Least Absolute Deviation Research Articles

Addressing Autocorrelation, Multicollinearity, and Heavy-Tail Errors in the Linear Regression Model

The most popular estimator for estimating parameters of linear regression models is the Ordinary Least Squares (OLS) Estimator. The OLS is considered the best linear unbiased estimator when certain assumptions are not violated. However, when autocorrelation, multicollinearity, and heavy-tail error are jointly present in the dataset, the OLS estimator is inefficient and imprecise. In this paper, we developed an estimator of linear regression model parameters that jointly handle multicollinearity, autocorrelation, and heavy tail errors. The new estimator, LADHLKL, was derived by combining the Hildreth-Lu (HL), the Kibria Lukman (KL), and the Least Absolute Deviation (LAD) estimators. The LADHLKL poses both the characteristics of the LAD, HL, and KL estimators which makes it resistant to both problems. We examined the properties of the proposed estimator and compared its performance with other existing estimators in terms of mean square error. An application to real-life data and simulation study revealed that the proposed estimator dominates other estimators in all the considered conditions in terms of mean square error.

ROBUST GEOGRAPHICALLY WEIGHTED REGRESSION WITH LEAST ABSOLUTE DEVIATION (LAD) ESTIMATION AND M-ESTIMATION ON GRDP OF WEST JAVA PROVINCE

Geographically Weighted Regression (GWR) is an analytical method for data that contains spatial heterogeneity effects. However, parameter estimation in the GWR model has a weakness, namely it is prone to outliers and can cause the parameter estimation to be biased. This can be overcome by the Robust Geographically Weighted Regression (RGWR) method which is more robust against the presence of outliers. This method is suitable for Gross Regional Domestic Product (GRDP) data in West Java Province, which contains outliers and also has spatial effects. The data used in this study are secondary data obtained from the Central Statistics Agency (BPS) of West Java Province. The purpose of this study is to compare the Robust Geographically Weighted Regression (RGWR) method with the Least Absolute Deviation (LAD) Estimation and M-estimation and also to find out the factors that affect the Gross Regional Domestic Product (GRDP) in West Java Province in 2021 based on the model resulting from. Selection of the best model is seen based on the value of the coefficient of determination (R2) and Mean Squared of Error (MSE). The research results show that the Robust Geographically Weighted Regression (RGWR) method with M-estimation is much more effective in estimating the distribution of GRDP in West Java Province in 2021, seen from the larger coefficient of determination and the smaller Mean Square Error (MSE). The variables that have a significant influence on GRDP in West Java Province in 2021 are the variables of foreign investment and local income.

A scale-span method to characterize the mechanical property of BCF/PEEK considering uncertain structural characteristics

The focus of this study is exploring a scale-span characterization method to predict the mechanical properties of Braided Carbon Fiber Reinforced Poly Ether Ether Ketone (BCF/PEEK) considering structural uncertainty. Firstly, a complicated micro-scale Representative Volume Element (RVE) model that considers the random position and size of fiber was established via the developed Python script. Analogously, a mathematical expression adopted by the trust region algorithm was proposed to accurately describe the detailed cross-sectional shapes and fluctuation amplitude characteristics of BCF/PEEK for the sake of establishing the precision meso-scale RVE model. Then, the corresponding elastic properties that consider fiber volume fraction and fiber distribution location were characterized via the span-scale characterization method. Meanwhile, the influence of fiber bundle fluctuation amplitude and fiber volume fraction on the mechanical properties was investigated as well. In addition, the mechanical properties of BCF/PEEK with the change of the braid angle between warp and weft yarn were predicted via the established meso-scale RVE model. Finally, a series of experiments have been carried out. The maximum and minimum absolute prediction deviation of all elastic property parameters were only 4.07 % and 1.41 %, respectively, which verified the proposed scale-span characterization method can predict the mechanical properties of composites well.

Predicting Alzheimer's disease CSF core biomarkers: a multimodal Machine Learning approach.

Alzheimer's disease (AD) is a progressive neurodegenerative disorder. Current core cerebrospinal fluid (CSF) AD biomarkers, widely employed for diagnosis, require a lumbar puncture to be performed, making them impractical as screening tools. Considering the role of sleep disturbances in AD, recent research suggests quantitative sleep electroencephalography features as potential non-invasive biomarkers of AD pathology. However, quantitative analysis of comprehensive polysomnography (PSG) signals remains relatively understudied. PSG is a non-invasive test enabling qualitative and quantitative analysis of a wide range of parameters, offering additional insights alongside other biomarkers. Machine Learning (ML) gained interest for its ability to discern intricate patterns within complex datasets, offering promise in AD neuropathology detection. Therefore, this study aims to evaluate the effectiveness of a multimodal ML approach in predicting core AD CSF biomarkers. Mild-moderate AD patients were prospectively recruited for PSG, followed by testing of CSF and blood samples for biomarkers. PSG signals underwent preprocessing to extract non-linear, time domain and frequency domain statistics quantitative features. Multiple ML algorithms were trained using four subsets of input features: clinical variables (CLINVAR), conventional PSG parameters (SLEEPVAR), quantitative PSG signal features (PSGVAR) and a combination of all subsets (ALL). Cross-validation techniques were employed to evaluate model performance and ensure generalizability. Regression models were developed to determine the most effective variable combinations for explaining variance in the biomarkers. On 49 subjects, Gradient Boosting Regressors achieved the best results in estimating biomarkers levels, using different loss functions for each biomarker: least absolute deviation (LAD) for the Aβ42, least squares (LS) for p-tau and Huber for t-tau. The ALL subset demonstrated the lowest training errors for all three biomarkers, albeit with varying test performance. Specifically, the SLEEPVAR subset yielded the best test performance in predicting Aβ42, while the ALL subset most accurately predicted p-tau and t-tau due to the lowest test errors. Multimodal ML can help predict the outcome of CSF biomarkers in early AD by utilizing non-invasive and economically feasible variables. The integration of computational models into medical practice offers a promising tool for the screening of patients at risk of AD, potentially guiding clinical decisions.

Leveraging open-source data to study solar-wind complementarity in the global perspective

Renewable energy sources, particularly solar and wind power, offer promising solutions for sustainable electricity generation. However, their inherent dependency on natural conditions and resulting intermittent generation pose challenges to the electricity grid.This study investigates the strategy of wind-solar complementarity to partly mitigate this issue, leveraging open-source data from the Slovak Republic. Our analysis reveals that combined solar and wind generation aligns more closely with real consumption compared to individual solar generation. We employ two quantitative methodologies, ordinary least squares (OLS) and least absolute deviations (LAD) regressions, to demonstrate the consistency of our findings. Additionally, we assess the prevalence of dunkelflaute events using real-generation data, finding them to be infrequent and posing a minimal risk in the context of Central Europe.We show that complementarity can be studied using open-source data for virtually any country in the world and thus quantitative methods can be used to advocate for renewable energy in general and balanced building of both wind and solar energy in particular. This research contributes to the broader understanding of renewable energy integration strategies and informs policymakers and stakeholders on optimizing energy systems for sustainability and cost-effectiveness.

A new Frontier in electric load forecasting: The LSV/MOPA model optimized by modified orca predation algorithm

Electric load forecasting is a vital task for energy management and policy-making. However, it is also a challenging problem due to the complex and dynamic nature of electric load data. In this paper, a novel technique, called LSV/MOPA, has been proposed for electric load forecasting. The technique is a hybrid model that combines the advantages of Long Short-Term Memory (LSTM) and Support Vector Regression (SVR), two powerful artificial intelligence algorithms. The hybrid model is further optimized by a newly Modified Orca Predation Algorithm (MOPA), which enhances the forecasting accuracy and efficiency. The LSV/MOPA model has been applied to historical electric load data from South Korea, covering four regions and 20 years. The LSV/MOPA model has been compared with other state-of-the-art forecasting techniques, including SVR/FFA, LSTM/BO, LSTM-SVR, and CNN-LSTM. The results show that the LSV/MOPA model with minimum average mean absolute percentage deviation error, including 365 in northern region, 12.8 in southern region, 8.6 in central region, and 30.8 in eastern region, provides the best fitting and outperforms the other techniques in terms of the Mean Absolute Percentage Deviation (MAPD) index, achieving lower values for all regions and years. The LSV/MOPA model also exhibits faster convergence and better generalization than the other techniques. This study demonstrates the effectiveness and superiority of the LSV/MOPA model for electric load forecasting and suggests its potential applications in other sectors where accurate forecasting is crucial.

OPTIMIZING THE ECONOMIC BENEFITS OF PUBLIC SPENDING FROM NATIONAL YOUTH DEVELOPMENT AGENCY GRANT FUNDING

This study examined the economic benefits of the National Youth Development Agency (NYDA) grant funding, in the Eastern Cape, using cost benefit analysis (CBA) and least absolute deviation (LAD) regression analysis on a sample size of 253 respondents. The study found that public investment towards youth entrepreneurship through NYDA grant funding yields positive social returns. The study further found that the development of youth entrepreneurship should go beyond just NYDA grant funding to include favorable policies towards closing gender gaps, supportive education systems as well ensuring diverse economic sectors.

Plane Waves Versus Correlation-Consistent Basis Sets: A Comparison of MP2 Non-Covalent Interaction Energies in the Complete Basis Set Limit.

Second-order Møller-Plesset perturbation theory (MP2) is the most expedient wave function-based method for considering electron correlation in quantum chemical calculations and, as such, provides a cost-effective framework to assess the effects of basis sets on correlation energies, for which the complete basis set (CBS) limit can commonly only be obtained via extrapolation techniques. Software packages providing MP2 energies are commonly based on atom-centered bases with innate issues related to possible basis set superposition errors (BSSE), especially in the case of weakly bonded systems. Here, we present noncovalent interaction energies in the CBS limit, free of BSSE, for 20 dimer systems of the S22 data set obtained via a highly parallelized MP2 implementation in the plane-wave pseudopotential molecular dynamics package CPMD. The specificities related to plane waves for accurate and efficient calculations of gas-phase energies are discussed, and results are compared to the localized (aug-)cc-pV[D,T,Q,5]Z correlation-consistent bases as well as their extrapolated CBS estimates. We find that the BSSE-corrected aug-cc-pV5Z basis can provide MP2 energies highly consistent with the CBS plane wave values with a minimum mean absolute deviation of ∼0.05 kcal/mol without the application of any extrapolation scheme. In addition, we tested the performance of 13 different extrapolation schemes and found that the X-3 expression applied to the (aug-)cc-pVXZ bases provides the smallest deviations against CBS plane wave values if the extrapolation sequence is composed of points D and T, while performs slightly better for TQ and Q5 extrapolations. Also, we propose as a reliable alternative to extrapolate total energies from the DTQ, TQ5, or DTQ5 data points. In spite of the general good agreement between the values obtained from the two types of basis sets, it is noticed that differences between plane waves and (aug-)cc-pVXZ basis sets, extrapolated or not, tend to increase with the number of electrons, thus raising the question of whether these discrepancies could indeed limit the attainable accuracy for localized bases in the limit of large systems.

Budget ratcheting in museums

PurposeThis study focuses on ratcheting and budget behavior in nonprofit museums. Specifically, the authors examine how performance compared with the budget affects future revenue budgets, and how this differs from the extant literature focused on for-profit organizations. The study focuses specifically on the relationship between museums and their sources of public funding and how this affects how museums prepare budgets.Design/methodology/approachBased on four years of data covering 97 state-subsidized Danish museums, the authors analyze budget ratcheting using least absolute deviation (LAD) estimations in the form of median regressions.FindingsThe authors find that when actual revenue from admission charges is below the budget, the decrease in the following year's budget is greater than the increase in the following year's budget when actual revenue from admission charges is above the budget (i.e. the authors find asymmetrical ratcheting).Research limitations/implicationsThe findings are based on a specific setting (Danish museums), and the results may not be generalizable to other settings.Practical implicationsThis study provides insights into the museum sector and other sectors with similar characteristics and contributes to understanding the differences between museums and for-profit organizations when it comes to budgeting. As private-sector management practices are gaining ground in the museum sector, it is important to learn more about budgeting-related issues in this sector.Originality/valueThe asymmetrical ratcheting the authors find is the opposite of ratcheting typically found in for-profit organizations. The authors attribute the results to the incentive conflict between museums and their public funding sources. The authors point to the museums' dependence on public funding as an explanation for the results and, thereby, extend the knowledge on ratcheting to organizations with different characteristics than traditional, for-profit organizations.

The LAD estimation of UMAR model with imprecise observations

Uncertain time series analysis is a method of predicting future values by analyzing imprecise observations. In this paper, the least absolute deviation (LAD) method is applied to solve for the unknown parameters of the uncertain max-autoregressive (UMAR) model. The predicted value and confidence interval of the future data are calculated using the fitted UMAR model. Moreover, the relative change rate of parameter is proposed to test the robustness of different estimation methods. Then, two comparative analyses demonstrate the LAD estimation can handle outliers better than the least squares (LS) estimation and the necessity of introducing the UMAR model. Finally, a numerical example displays the LAD estimation in detail to verify the effectiveness of the method. The LAD estimation is also applied to a collection of actual data with cereal yield.

Eliminate the Heterogeneous Variances Effect Using Quantile Regression

Quantile regression (QR) is a statistical method that addresses the issue of inconsistent data errors. QR utilizes minimum absolute deviation to reduce the absolute deviation by employing percentile estimators such as the median, 1st and 3rd quartiles, and 10th and 90th percentiles. This study focuses on the qth percentile estimators of QR. QR models not only detect varying effects of explanatory variables at different quantiles of the response variable but also provide more robust and accurate estimates compared to mean regression when normality assumptions are violated or when outliers and long tails are present. This study conducts several simulation studies to compare the suggested qth percentile estimators of QR under different sample sizes, explanatory variables, and qth percentiles. Additionally, the study examines the impact of error terms dependency on normal/non-normal distribution. The asymptotic properties of these estimators are also investigated. The study concludes with a discussion of the advantages and disadvantages of using these qth percentile estimators of QR.

Performance evaluation of estimators in the presence of outliers or omitted predictors: a study on the Poisson-Exponential regression model

The Poisson regression model is vulnerable for overdispersion in the data when estimating model parameters and their standard errors. Overdispersion may occur due to outliers in the data and/or removal of important predictors from the model. This paper employs a regression model that can be used to better cope with outliers and omitted predictor bias in count data compared to the Poisson regression model, namely the Poisson exponential (PE) model which is a reparameterization of the geometric regression model. Along with investigating the distributional properties of the PE distribution, the usual maximum likelihood (ML-I), maximum likelihood with Expectation-maximization algorithm (ML-II), least-square (LS), weighted least-square (WLS), least-absolute deviation (LAD), weighted least-absolute deviation (WLAD), and Cramer-von mises (CVM) estimation methods are utilized in the context of the PE regression model. The performance of these estimation methods with the PE regression model are inspected through two comprehensive simulation studies. The first is conducted on data sets with and without outliers. The second investigates the performance of the estimation methods for the PE regression model with and without omitted predictors. Two real-life applications illustrate the applicability of the PE regression model with the estimation methods for these two situations.

Robust dynamic and algebraic state estimation for microgrids: A generalized approach

AbstractNetwork control, optimization, and security analysis are facilitated by accurate microgrid state estimation. By utilizing phasor measurement units (PMUs), a combined robust centralized dynamic algebraic approach is proposed in this paper for estimating algebraic states (voltage phasors) as well as dynamic states (associated with synchronous generators and wind turbines). Assuming that a load is placed on each bus, an innovative PMU placement method is also presented to provide measurements for all dynamic and algebraic state variables. As a robust link between algebraic state estimation and dynamic state estimation, the output results of the least absolute value (LAV) estimator, which is robust against bad data, are fed to dynamic state estimators as pseudo measurements. Next, to address the nonlinearity of synchronous generator and wind turbine models, an unscented Kalman filter (UKF) is applied to estimate dynamic states precisely. The numerical tests on a microgrid test system show that the suggested approach is suitable for both algebraic and dynamic state estimation. Synchronous generators and wind turbines are modeled using nonlinear models of the 9th and third orders, respectively, and static loads are modeled as voltage‐frequency dependent ones.

Confidence intervals from local minimums of objective function

The weighted median plays a central role in the least absolute deviations (LAD). We propose a nonlinear regression using (LAD). Our objective function $f(a, l, s)$ is non-convex with respect to the parameters a, l, s, and is such that for each fixed l, s the minimizer of $a\to f (a, l, s)$ is the weighted median $med(x(l, s), w(l, s))$ of a sequence $x(l, s)$ endowed with the weights $w(l, s)$ (all depend on $l$, $s$). We analyse and compare theoretically the minimizers of the function $(a, l, s)\to f (a, l, s)$ and the surface $(l, s) \to f (med(x(l, s), w(l, s)), l, s)$. As a numerical application we propose to fit the daily infections of COVID 19 in China using Gaussian model. We derive confident interval for the daily infections from each local minimum.

The parameter estimations for uncertain regression model with autoregressive time series errors

Uncertain regression model with autoregressive time series errors studies the relations between response variables and explanatory variables when the errors are dependence. The estimations of the unknown parameters are worth exploring in further research. The least square (LS) estimations were proposed to estimate the unknown parameters. However, when the outliers appear, we find that the LS is not effective. So, in this article, the least absolute deviations (LAD) and the maximum likelihood estimations (MLE) are proposed to estimate the unknown parameters. Moreover, some examples are given to verify the applicability and practicability of these two methods. The comparative analysis is given to verify that the proposed methods are more advantageous and effective than the least square method when the observed data are affected by outliers. Finally, the example of exploring the relationships between GDP and related influencing factors for China, from 2004 to 2020, is given to testify the practicability of the methods.

Statistical Modelling of Road Traffic Accidents: Pattern and Trend in Kogi State, Nigeria

Road traffic accident (RTA) is defined as unplanned car crash that causes injuries, fatalities, and property damage. In order to better understand the pattern and trend of road traffic accident in Kogi state, Nigeria, we statistically modeled RTA data collected from Federal Road Safety Corps, Lokoja from January 2017 to December 2021. The data consisted of monthly RTA types and outcomes. The RTA types considered were fatal, serious and minor while the RTA outcomes were death, injury and no injury. Time series modeling was adopted for modeling and predicting the accident rates while Pearson correlation was used to determine the degree of relationship between RTA types and outcomes. Results showed that there were steady fluctuations in the patterns of RTA types and outcomes between February and October while there were upward trend in RTA from November to January. The augmented Dickey-Fuller test showed that RTA series was stationary and out of 10 candidate models obtained using ACF and PACF plots, the best model suitable for forecasting RTA rate was found to be ARIMA(1,0,1) using mean absolute deviation (MAD) and mean square error (MSE) selection criteria. In order to estimate the parameters of the model, the Shapiro-Wilk test was conducted on the RTA values and its residuals to confirm normality. Since p < 0.05 in both cases, they were both found to be non-normal, then the least absolute deviation (LAD) estimator was used for estimation. This gives rise to Yt = 29.0574 + 0.492151Xt-1 + 0.99994et-1 + εt as the best fitted model, which was found to be statistically significant at α=0.05. The estimated model was used to forecast RTA for 30months with 95percent confidence level and result showed that the forecast were good and there will continually be occurrence of RTA nearly every month and there will be higher RTA rates between November and January. The result of the Pearson correlation showed that fatal accident were 71percent more likely associated to death while serious accident were 61percent more likely associated to injury.

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The military aggression of the russian federation against Ukraine and the introduction of martial law in Ukraine caused serious problems with the collection, processing and analysis of the necessary statistical and administrative information. In particular, it was necessary to predict the number of first-graders and enrollment of pupils in general secondary schools at the beginning of the 2022/2023 school year and especially school leavers, who are expected to become potential entrants to higher education, pre-tertiary vocational and vocational education institutions. When developing a model for forecasting the number of first-graders, a functional dependence was determined that adequately describes the development trends of this indicator, and consisted in obtaining the minimum average absolute deviation of the forecast value from the actual. In the course of the study, we developed trend models for forecasting the number of first-grade students for each region and determined the mathematical characteristics of the forecast model. For a more detailed study, we consider factor analysis models in order to examine the relationship between the number of first-graders and the number of children born. Based on the regression analysis, the type of function was determined; regression coefficients and theoretical values of the resulting indicator were calculated; and the statistical significance of the equation and regression coefficients was tested. In this way, we received a target forecast of the number of students for the 2022/2023-2024/2025 school years. Given the large-scale temporary displacement of the population, in particular families with children to safer regions, we consider it expedient to calculate the forecast values of the number of first-grade students using trend models for Ukraine as a whole and by region, taking into account internally displaced persons. Factor models should be used only to develop a forecast for Ukraine as a whole, since forecasting from the number of births by region is not meaningful in today�s conditions and is possible only in the post-war period. The prospect of further research in this direction is the development of economic and mathematical models for forecasting the total number of school students, the number of pedagogical staff and teachers of certain subjects in general secondary schools.

Research on denoising method of chinese ancient character image based on chinese character writing standard model

Ancient documents are historical evidence of cultural inheritance, and the damage brought by natural and human factors to ancient documents is inevitable, resulting in the collected images of ancient Chinese characters containing a large amount of noise, which seriously affects the accuracy of subsequent image recognition and thus creates a great obstacle to the digitization of ancient documents. To address the complexity of ancient text structure, this paper proposes a Chinese ancient text image denoising method based on the Chinese character writing standard model. The method firstly adds four additional local branches based on the global branching, and uses the supplementary character detail information to weaken the phenomenon of strokes adhering to noise due to the lack of local details; secondly, it introduces the simulation noise of ancient documents to simulate the real ancient character image morphology, which can be used for the adversarial training of this method. In the training process, the minimum absolute value deviation, smoothing loss, structural consistency loss and the refined loss function formed by the adversarial loss are used to iteratively optimize the parameters. Finally, experiments prove that the model in this paper can increase the peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) of the image by at least 23.8% and 11.4%, and the user evaluation index (UV) has also reached more than 80%.

Distribution Grid Modeling Using Smart Meter Data

The knowledge of distribution grid models, including topologies and line impedances, is essential for grid monitoring, control and protection. However, such information is often unavailable, incomplete or outdated. The increasing deployment of smart meters (SMs) provides a unique opportunity to tackle this issue. This paper proposes a two-stage framework for distribution grid modeling using SM data. In the first stage, the network topology is identified by reconstructing a weighted Laplacian matrix of distribution networks. In the second stage, a least absolute deviations (LAD) regression model is developed for estimating line impedance of a single branch based on the nonlinear (inverse) power flow model, wherein a conductor library is leveraged to narrow down the solution space. The LAD regression model is originally a mixed-integer nonlinear program whose continuous relaxation is still non-convex. Thus, we specially address its convex relaxation and discuss the exactness. The modified regression model is then embedded within a bottom-up sweep algorithm to achieve the identification across the network in a branch-wise manner. Numerical results on the IEEE 13-bus, 37-bus and 69-bus test feeders validate the effectiveness of the proposed methods.

Deduction of the transformation regulation on voltage curve for lithium-ion batteries and its application in parameters estimation

States estimations play a vital role in the normal operation of the battery system. However, the existing state estimation methods are not fully applicable to the needs for simplicity, speed, and accuracy in cloud-based data analysis. To solve the above problems, we propose a parameter estimation method based on voltage curve transformation. In this paper, the charging voltage curve is studied for the state-of-charge (SOC) and state-of-health (SOH) estimation. By comparing the voltage curve with an open-circuit voltage (OCV) curve, it is proved that the parameters including initial SOC and capacity have a linear relationship with the curve shape. Furthermore, the dynamic time warping (DTW) algorithm is utilized to visualize the relationship. The data of cells with different state parameters are employed to verify the correction. For implementation, a curve fitting method based on the Least Absolute Deviations (LAD) is adopted to achieve the estimation of state parameters of the battery. Under the condition that SOC range is from 40% to 85%, the root-mean-square error (RMSE) of initial SOC is about 1.6% and the RMSE of SOH is about 2.1%.