Least-squares Estimation Research Articles

Trend analysis in the presence of short- and long-range correlations with application to regional warming.

Many real-world time series exhibit both significant short- and long-range temporal correlations. Such correlations enhance the errors of linear trend analysis. In this paper, we provide a general framework for trend analysis under the consideration of such correlations. We propose a parsimonious model containing both a single short-range autoregressive parameter and long-range fractional parameter. We derive analytical closed-form results for the error bars of the least-squares estimate of the trend for such time series, highlighting the different effects of short- and of long-range correlations. We employ an ensemble method for the automated extraction of scaling regions to estimate the fractional parameter of the data model together with its error bar, and the Grünwald-Letnikov derivative for the identification of the autoregressive parameter. We apply this framework to the study of warming trends on gridded temperature data in central Europe. We make use of the redundancy of the trend signal in adjacent grid points using methods of spatial averaging and the first principal component of empirical orthogonal function analysis. We find good agreement between the results of these two methods. We find a statistically significant decadal warming trend in central Europe over the past 70 years, which shows a particularly dramatic increase over the past 20 years.

Joint Channel Estimation and Data Detection for IRS-Assisted OFDM Systems

Intelligent reconfigurable surface (IRS) becomes a promising technology for improving spectrum efficiency and reducing the energy consumption in the next-generation networks. To reap the passive beamforming gain of IRS, accurate channel estimation is essentially required. However, the existing channel estimation methods for the IRS-assisted orthogonal frequency division multiplexing (OFDM) systems suffer from serious performance loss, due to using the least-squares (LS) estimator and ignoring the channel sparsity in the time domain. Another drawback of the existing methods is that the channel estimation and data detection are separated from each other so that any inaccurate channel estimation would cause an error accumulation problem for the data detection. To overcome these drawbacks, we propose a novel joint sparse channel estimation and data detection method for the IRS-assisted OFDM systems. The novelties of the proposed method are twofold: (i) present a new common sparse representation model for the joint channel estimation and data detection, which can utilize the common channel sparsity between the pilots and data streams to significantly improve the channel estimation performance and reduce the training overhead; and (ii) propose an efficient variational Bayesian inference (VBI) framework to simultaneously perform the Bayesian inference for the sparse channel recovery and data detection, where the coupling effect caused by the reflection pattern is trickly evaded by adopting an additional column-independent factorization. Besides exploiting the common sparsity for the channel estimation and data detection, the proposed method also avoids using the LS estimator, and thus its performance can be greatly enhanced. Simulation results verify the superiority of the proposed method.

Optimal Power Flow With State Estimation in the Loop for Distribution Networks

In this article, we propose a framework for running optimal control-estimation synthesis in distribution networks. Our approach combines a primal-dual gradient-based optimal power flow solver with a state estimation feedback loop based on a limited set of sensors for system monitoring, instead of assuming exact knowledge of all states. The estimation algorithm reduces uncertainty on unmeasured grid states based on certain online state measurements and noisy “pseudomeasurements.” We analyze the convergence of the proposed algorithm and quantify the statistical estimation errors based on a weighted least-squares estimator. The numerical results on a 4521-node network demonstrate that this approach can scale to extremely large networks and provide robustness to both large pseudomeasurement variability and inherent sensor measurement noise.

Least Square Estimation-Based Different Fast Fading Channel Models in MIMO-OFDM Systems

In cellular wireless communication systems, channel estimation (CE) plays a pivotal role as a crucial technique applied in orthogonal frequency division multiplexing (OFDM) modulation. CE utilizes a variety of methods, including decision-directed channel estimation, pilot-assisted channel estimation (PACE), and blind channel estimation. Among these options, PACE is widely favored for its remarkable stability and consistent superior performance. The idea of massive multiple-input multiple-output (MIMO) shows tremendous potential for the future of wireless communications. However, existing massive MIMO systems face challenges with their high computational complexity and intricate spatial structures, preventing efficient utilization of channel and sparsity features in these multiantenna systems. In communication channels, the signal received is often influenced by the characteristics of the channel and noise present at the receiver. To address this issue, an efficient dataset is utilized, employing the least square (LS) algorithm for minimization. OFDM is a commonly and widely used modulation method in communication systems utilized to specifically combat resonance fading in wireless channels. In wireless communication systems employing OFDM-MIMO, frequency selectivity and time-varying attributes due to multipath channels cause Intercarrier Interference (ICI) among symbols. Channel estimation is a vital aspect for mitigating the effects of fading channels. This investigation focuses on the application of a method examined in the study, which involves a block-type pilot symbol-assisted estimation technique for Rayleigh and Rician fading channel models. The research assesses the performance of the least square (LS) channel estimators in fast-fading channel models while employing various symbol mapping techniques focusing on bit error rate, throughput, and mean square error. The results indicate that the LS estimator exhibits excellent performance in Rayleigh and AWGN channels within the pedestrian A (PedA) model for both uplink and downlink scenarios. It outperforms the PedA model without channel estimation.

Positioning Control Strategy of Hydraulic Support Pushing System in Fully Mechanized Coal Face

At present, the hydraulic support pushing system in coal mines usually uses an electrohydraulic directional valve as the control component. However, the existing control methods based on high-speed on–off valve, servo, and proportional control methods are not suitable for solving such problems because of the nonideal characteristics of the electrohydraulic directional valve, such as discrete input values, low switching frequency, and time delay. This paper proposes a positioning control scheme based on online predictive feedback for the control of hydraulic cylinders by electrohydraulic directional valves. In this scheme, the recursive least-squares estimation algorithm with genetic factors is used to identify the required prediction model in real time, and an improved radial basis function network based on generalized growth and shear is used to realize the online fitting of the target trajectory function. The online learning algorithm provides accurate prediction information for the switching control method, and finally, the hydraulic cylinder can be positioned near the target position using the optimal control method. By using the above methods, a well-designed model can be accurately identified, fundamentally solving the problem of control difficulties caused by the nonideal characteristics of the electrohydraulic directional valve. Finally, the effectiveness of the control scheme is verified through simulation analysis and physical experiment research, which proves that the control strategy can realize accurate and fast positioning control for the hydraulic support pushing system of a fully mechanized mining face.

Adaptive threshold for discrete fourier transform‐based channel estimation in generalized frequency division multiplexing system

AbstractEven though generalized frequency division multiplexing is an alternative waveform method expected to replace the orthogonal frequency division multiplexing in the future, its implementation must alleviate channel effects. Least‐squares (LS), a low‐complexity channel estimation technique, could be improved by using the discrete Fourier transform (DFT) without increasing complexity. Unlike the usage of the LS method, the DFT‐based method requires the receiver to know the channel impulse response (CIR) length, which is unknown. This study introduces a simple, yet effective, CIR length estimator by utilizing LS estimation. As the cyclic prefix (CP) length is commonly set to be longer than the CIR length, it is possible to search through the first samples if CP is larger than a threshold set using the remaining samples. An adaptive scale is also designed to lower the error probability of the estimation, and a simple signal‐to‐interference‐noise ratio estimation is also proposed by utilizing a sparse preamble to support the use of the scale. A software simulation is used to show the ability of the proposed system to estimate the CIR length. Due to shorter CIR length of rural area, the performance is slightly poorer compared to urban environment. Nevertheless, satisfactory performance is shown for both environments.

Extended Kumaraswamy Exponential Distribution with Application to COVID-19 Data set

There are many probability models describing the time related events data. In this study, the exponential distribution is modified by adding one more parameter to get more flexible probability model called Extended Kumaraswamy Exponential (EKwE) distribution using the New Kw-G family (NKwG) of distributions. We have studied some of the statistical characteristics of the model, such as its reliability function, hazard rate function, and quantile function. For testing the applicability of the model, a real data set based on COVID-19 data is taken. The Cramer-von Mises (CVM) approach, Least Square Estimation (LSE), and Maximum Likelihood Estimation (MLE) are used to estimate the model’s parameters. Validity of the model is checked by using P-P plot and Q-Q plot. Akaike Information Criterion (AIC), Corrected Akaike Information Criterion (CAIC), Bayesian Information Criterion (BIC) and Hannan-Quinn Information Criterion (HQIC) are also used for model comparison. Goodness of fit of the proposed model is tested using Kolmogrov-Smirnov (KS), Cramer-Von Mises (CVM) and Anderson-Darling (An) test statistics along with respective p-values. All the analysis of the study is performed by using R programming.

Correlation analysis of quantitative MRI measurements of thigh muscles with histopathology in patients with idiopathic inflammatory myopathy

ObjectivesTo validate the correlation between histopathological findings and quantitative magnetic resonance imaging (qMRI) fat fraction (FF) and water T2 mapping in patients with idiopathic inflammatory myopathy (IIM).MethodsThe study included 13 patients with histopathologically confirmed IIM who underwent dedicated thigh qMRI scanning within 1 month before open muscle biopsy. For the biopsied muscles, FF derived from the iterative decomposition of water and fat with echo asymmetry and least-squares estimation quantitation (IDEAL-IQ) and T2 time from T2 mapping with chemical shift selective fat saturation were measured using a machine learning software. Individual histochemical and immunohistochemical slides were evaluated using a 5-point Likert score. Inter-reader agreement and the correlation between qMRI markers and histopathological scores were analyzed.ResultsReaders showed good to perfect agreement in qMRI measurements and most histopathological scores. FF of the biopsied muscles was positively correlated with the amount of fat in histopathological slides (p = 0.031). Prolonged T2 time was associated with the degree of variation in myofiber size, inflammatory cell infiltration, and amount of connective tissues (p ≤ 0.008 for all).ConclusionsUsing the machine learning-based muscle segmentation method, a positive correlation was confirmed between qMRI biomarkers and histopathological findings of patients with IIM. This finding provides a basis for using qMRI as a non-invasive tool in the diagnostic workflow of IIM.Relevance statementBy using ML-based muscle segmentation, a correlation between qMRI biomarkers and histopathology was found in patients with IIM: qMRI is a potential non-invasive tool in this clinical setting.Key points• Quantitative magnetic resonance imaging measurements using machine learning-based muscle segmentation have good consistency and reproductivity.• Fat fraction of idiopathic inflammatory myopathy (IIM) correlated with the amount of fat at histopathology.• Prolonged T2 time was associated with muscle inflammation in IIM.Graphical

Association between IDEAL-IQ MRI fat fraction quantification and pelvic bone marrow reserve function in concurrent chemoradiotherapy for cervical cancer

ObjectiveTo analyze the association between iterative decomposition of water and fat with echo asymmetry and least-squares estimation quantification sequence (IDEAL-IQ) magnetic resonance imaging (MRI) of bone marrow fat fraction and bone marrow reserve function during concurrent chemoradiotherapy for cervical cancer. MethodsThe study retrospectively analyzed twenty-six patients with stage IB1 to IVA cervical cancer treated between February 2020 and November 2020. All patients received concurrent chemoradiotherapy that included platinum alone or combined paclitaxel and platinum. Pelvic IDEAL-IQ MRI (plain and enhanced) was performed before and after treatment. Regions of interest, including the fifth lumbar vertebra, sacrum, ilium, ischium, and femoral neck, were manually delineated, and the bone marrow fat fraction was measured. Peripheral blood cell counts were recorded during treatment, and the relationship between the fat fraction values and changes in the blood cell counts was explored. ResultsIDEAL-IQ MRI bone marrow fat fraction was associated with platelet nadir and platelet decline during treatment. The average pelvic bone marrow fat fraction before chemoradiotherapy was moderately negatively correlated with platelet count nadir during concurrent chemoradiotherapy (r ​= ​−0.450, P ​= ​0.021). The change in average pelvic bone marrow fat fraction through chemoradiotherapy was moderately positively correlated with the degree of thrombocytopenia (r ​= ​0.399, P ​= ​0.044). ConclusionBone marrow fat content quantified by IDEAL-IQ was associated with platelet count nadir and the degree of thrombocytopenia in patients with cervical cancer undergoing concurrent chemoradiotherapy.

Estimation of the Deformation Gradient Tensor by Particle Tracking Near a Free Boundary with Quantified Error

BackgroundObtaining accurate displacement measurements for large material deformation and/or rotation presents a distinct challenge to digital image correlation (DIC) due to cumulative and decorrelation errors, particularly near material boundaries.ObjectiveWe aim to accurately measure the deformation gradient tensor near boundary discontinuities in situations of large deformation and large deformation gradients.MethodsTo achieve this goal, the locations of randomly distributed particles are tracked using an open-source particle-tracking software, Trackpy. A least-squares estimate of the deformation gradient tensor field uses nearest-neighbor material vectors and a first-order Finite Difference (FD) approximation, circumventing common errors in other methods. The error caused by FD approximation and that incurred by measurement are derived and tested with exhaustive numerical simulations. Furthermore, a uniaxial tensile test and mode-I fracture experiment are conducted with particle-embedded hydrogels to validate the method.ResultsNumerical results corroborate a theoretical expression of measurement error. They show that the FD error increases while the measurement error decreases for a growing estimating radius. Moreover, measurement error is linearly correlated to displacement noise. A benchmark uniaxial tensile test validates the accuracy of the proposed estimator, and the near-crack-tip measurements in a tensile fracture experiment demonstrate the estimator’s capabilities near a free surface, when a material undergoes large deformation and rotation. The results of the displacement and strain data are benchmarked against kinematic data obtained using an open-source DIC software, Ncorr. Computation time for both methods is compared.ConclusionsA deformation gradient tensor estimator is developed based on a particle tracking technique and a least squares routine. Theoretical error bounds on the estimator are verified by numerical simulations, and the method’s capability is confirmed by physical experiments in evaluating large deformation and rotation near a free boundary. The proposed estimator is expected to open a door towards future material tests and experimental mechanics studies, especially in large deformation and large rotation scenarios.

Studying the factors influencing user satisfaction and reuse intention towards monorail service using a PLS-SEM approach: A case study in Kuala Lumpur, Malaysia

This work aims to examine the factors that influence users’ satisfaction and reuse intention in respect of the monorail system in Kuala Lumpur, Malaysia. The hypotheses were tested with 417 survey data collected among monorail users. The newly developed model of users’ satisfaction and reuse intention was evaluated through structural equation modelling, the basis of which was a parameter estimation of partial least squares (PLS-SEM). Findings reported that the proposed model led to 70.4% and 59.5% of the variances explained by user satisfaction and reuse intention towards the service provided. The findings demonstrated convincingly that overall satisfaction and reuse intention are affected by two key factors from the users’ perspectives: perceived quality and perceived value. The results are useful for service providers and related bodies in their effort to enhance user satisfaction as well as increase the monorail service ridership.

Modelling of Passenger Satisfaction and Reuse Intention with Monorail Services in Kuala Lumpur, Malaysia: A Hybrid SEM-ANN Approach

This study employs the fundamental concept of the American Customer Satisfaction Index (ACSI) model to explore the factors influencing passengers’ satisfaction with monorail service in Kuala Lumpur, Malaysia and their reuse intention. The study tests the hypotheses on 417 monorail passengers using a hybrid structural equation modelling based on parameter estimation of partial least squares (PLS-SEM) and an artificial neural network (ANN) method to estimate the proposed model. The results showed that the proposed model explains 70.4% and 59.5% of the variance in passenger satisfaction with the monorail service and reuse intention. The PLS-SEM results for Stage 1 showed that perceived quality and perceived value have a statistically significant influence on passenger satisfaction. Furthermore, all critical factors in the output from Stage 1 were used as the input in the ANN model to overcome the simplistic nature of the SEM model. The results for the ANN model (Stage 2) showed that perceived quality is the most crucial predictor of passenger satisfaction with the monorail service, followed by perceived quality. The outcomes of this study can help service providers, policymakers, and planners develop effective strategies for enhancing user satisfaction and improving monorail ridership.

Weighted least squares: A robust method of estimation for sinusoidal model

In this article, we consider the weighted least squares estimators (WLSEs) of the unknown parameters of a multiple sinusoidal model. Although, the least squares estimators (LSEs) are known to be the most efficient estimators in case of a multiple sinusoidal model, they are quite susceptible in presence of outliers. In presence of outliers, robust estimators like the least absolute deviation estimators (LADEs) or Huber’s M-estimators (HMEs) may be used. But implementation of the LADEs and HMEs are quite challenging in case of a sinusoidal model, the problem becomes more severe in case of multiple sinusoidal model. Moreover, to derive the theoretical properties of the robust estimators, one needs stronger assumptions on the error random variables than what are needed for the LSEs. The proposed WLSEs are used as robust estimators and they have the following two major advantages. First, they can be implemented very easily in case of multiple sinusoidal model, and their properties can be obtained under the same set of error assumptions as the LSEs. Extensive simulation results suggest that in presence of outliers, the WLSEs behave better than the LSEs, and at par with the LADEs and HEMs. It is observed that the performance of the WLSEs depend on the weight function, and we discuss how to choose a proper weight function for a given data set. We have analyzed one synthetic data set to show how the proposed methods can be implemented in practice.

Inference for the VEC(1) model with a heavy-tailed linear process errors*

This article studies the first-order vector error correction (VEC(1)) model when its noise is a linear process of independent and identically distributed (i.i.d.) heavy-tailed random vectors with a tail index . We show that the rate of convergence of the least squares estimator (LSE) related to the long-run parameters is n (sample size) and its limiting distribution is a stochastic integral in terms of two stable random processes, while the LSE related to the short-term parameters is not consistent. We further propose an automated approach via adaptive shrinkage techniques to determine the cointegrating rank in the VEC(1) model. It is demonstrated that the cointegration rank r 0 can be consistently selected despite the fact that the LSE related to the short-term parameters is not consistently estimable when the tail index . Simulation studies are carried out to evaluate the performance of the proposed procedure in finite samples. Last, we use our techniques to explore the long-run and short-run behavior of the monthly prices of wheat, corn, and wheat flour in the United States.

Assessment of Osteoporosis at the Lumbar Spine Using Ultrashort Echo Time Magnetization Transfer (UTE-MT) MRI.

Bone collagen-matrix contributes to the mechanical properties of bone by imparting tensile strength and elasticity, which can be indirectly quantified by ultrashort echo time magnetization transfer ratio (UTE-MTR) to assess osteoporosis. To evaluate osteoporosis at the human lumbar spine using UTE-MTR. Prospective. One hundred forty-eight-volunteers (age-range, 50-85; females, N = 90), including 81-normal bone density, 35-osteopenic, and 32-osteoporotic subjects. Ten additional healthy volunteers were recruited to study the intrasession reproducibility of the UTE-MT. 3T/UTE-MT, short repetition-time adiabatic inversion recovery prepared UTE (STAIR-UTE), and iterative decomposition of water-and-fat with echo-asymmetry and least-squares estimation (IDEAL-IQ). Fracture risk was calculated using Fracture-Risk-Assessment-Tool (FRAX). Region-of-interests (ROIs) were delineated on the trabecular area in the maps of bone-mineral-density, UTE-MTR, collagen-bound water proton-fraction (CBWPF), and bone-marrow fat fraction (BMFF). Linear-regression and Bland-Altman analysis were performed to assess the reproducibility of UTE-MTR measurements in the different scans. UTE-MTR and BMFF were correlated with bone-mineral-density using Pearson's regression and with FRAX scores using nonlinear regression. The abilities of UTE-MTR, CBWPF, and BMFF to discriminate between the three patient subgroups were evaluated using receiver-operator-characteristic (ROC) analysis and area-under-the-curve (AUC). Decision-curve-analysis (DCA) and clinical-impact curves were used to evaluate the value of UTE-MTR in clinical diagnosis. The DeLong test was used to compare the ROC curves. P-value <0.05 was considered statistically significant. Excellent reproducibility was obtained for the UTE-MT measurements. UTE-MTR strongly correlated with bone-mineral-density (r = 0.76) and FRAX scores (r = -0.77). UTE-MTR exhibited higher AUCs (≥0.723) than BMFF, indicating its superior ability to distinguish between the three patient subgroups. The DCA and clinical-impact curves confirmed the diagnostic value of UTE-MTR. UTE-MTR and CBWPF showed similar performance in correlation with bone-mineral-density and cohort classification. UTE-MTR strongly correlates with bone-mineral-density and FRAX and shows great potential in distinguishing between normal, osteopenic, and osteoporotic subjects. 1 TECHNICAL EFFICACY: Stage 2.

Slice weighted average regression

AbstractIt has previously been shown that ordinary least squares can be used to estimate the coefficients of the single-index model under only mild conditions. However, the estimator is non-robust leading to poor estimates for some models. In this paper we propose a new sliced least-squares estimator that utilizes ideas from Sliced Inverse Regression. Slices with problematic observations that contribute to high variability in the estimator can easily be down-weighted to robustify the procedure. The estimator is simple to implement and can result in vast improvements for some models when compared to the usual least-squares approach. While the estimator was initially conceived with the single-index model in mind, we also show that multiple directions can be obtained, therefore providing another notable advantage of using slicing with least squares. Several simulation studies and a real data example are included, as well as some comparisons with some other recent methods.

Robust estimators of two dimensional sinusoidal model parameters

In this paper we consider the two dimensional (2-D) sinusoidal model. This particular model has several applications in the statistical signal processing and in texture analysis. Extensive work has been done in developing several efficient procedures and establishing their properties. The least squares estimators (LSEs) are known to be the most efficient estimators in presence of additive noise. But it is observed that the LSEs are quite sensitive in presence of outliers. In this paper we propose to use the weighted least squares estimators (WLSEs) of the unknown parameters in presence of additive white noise. It is observed that in presence of outliers, the WLSEs are more robust than the least squares estimators (LSEs) and they behave very similarly to some of the other well known robust estimators, for example the least absolute deviation estimators (LADEs). It is observed that developing the properties of the LADEs is not immediate. We derive the consistency and asymptotic normality properties of the WLSEs. Extensive simulations have been performed to show the effectiveness of the proposed method. One synthetic data set has been analyzed to illustrate how the proposed method can be used in practice.

Remaining Useful Life Prediction of PV Systems Under Dynamic Environmental Conditions

Solar power is one of the least carbon-intensive approaches for electricity generation, and so photovoltaic (PV) systems have great potential as a low-carbon technology during their long lifecycle. Consequently, remaining useful life (RUL) prediction is critical for the prognostics and health management of PV systems, potentially preventing unexpected failure and maintenance due to PV degradation. One of the major root causes of PV degradation is the dynamic environmental conditions associated with PV outdoor operation. However, RUL prediction under such dynamic environmental conditions remains challenging. This article presents a semiparametric prognostic framework for PV systems under dynamic environmental conditions. The quantitative relationship between PV degradation and environmental conditions is established to integrate environmental condition information into RUL prediction, combining the cumulative damage model with multivariate Bernstein bases. The block bootstrap method is used to estimate future environmental conditions as inputs for RUL prediction. The least-squares estimators of the model parameters can be obtained through the block coordinate descent method. Finally, applications to field data of Australian PV systems are presented to demonstrate the effectiveness of the proposed method. The proposed framework is applicable to most PV technologies.

Lane Change–Intention Inference and Trajectory Prediction of Surrounding Vehicles on Highways

The behavior prediction of the surrounding vehicles is crucial when planning a minimal-risk path when realizing a collision-avoidance system. Herein, we propose a multiple model–based adaptive estimator (MMAE) that infers the lane-change intention of the surrounding vehicles and then predicts their trajectories. Specifically, first, a path is generated in the form of a cubic spline curve using the Frenet coordinate system, which is robust to changes in road curvatures. Linearized recursive least-squares estimation (LRLSE) method is used to adaptively predict a future trajectory based on the past trajectory of the target vehicle. Preview time is defined as a time-varying parameter that determines the final point of the path, and LRLSE updates it in real time. The MMAE applies LRLSEs to multiple paths and obtains the mode probability for each path, then the lane-change intention is inferred using the mode probability and preview time. The predicted future trajectory is the cubic spline curve determined based on the preview time. Further, we verify the performance of our approach using highD, a naturalistic dataset of vehicle trajectories, and compare it with those of existing methods. The proposed method does not require a large amount of data for training and has a low computational burden and high real-time performance.

Coefficient estimation of simultaneous equations in the case of stochasticity of exogenous variables

The paper deals with the question of obtaining such an estimate of the parameters of the model of simultaneous equations, which would have better statistical properties in comparison with the estimates of both the usual method of least squares and two-, three-step methods of least squares, as well as the method of fixed point and other methods of evaluating the coefficients of the equations considered in the system simultaneously. The main drawback of methods based on minimization of the sum of squares of deviations of real observations from some theoretical dependence is that the sum of squares of errors that correlate with the values of variables included in the expression for these errors is minimized. A violation of the basic assumption of least-squares methods about the independence of predetermined variables and errors leads to the fact that least-squares estimation methods in this case lose their best properties: unbiasedness, efficiency, and consistency. The paper proves the theorem about the efficiency of estimates obtained using two-step least squares methods and that of estimates obtained using the method of factorization of simultaneous equations.