Abstract
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.
Purpose
– Partial least squares (PLS) path modeling is a variance-based structural equation modeling (SEM) technique that is widely applied in business and social sciences. Its ability to model ...composites and factors makes it a formidable statistical tool for new technology research. Recent reviews, discussions, and developments have led to substantial changes in the understanding and use of PLS. The paper aims to discuss these issues.
Design/methodology/approach
– This paper aggregates new insights and offers a fresh look at PLS path modeling. It presents new developments, such as consistent PLS, confirmatory composite analysis, and the heterotrait-monotrait ratio of correlations.
Findings
– PLS path modeling is the method of choice if a SEM contains both factors and composites. Novel tests of exact fit make a confirmatory use of PLS path modeling possible.
Originality/value
– This paper provides updated guidelines of how to use PLS and how to report and interpret its results.
We develop randomized neural networks (RNNs) with Petrov–Galerkin (RNN-PG) methods to solve linear elasticity and Navier–Stokes equations. RNN-PGs use the Petrov–Galerkin variational framework, where ...the solution is approximated by randomized neural networks and the test functions are piecewise polynomials. Unlike conventional neural networks, the parameters of the hidden layers of randomized neural networks are fixed randomly while the parameters of the output layer are determined by the least-squares method, which can effectively approximate the solution. We also develop mixed RNN-PG (M-RNN-PG) methods for linear elasticity problems to ensure symmetry of the stress tensor and avoid locking effects. For the Stokes problem, we present various M-RNN-PG methods that enforce the divergence-free constraint by different techniques. For the Navier–Stokes equations, we propose a space-time M-RNN-PG that uses Picard or Newton iteration to deal with the nonlinear term. Using several examples, we compare RNN-PG methods with the finite-element method, the mixed discontinuous Galerkin method, and the physics-informed neural network. The numerical results demonstrate that RNN-PG methods achieve higher accuracy and efficiency.
We present the analysis performed on spectropolarimetric data of 97 O-type targets included in the framework of the Magnetism in Massive Stars (MiMeS) Survey. Mean least-squares deconvolved Stokes I ...and V line profiles were extracted for each observation, from which we measured the radial velocity, rotational and non-rotational broadening velocities, and longitudinal magnetic field B sub( l). The investigation of the Stokes I profiles led to the discovery of two new multiline spectroscopic systems (HD 46106, HD 204827) and confirmed the presence of a suspected companion in HD 37041. We present a modified strategy of the least-squares deconvolution technique aimed at optimizing the detection of magnetic signatures while minimizing the detection of spurious signatures in Stokes V. Using this analysis, we confirm the detection of a magnetic field in six targets previously reported as magnetic by the MiMeS collaboration (HD 108, HD 47129A2, HD 57682, HD 148937, CPD-28 2561, and NGC 1624-2), as well as report the presence of signal in Stokes V in three new magnetic candidates (HD 36486, HD 162978, and HD 199579). Overall, we find a magnetic incidence rate of 7 plus or minus 3 per cent, for 108 individual O stars (including all O-type components part of multiline systems), with a median uncertainty of the B sub( l) measurements of about 50 G. An inspection of the data reveals no obvious biases affecting the incidence rate or the preference for detecting magnetic signatures in the magnetic stars. Similar to A- and B-type stars, we find no link between the stars' physical properties (e.g. T sub( eff), mass, and age) and the presence of a magnetic field. However, the Of?p stars represent a distinct class of magnetic O-type stars.
•We propose an ensemble STLF method based on the ELM.•A wavelet-based ensemble scheme is introduced to STLF.•A parallel model of 24 ELMs is established for 24-h load prediction.•Both 1-h and 24-h ...ahead load forecasting are evaluated.•The proposed method outperforms other techniques on the public datasets.
This paper proposes a novel ensemble method for short-term load forecasting based on wavelet transform, extreme learning machine (ELM) and partial least squares regression. In order to improve forecasting performance, a wavelet-based ensemble strategy is introduced into the forecasting model. The individual forecasters are derived from different combinations of mother wavelet and number of decomposition levels. For each sub-component from the wavelet decomposition, a parallel model consisting of 24 ELMs is invoked to predict the hourly load of the next day. The individual forecasts are then combined to form the ensemble forecast using the partial least squares regression method. Numerical results show that the proposed method can significantly improve forecasting performance.
•Compilation of analytical calibration information from validation guidelines.•Report of very common mistakes in the analytical calibration process.•Compilation of methods for assessing linearity of ...calibration curves.•The correlation and determination coefficients are misleading for testing linearity.•Deviation from back-calculated concentration is very useful for testing linearity.
The analytical calibration of an instrumental method is very important, being considered as a key point in method validation. There are different validation guidelines; showing that analytical calibration process variety prevails in terms of nomenclature, methodology employed and acceptance criteria. Very common mistakes in the analytical calibration process are the use of correlation and/or determination coefficients as a test for linearity, the negligence in the heteroscedasticity of the experimental data and selection of appropriate weighting factor, misunderstanding about the regression through the origin and using zero-point calibration. Once the calibration function is established, their linearity can be confirmed by using different procedures such as graphical plots, statistical significance tests and numerical parameters. In particular, deviation from back-calculated concentrations expressed in the form of percentage of relative error (%RE) can be considered very useful for unambiguous linearity evaluation. Some case studies were included to explain the linearity assessment from a practical viewpoint.
This paper is concerned with a Legendre Ritz-Least squares technique for the non-singular and singular delay differential equations (DDEs) of multi-pantograph type. This tech-nique is based on ...Legendre polynomials and Least squares. The Legendre Ritz-Least squarestechnique (LRLS) is used to decrease the problem to a set of the algebraic equation system.The efficiency and reliability of the proposed method are shown by some numerical results. Allof the numerical implementations have been performed on a PC using some programs written inMATHEMATICA.
An augmented Kalman filter for force identification in structural dynamics is developed, in which the unknown forces are included in the state vector and estimated in conjunction with the states. ...Noise is modeled as a stochastic process and is assumed to be present not only on the measurements, but also on the state variables, thus accounting to some extent for modeling errors. This distinguishes the proposed technique from purely deterministic methods for force identification in which no errors are assumed on the states. To analyze the effect hereof on the quality of the identification, the results obtained with a commonly used recursive least-squares method, the Dynamic Programming algorithm, are compared to those obtained using the augmented filter in a laboratory experiment on an instrumented steel beam. It is shown how, in the collocated case, more accurate results can be obtained with the augmented filter due to its incorporation of modeling errors. In the non-collocated case, however, better solutions are produced by classical deterministic methods as Dynamic Programming in which only the forces are estimated, and not the states as well.
► An augmented Kalman filter for force identification in structural dynamics is proposed. ► The filter estimates the unknown forces in conjunction with the states. ► By also estimating the states it accounts to some extent for modeling errors. ► This leads to more accurate results than when modeling error is not accounted for. ► The filter does, however, require at least one collocated measurement.
Non-line-of-sight (NLOS) propagation of radio signals can significantly degrade the performance of ultra-wideband localization systems indoors, it is hence crucial to mitigate the NLOS effect to ...enhance the accuracy of positioning. The existing NLOS mitigation algorithms to improve localization accuracy are either by compensating range errors through NLOS identification and mitigation methods for ranging or by using dedicated localization techniques. However, they are only applicable to some specific scenarios due to some special assumptions or the need of a priori knowledge, such as thresholds and distribution functions. Another disadvantage is that they neither have the capability to evaluate the magnitude of NLOS effect nor take account of the residual NLOS range errors during location estimation. To remedy these problems, this paper proposes a less environment-dependent and a priori knowledge-independent NLOS identification and mitigation method for ranging which is able to determine the specific NLOS channel. Based on the identified channel information, a rule is developed to select appropriate NLOS ranges for location estimation. Meanwhile, an equality constrained Taylor series robust least squares (ECTSRLS) technique is proposed to suppress residual NLOS range errors by introducing robustness to Taylor series least squares method. All these constitute our FCE-ECTSRLS NLOS mitigation algorithm. The performance of the proposed algorithm is compared with four existing NLOS mitigation algorithms by both static and mobile localization experiments in a harsh indoor environment. Experimental results have demonstrated that the proposed FCE-ECTSRLS algorithm outperforms the other four algorithms significantly.
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