD) is a key indicator of soil water content changes and is valuable to a variety of applications, such as weather and climate, natural disasters, agricultural water management, etc. Soil Moisture and Ocean Salinity (SMOS) is a dedicated mission focused on soil moisture retrieval and can be utilized for SMD estimation. In this study, the use of soil moisture derived from SMOS has been provided for the estimation of SMD at a catchment scale. Several approaches for the estimation of SMD are implemented herein, using algorithms such as Random Forests (RF) and Genetic Algorithms coupled with Least Trimmed Squares (GALTS) regression. The results show that for SMD estimation, the RF algorithm performed best as compared to the GALTS, with Root Mean Square Errors (RMSEs) of 0.021 and 0.024, respectively. All in all, our study findings can provide important assistance towards developing the accuracy and applicability of remote sensing-based products for operational use.

Stratified sampling in highly polluted data as an effective and reliable alternative to high breakdown point estimators

Observations on certain real-life cases include units that are incompatible with other data sets. Values that are extreme in nature do influence estimates obtained by conventional estimators. Robust estimators are therefore necessary for efficient estimation of parameters. This paper uses stratification with simple random sampling without replacement to optimize sample allocation in stratum for efficient parameter estimation as an alternative method of handling highly contaminated samples. Our proposed method stratifies the highly contaminated population into two non-overlapping sub-populations, and stratified samples of sizes 50, 200, and 500 was drawn. We estimate the model parameters form the contaminated sampled data using ordinary least squares under the proposed method, and using the two high breakdown point estimators; the Least Median of Squares and Least Trimmed Squares. Our findings shows that the proposed method did not perform well for low contamination levels (⩽ 30%) but outperformed Least Median of Squares and Least Trimmed Squares for higher contamination rates (⩾ 40%). This indicates that our proposed method compares well and compete favorably with the two high breakdown point estimators.

On the least trimmed squares estimators for JS circular regression model

The least trimmed squares (LTS) estimation has been successfully used in the robust linear regression models. This article extends the LTS estimation to the Jammalamadaka and Sarma (JS) circular regression model. The robustness of the proposed estimator is studied and the used algorithm for computation is discussed. Simulation studied, and real data show that the proposed robust circular estimator effectively fits JS circular models in the presence of vertical outliers and leverage points.

Leveraged least trimmed absolute deviations

The design of regression models that are not affected by outliers is an important task which has been subject of numerous papers within the statistics community for the last decades. Prominent examples of robust regression models are least trimmed squares (LTS), where the k largest squared deviations are ignored, and least trimmed absolute deviations (LTA) which ignores the k largest absolute deviations. The numerical complexity of both models is driven by the number of binary variables and by the value k of ignored deviations. We introduce leveraged least trimmed absolute deviations (LLTA) which exploits that LTA is already immune against y-outliers. Therefore, LLTA has only to be guarded against outlying values in x, so-called leverage points, which can be computed beforehand, in contrast to y-outliers. Thus, while the mixed-integer formulations of LTS and LTA have as many binary variables as data points, LLTA only needs one binary variable per leverage point, resulting in a significant reduction of binary variables. Based on 11 data sets from the literature, we demonstrate that (1) LLTA’s prediction quality improves much faster than LTS and as fast as LTA for increasing values of k and (2) that LLTA solves the benchmark problems about 80 times faster than LTS and about five times faster than LTA, in median.

Using Robust Ridge Regression Diagnostic Method to Handle Multicollinearity Caused High Leverage Points

Statistics practitioners have been depending on the ordinary least squares (OLS) method in the linear regression model for generation because of its optimal properties and simplicity of calculation. However, the OLS estimators can be strongly affected by the existence of multicollinearity which is a near linear dependency between two or more independent variables in the regression model. Even though in the presence of multicollinearity the OLS estimate still remained unbiased, they will be inaccurate prediction about the dependent variable with the inflated standard errors of the estimated parameter coefficient of the regression model. It is now evident that the existence of high leverage points which are the outliers in x-direction are the prime factor of collinearity influential observations. In this paper, we proposed some alternative to regression methods for estimating the regression parameter coefficient in the presence of multiple high leverage points which cause the multicollinearity problem. This procedure utilized the ordinary least squares estimates of the parameter as the initial followed by an estimate of the ridge regression. We incorporated the Least Trimmed Squares (LTS) robust regression estimate to down weight the effects of multiple high leverage points which lead to the reduction of the effects of multicollinearity. The result seemed to suggest that the RLTS give a substantial improvement over the Ridge Regression.