Least-squares Estimation Method Research Articles

Reliability evaluation for Weibull distribution with heavily Type II censored data

AbstractThe lifetime data collected from the field are usually heavily censored, in which case, getting an accurate reliability evaluation based on heavily censored data is challenging. For heavily Type‐II censored data, the parameters estimation bias of traditional methods (i.e., maximum likelihood estimation (MLE) and least squares estimation (LSE)) are still large, and Bayesian methods are hard to specify the priors in practice. Therefore, considering the existing range of shape parameter for Weibull distribution, this study proposes two novel parameter estimation methods, the three‐step MLE method and the hybrid estimation method. For the three‐step MLE method, the initial estimates of shape and scale parameters are first respectively derived using MLE, then are updated by the single parameter MLE method with the range constraint of shape parameter. For the hybrid estimation method, the shape parameter is estimated by the LSE method with the existing range constraint of shape parameter, then the scale parameter estimate can be obtained by MLE. On this basis, two numerical examples are performed to demonstrate the consistency and effectiveness of the proposed methods. Finally, a case study on turbine engines is given to verify the effectiveness and applicability of the proposed methods.

Validating Tools to Measure Life Skills Among Adolescents in India

Life skill education is critical for developing various competencies among the adolescent population, especially in India, given the recent shift in policy focus. This article examines the reliability, factor structure, and the validity of scales measuring gender attitudes, perceived self-efficacy, resilience, and problem-solving developed to assess the effectiveness of a life skill program among Indian adolescents. Baseline data, before a life skill intervention program by Magic Bus India Foundation, were collected from over 16000 Indian adolescents between 11 and 15 years on different measures. Results from principal component analyses with promax rotation indicated a one-factor solution for all the scales. Further, confirmatory factor analyses indicated an excellent model fit using the diagonally weighted least squares method of estimation for the above-mentioned scales. The models for each scale were gender invariant, indicating that gender attitudes, perceived self-efficacy, resilience, and problem solving were assessed similarly between boys and girls. Additionally, correlation analysis indicated a positive relationship between gender attitudes and self-efficacy, a negative relation between gender attitudes and resilience, and a negative association between self-efficacy and resilience. Implications are discussed.

Full-LSPIA: A Least-Squares Progressive-Iterative Approximation Method with Optimization of Weights and Knots for NURBS Curves and Surfaces

The Least-Squares Progressive-Iterative Approximation (LSPIA) method offers a powerful and intuitive approach for data fitting. Non-Uniform Rational B-splines (NURBS) are a popular choice for approximation functions in data fitting, due to their robust capabilities in shape representation. However, a restriction of the traditional LSPIA application to NURBS is that it only iteratively adjusts control points to approximate the provided data, with weights and knots remaining static. To enhance fitting precision and overcome this constraint, we present Full-LSPIA, an innovative LSPIA method that jointly optimizes weights and knots alongside control points adjustments for superior NURBS curves and surfaces creation. We achieve this by constructing an objective function that incorporates control points, weights, and knots as variables, and solving the resultant optimization problem. Specifically, control points are adjusted using LSPIA, while weights and knots are optimized through the LBFGS method based on the analytical gradients of the objective function with respect to weights and knots. Additionally, we present a knot removal strategy known as Decremental Full-LSPIA. This strategy reduces the number of knots within a specified error tolerance, and determines optimal knot locations. The proposed Full-LSPIA and Decremental Full-LSPIA maximize the strengths of LSPIA, with numerical examples further highlighting the superior performance and effectiveness of these methods. Compared to the classical LSPIA, Full-LSPIA offers greater fitting accuracy for NURBS curves and surfaces while maintaining the same number of control points, and automatically determines suitable weights and knots. Moreover, Decremental Full-LSPIA yields fitting results with fewer knots while maintaining the same error tolerance.

Testing of Thermal Resistance and Heat Loss Simulator Design of the Fluid Flow in insulated pipe using Adaptive Neuro Fuzzy Inference System (ANFIS) and Least-squares Estimation (LSE) Method

Testing of Thermal Resistance and Heat Loss Simulator Design of the Fluid Flow in insulated pipe using Adaptive Neuro Fuzzy Inference System (ANFIS) and Least-squares Estimation (LSE) Method

Estimating Optimal Cost, Insulation Layer Thickness, and Structural Layer Thickness of Different Composite Insulation External Walls Using Computational Methods

All the modern gadgets and space conditioning in buildings consume lots of energy. Energy consumption can be optimized using Composite Insulation External Walls (CIEW) built from mortar plaster and structural and insulation layers. This study aimed to improve the overall performance of CIEW by optimizing the structural and insulation layer thickness. The objective was to minimize the Life Cycle Cost (LCC) and maximize the Life Cycle Savings (LCS) of CIEW. The nonlinear Least Squares Estimation (LSE) optimization technique for optimizing LCC and LCS of CIEW was used in the study. The study considered three insulation materials—Extruded Polystyrene (XPS), Rock Wool (RW), and Glass Wool (GW)—across three heat sources, including Circulating Fluidized Bed (CFB), Grate-Fired Boiler (GFB), and Air-Source Heat Pump (ASHP). The Life Cycle Cost Analysis (LCCA) methodology suggested by Huang using a traditional optimization technique was used as a basis for mathematical formulations and result comparison. The payback period of CIEW with optimal structural and insulation layer thickness was computed. The findings revealed that applying the LSE method enabled greater economic efficiency than the LCCA method, with an up to 9.12% increase in LCS value and an up to 7.41% decrease in LCC value. The research also revealed significant correlations between insulation and structural layer thicknesses and economic parameters.

Economic Complexity and Renewable Energy Effects on Carbon Dioxide Emissions: a Panel Data Analysis of Middle East and North Africa Countries

AbstractWith the rising economic complexity of the world economy, applied research has been focusing on the economic complexity-environmental quality nexus. Many of the Middle East and North Africa (MENA) countries and Turkey show relatively low economic complexity with undiversified product spaces. The present study is thereby motivated to investigate the economic complexity-environmental quality relation for the MENA countries and Turkey. Using panel data for eighteen MENA countries and Turkey over the period 1990–2020, the fully modified ordinary least squares method of estimation is employed in two separate models, and Granger causality tests are performed. Each model includes the relation of economic complexity to carbon dioxide (CO2) emissions, one form of energy (renewable or non-renewable), population density and variables to validate the environmental Kuznets curve (EKC) hypothesis. In model (1), a negative and statistically significant renewable energy consumption has a mitigating effect on CO2 emissions, though economic complexity and its interaction with renewable energy consumption are not statistically significant. In model (2), a positive and statistically significant non-renewable energy indicates that increased fossil fuel reliance increases CO2 emissions (deteriorating environmental quality), while a negative and statistically significant economic complexity and population density reduce CO2 emissions (improving environmental quality), respectively. The EKC hypothesis is validated for the MENA countries and Turkey in both models (1) and (2), and Granger causality test results are given. Among the key policy implications are that the MENA countries and Turkey must recognize that increasing GDP and industrialization must be coupled with moving from less- to more-knowledge-based structures.

Monitoring of recently sea level changes on the coast of New Zealand using XTRACK coastal altimetry and tide gauge data

The rise in sea level along the coasts of New Zealand has accelerated in recent decades due to the impact of climate change. Determining the effects of these changes on the coastal regions is critical for their sustainability. In order to gain insight into these impacts, the present study aimed to analyze sea level changes using satellite altimetry and tide gauge data from 11 tide gauge stations along the New Zealand coast between 1993 and 2022, as well as XTRACK data processed with the coastal altimetry approach to minimize the effects of classical altimetry near coasts. The least-squares parameter estimation method was used to analyze the data and determine annual and semi-annual seasonal effects. The results showed that a significant increase have been observed in sea level of 3.8+0.5 mm/yr along the coast of New Zealand from 1993 to 2022 using coastal altimetry data. The results of this study demonstrate the importance of closely monitoring the impacts of sea level rise on the coastal regions of New Zealand to ensure their long-term sustainability. The results also highlight the utility of using multiple data sources and methods to provide a comprehensive understanding of these changes.

Tidal harmonics retrieval using GNSS-R dual-frequency complex observations

Tidal analysis and methods for estimation and prediction of ocean tidal constitutes are essential in a large area of scientific disciplines, for example, navigation, onshore and offshore engineering, and production of green energy. Ground-based Global Navigation Satellite System-Reflectometry (GNSS-R) has been proposed as an alternative method for measuring sea surface height. We use 6 years of GNSS-R observations at In-phase and Quadrature levels from July 2015 to May 2021 obtained from a dedicated receiver and sea-looking left hand circular polarization antenna for estimating sea level (SL). In the first step, the multivariate least-square harmonic estimation (LS-HE) method is applied for SL estimation. Then, final SL time series are generated by combining estimated SL from all satellites at L1 and L2 frequencies in the averaging step. The 6-year root-mean-square error between GNSS-R L12 sea surface heights and a collocated tide gauge (TG) is 5.8 cm with a correlation of 0.948 for a high temporal resolution of 5 min with 15 min averaging window. Afterward, using the univariate LS-HE, we detect tidal harmonics with periods between 30 min to 1 year. The detection results highlight a good match between GNSS-R and TG. Higher harmonics, i.e., the periods shorter than 3 h, show stronger signatures in GNSS-R data. Finally, we estimate the amplitude and phase of standard tidal harmonics from the two datasets. The results show an overall good agreement between the datasets with a few exceptions.

An atomistic-continuum concurrent statistical coupling technique for amorphous materials using anchor points

A generalized framework for anchor point based concurrent coupling of finite element method (FEM) and molecular dynamics (MD) domains, incorporating previous related methods, is presented. The framework is robust and is agnostic of material crystallinity and atomistic description. The method follows an iterative approach to minimize the total energy of the coupled FEM-MD system, while maintaining displacement constraints between the domains. Two distinct forms of the coupling method are discussed in detail, differing in the nature of the constraint, both of which are able to make use of specialized MD solvers such as LAMMPS with little or no modification. Both methods make use of springs that join groups of atoms in the MD to the FEM domain. Method 1, termed ‘Direct Coupling’, couples MD anchor points directly to the FEM domain in a force-based manner and has the added advantage of being able to couple to specialized FEM solvers such as ABAQUS. Method 2 couples the MD to the FEM domain in a more ‘soft’ manner using the method of Lagrange multipliers and least squares approximation. The relative performance of these two methods are tested against each other in a uniaxial tension test using a graphene monolayer at 300 K temperature and a block of thermosetting polymer EPON862 at low temperature, showing comparable results. Convergence behaviour of the two coupling methods are studied and presented. The methods are then applied to the fracture of a centre-cracked graphene monolayer and compared with results from an identical pure MD simulation. The results corroborate the effectiveness of the developed method and potential use as a plug-and-play tool to couple pre-existing specialized FEM and MD solvers. Future work will focus on applying these methods to simulate elevated-temperature amorphous polymer models and their brittle fracture.

Mapping site index in coniferous forests using bi-temporal airborne laser scanning data and field data from the Swedish national forest inventory

Recent advancements in remote sensing of forests have demonstrated the capabilities of three-dimensional data acquired by airborne laser scanning (ALS) and, consequently, have become an integral part of enhanced forest inventories in Northern Europe. In Sweden, the first national laser scanning revolutionised forest management planning through low-cost production of large-scale and spatially explicit maps of forest attributes such as basal area, volume, and biomass, compared to the earlier practice based on field survey data. A second scanning at the national level was launched in 2019, and it provides conditions for the estimation of height growth and site index. Accurate and up-to-date information about site productivity is relevant for planning silvicultural treatments and for the prognosis of forest status and development over time. In this study, we explored the potential of bi-temporal ALS data and other auxiliary information to predict and map site productivity by site index according to site properties (SIS) of Norway spruce (Picea abies (L.) Karst) and Scots pine (Pinus sylvestris L.) in even-aged stands in Sweden. We linked ground survey data of SIS from more than 11,500 plots of the Swedish National Forest Inventory (NFI) to bi-temporal ALS data to predict and map site index using an area-based method and two regression modelling strategies: (1) a multiple linear regression (MLR) model with an ordinary least-squares parameter estimation method, and (2) a non-parametric random forests (RF) model optimised for hyper-parameter tuning. For model development, permanent plots were used, whereas the validation was done on the temporary plots of the Swedish NFI and an independent stand-level dataset. Species-specific models were developed, and the root mean square error (RMSE) metric was used to quantify the residual variability around model predictions. For both species, the MLR model gave precise and accurate estimates of SIS. The RMSE for SIS predictions was in the range of 1.96 – 2.11 m, and the relative RMSE was less than 10 % (7.68 – 9.49 %) of the reference mean value. Final predictors of site index include metrics of 90th percentile height and annual increment in the 95th percentile height, altitude, distance to coast, and soil moisture. Country-wide maps of SIS and the corresponding pixel-level prediction errors at a spatial resolution of 12.5 m grid cells were produced for the two species. Independent validations show the site index maps are suitable for use in operational forest management planning in Sweden.

The Sharing Economy: Personal Norm and Awareness to Participate in Collaborative Consumption

The emergence of sharing economy give rise to the popularity of collaborative consumption, which is known as events in which people consume items or services in joint activities with others. It being said that personal norms act as a major component in examining consumer intentions. The personal norms are based on individual values and motivation to protect them with appropriate behaviour. On the other hand, awareness of collaborative consumption found to have an impact on personal norm, thus influence the collaborative consumption. This study conducted a self-administrated survey to collect data from respondents in Klang Valley through purposive and convenience sampling methods. A total of 825 respondents were collected through the internet. Analysis method of Structural equation modelling-partial least squares estimation was applied to analyse the data in the study using SmartPLS version 3.3.9 software. The analysis of SEM-PLS comprises the measurement model on convergent validity analysis including factor loadings, average variance extracted (AVE), and composite reliability (CR). The findings revealed that awareness and responsibility of collaborative consumption have significant effect on personal norm. This indicates that consumers’ cognitive appraisal of potential consequences and accountability has significant influence on their pro-environmental behaviour. Furthermore, the findings showed a positive significant of personal norm and awareness of CC on collaborative consumption participation, indicating that collaborative consumption participation intention is due to a perceived obligation towards the societal and ecological surroundings.

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.

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.

HALF CAUCHY GENERALIZED RAYLEIGH DISTRIBUTION: THEORY AND APPLICATION

We develop a new three parameter distribution using the half-Cauchy family of distributions, called the half-Cauchy generalized Rayleigh distribution. Some statistical properties and characteristics of the proposed distribution are provided and obtained, including the explicit expressions for the survival function, median, hazard function, mode, moments, mean deviation, order statistics, cumulative hazard function, quantiles, and the measures of dispersion based on quartiles and octiles. For the parameter estimation of the proposed model, three widely used estimation techniques namely, maximum likelihood estimators (MLE), Cramer-Von-Mises (CVM), and least-square estimation (LSE) methods are applied. Two real datasets are used for the illustration, and the goodness-of-fit test is run. It is discovered that the proposed model fits the real data very well and is more flexible than some well-known models under consideration.

Stochastic Modeling of Smartphones GNSS Observations Using LS-VCE and Application to Samsung S20

In recent years, numerous smartphones have been equipped with global navigation satellite system (GNSS) technology, enabling individuals to utilize their own devices for positioning and navigation purposes. In 2016, with the launch of a mobile app by Google, namely GnssLogger, smartphone users with Android version 7 or higher were able to record raw GNSS measurements (i.e., pseudorange, carrier phase, Doppler, and carrier-to-noise density ratio (C/N0)). Since then, enhancing the accuracy and efficiency of smartphone positioning has become an interesting area of research. Precise point positioning (PPP) is a powerful method providing precise real-time positioning of a single receiver, and it can be applied to smartphone observations as well. Achieving high-precision PPP requires selecting appropriate functional and stochastic models. In this study, we investigate the development of more reliable stochastic models for smartphone GNSS observations. The least-square variance component estimation (LS-VCE) method is applied to double-difference (DD) pseudorange and carrier phase observations from two Samsung S20s to obtain appropriate variances for GPS and GLONASS. According to the results, there is no significant correlation between the pseudorange and carrier phase observations of GPS and GLONASS on the L1 frequency. Furthermore, the quality of GLONASS carrier phase observations is comparable to that of GPS. The model's performance is then assessed with respect to single-frequency precise point positioning (SF-PPP) using a dataset collected in kinematic mode from a Samsung S20 smartphone. A significant improvement of 25.1% and 32.7% on the root-mean-square (RMS) of horizontal positioning and the 50th percentile error, respectively, was achieved when employing the obtained stochastic model.

Review of Discrete Fourier Transform During Dynamic Phasor Estimation and the Design of Synchrophasor Units

In a large and complex interconnected power system, the measurement of synchronized bus voltage and line current plays a vital role in the monitoring and precise control of various sophisticated electrical equipment for secure and reliable operation. Phasor measurement units (PMUs) are incorporated into a wide area of the power system to extract the different signals of synchronized phasors. In this paper, the capacity of the PMU phasor estimation algorithm is explored based on discrete Fourier transform (DFT) under different sampling frequency rates during various dynamic scenarios in accordance with the IEEE C37.118.1a-2014 standard. Furthermore, the performance of the DFT algorithm varies according to the phase angle and dynamic parameters such as frequency, frequency ramp rates, modulation frequency, harmonic levels, step change, decaying dc, and noise levels. The simulation results reveal that accuracy of the phasor estimation algorithm based on DFT can be achieved at high sampling frequency rates. Furthermore, the results of DFT-based phasor estimation are compared with Shank’s estimation method (SEM) and the least-squares estimation method (LEM). The presented method is best suited to PMU algorithms development based on DFT for better visualization of the smart electric grid.

A New Extension of the Kumaraswamy Generated Family of Distributions with Applications to Real Data

In this paper, we develop the new extended Kumaraswamy generated (NEKwG) family of distributions. It aims to improve the modeling capability of the standard Kumaraswamy family by using a one-parameter exponential-logarithmic transformation. Mathematical developments of the NEKwG family are provided, such as the probability density function series representation, moments, information measure, and order statistics, along with asymptotic distribution results. Two special distributions are highlighted and discussed, namely, the new extended Kumaraswamy uniform (NEKwU) and the new extended Kumaraswamy exponential (NEKwE) distributions. They differ in support, but both have the features to generate models that accommodate versatile skewed data and non-monotone failure rates. We employ maximum likelihood, least-squares estimation, and Bayes estimation methods for parameter estimation. The performance of these methods is discussed using simulation studies. Finally, two real data applications are used to show the flexibility and importance of the NEKwU and NEKwE models in practice.

Parotid gland evaluation of menopausal women with xerostomia using the iterative decomposition of water and fat with echo asymmetry and least-squares estimation (IDEAL-IQ) method of MRI: a pilot study.

This study aimed to analyze the quantitative fat fraction (FF) of the parotid gland in menopausal females with xerostomia using the iterative decomposition of water and fat with echo asymmetry and least-squares estimation (IDEAL-IQ) method. A total 138 parotid glands of 69 menopausal females were enrolled in our study and participants were divided into normal group and xerostomia group. The xerostomia group was divided into those with or without Sjögren's syndrome. Participants underwent IDEAL-IQ sequences of MRI and the stimulated salivary flow test (s-SFR). The unpaired t-test was used to compare the FFs between the normal and xerostomia groups and between the subgroups with and without Sjögren's syndrome. The correlation between FF and s-SFR was analyzed by Pearson's correlation. Excellent intra- and interobserver agreement during the measurement of FFs by IDEAL-IQ method (ICC>0.99, respectively). FF value in the xerostomia group was statistically significantly higher than the value in the normal group (p < 0.05). Within the xerostomia group, the average FF value of females with Sjögren's syndrome was higher than that of females without Sjögren's syndrome. However, the difference was not statistically significant (p > 0.05). Within the xerostomia group, FF value correlated negatively with s-SFR (p < 0.05). The FF of the parotid gland was higher in the xerostomia group than in the normal group and FF value and s-SFR showed a negative correlation. Analyses of the FF using IDEAL-IQ in menopausal females can be helpful for the quantitative diagnosis of xerostomia.

A new least squares method for estimation and prediction based on the cumulative Hazard function

&lt;abstract&gt;&lt;p&gt;In this paper, the cumulative hazard function is used to solve estimation and prediction problems for generalized ordered statistics (defined in a general setup) based on any continuous distribution. The suggested method makes use of Rényi representation. The method can be used with type Ⅱ right-censored data as well as complete data. Extensive simulation experiments are implemented to assess the efficiency of the proposed procedures. Some comparisons with the maximum likelihood (ML) and ordinary weighted least squares (WLS) methods are performed. The comparisons are based on both the root mean squared error (RMSE) and Pitman's measure of closeness (PMC). Finally, two real data sets are considered to investigate the applicability of the presented methods.&lt;/p&gt;&lt;/abstract&gt;

Some properties and applications of half-Cauchy exponential extension distribution

In this article, we have proposed a new distribution having three parameters using half Cauchy family of distribution called Half-Cauchy Exponential extension Distribution. The statistical properties as well as different characteristics like the hazard rate function (HRF), the probability density function (PDF), the cumulative distribution function (CDF), quantile function, skewness, and kurtosis of the proposed distribution are discussed. The parameters of the proposed distribution are estimated by using the least-square estimation (LSE), Cramer-Von-Mises (CVM) and maximum likelihood estimators (MLE) methods. All the computations are performed in R programming software. To assess the application of the proposed distribution, a real lifetime data set is analyzed and performed the goodness-of-fit. It is found that the Half -Cauchy exponential extension distribution performed better as compared to some existing distributions.