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The purpose of this study is to build a high accuracy thrust model under various small turbojet engine shaft speeds by using robust, ordinary, linear and nonlinear least squares estimation methods for target drone applications.

The dynamic shaft speeds from the test experiment of a target drone engine is conducted. Then, thrust values are calculated. Based on these, the engine thrust is modeled by robust linear and nonlinear equations. The models are benefited from quadratic, power and various series expansion functions with several coefficients to optimize the model parameters.

The error terms and accuracy of the model are given using sum of squared errors, root mean square error (RMSE) and R-squared (R²) error definitions. Based on the multiple analyses, it is seen that the RMSE values are no more than 17.7539 and the best obtained result for robust least squares estimation is 15.0086 for linear at all cases. Furthermore, the R² value is found to be 0.9996 as the highest with the nonlinear Fourier series expansion model.

The motivation behind this paper is to propose robust nonlinear thrust models based on power, Fourier and various series expansion functions for dynamic shaft speeds from the test experiments.

The purpose of this paper is to focus on the performance of three typical nonlinear least-squares estimation algorithms in atmospheric density model calibration.

The error of Jacchia-Roberts atmospheric density model is expressed as an objective function about temperature parameters. The estimation of parameter corrections is a typical nonlinear least-squares problem. Three algorithms for nonlinear least-squares problems, Gauss–Newton (G-N), damped Gauss–Newton (damped G-N) and Levenberg–Marquardt (L-M) algorithms, are adopted to estimate temperature parameter corrections of Jacchia-Roberts for model calibration.

The results show that G-N algorithm is not convergent at some sampling points. The main reason is the nonlinear relationship between Jacchia-Roberts and its temperature parameters. Damped G-N and L-M algorithms are both convergent at all sampling points. G-N, damped G-N and L-M algorithms reduce the root mean square error of Jacchia-Roberts from 20.4% to 9.3%, 9.4% and 9.4%, respectively. The average iterations of G-N, damped G-N and L-M algorithms are 3.0, 2.8 and 2.9, respectively.

This study is expected to provide a guidance for the selection of nonlinear least-squares estimation methods in atmospheric density model calibration.

The study analyses the performance of three typical nonlinear least-squares estimation methods in the calibration of atmospheric density model. The non-convergent phenomenon of G-N algorithm is discovered and explained. Damped G-N and L-M algorithms are more suitable for the nonlinear least-squares problems in model calibration than G-N algorithm and the first two algorithms have slightly fewer iterations.

In the last two decades there has been considerable progress made in the development of alternative estimation techniques to ordinary least squares (OLS) regression. The search for alternative estimators has no doubt been motivated by the observance of erratic OLS estimator behavior in cases where there are too few observations, multicollinearity problems, or simply “information‐poor” data sets. Imprecise and unreliable OLS coefficient estimates have been the result.

The main purpose of this paper is to estimate the resistance and inductor in the RL electrical circuit when these are unavailable or missing data that it is a concern in electrical engineering. The input voltage is assumed to be corrupted by the noise and the current is observed at discrete time points.

The authors propose a computationally efficient framework for parameters estimation using least square estimator and Bayesian Monte Carlo scheme.

The explicit formulas for least square estimator are derived and the strong consistency of resistance estimator is verified when inductor is a known parameter, then Bayesian estimation of parameters governed by using Markov chain Monte Carlo methods. The applicability of the results is demonstrated by using numerical examples. Several numerical results and figures are presented via Matlab and R programming to illustrate the performance of the estimators.

The paper can be used in various types of electrical engineering real time projects. The projects include electrical circuits, electrical machines theory and drives, especially when the parameters are uncertain that it is a worry in electrical engineering.

To the author's best knowledge, least square and Bayesian estimation of resistance and inductor have not been studied before. The proposed model is nonlinear with respect to inductor (L); therefore the present work has fundamental difference in comparison with the similar models.

The different types of estimators of rational expectations models are surveyed. A key feature is that the model′s solution has to be taken into account when it is estimated. The two ways of doing this, the substitution and errors‐in‐variables methods, give rise to different estimators. In the former case, a generalised least‐squares or maximum‐likelihood type estimator generally gives consistent and efficient estimates. In the latter case, a generalised instrumental variable (GIV) type estimator is needed. Because the substitution method involves more complicated restrictions and because it resolves the solution indeterminacy in a more arbitary fashion, when there are forward‐looking expectations, the errors‐in‐variables solution with the GIV estimator is the recommended combination.

This study aims to examine the determinants of the allowance for loan losses (ALL) and loan loss provisions (LLP) for banks in the Middle East and North African (MENA) region using both a two-stage approach and simultaneous equation system to address the potential problem of estimation bias introduced by estimating the ALL and LLP separately. The paper also tests three competing hypotheses: the earnings management hypothesis, the capital management hypothesis, and the signaling hypothesis.

The authors adopt a simultaneous equation and three-stage approaches to test whether MENA banks jointly determine LLP and ALL and the determinants of the two accounts. The sample consists of all available electronic data for 75 banks (451 bank-year observations) in nine MENA countries over the period 2000-2008.

Evidence suggests that the two accounts are jointly determined. The results support the earnings management hypothesis – meaning that MENA banks have engaged in year-to-year income smoothing. The authors also find that LLP and ALL provide signals about future earnings.

The authors acknowledge that the LLP account is only one of many accounts on the income statement that could be used for signaling or to manage earnings, and that the ALL is one of several accounts that could be used for signaling, earnings or capital management. Future studies could examine other accruals for their role in managing earnings, signaling and capital.

The results indicate that bank managers use LLP and ALL accounts to manage earnings management, policy makers may want to limit the ability of banks to manipulate earnings.

Prior research on the loan loss accounting practices has been based on single equation models of the determinants of LLP and ALL. An issue that has not been adequately addressed in this literature is that ALL and LLP may be interrelated and jointly determined by banks. If the two accounts are not independent of each other, failure to include one when estimating the other may lead to an omitted variable problem, while including both in the same equation induces a potential simultaneity bias. The study is the first empirical work examining whether ALL and LLP are jointly determined by banks. By jointly estimating LLP and ALL, the study permits an assessment of the magnitude of the potential error from adopting ordinary least squares estimation of a single equation model.

The great value of offline identification of machine parameters is when the machine manufacturer does not provide its parameters. Most machine control strategies require parameter values, and some circumstances in the industrial sector only require offline identification. This paper aims to present a new offline method for estimating induction motor parameters based on least squares and a salp swarm algorithm (SSA).

The central concept is to use the classic least squares (LS) method to acquire the majority of induction machine (IM) constant parameters, followed by the SSA method to obtain all parameters and minimize errors.

The obtained results showed that the LS method gives good results in simulation based on the assumption that the measurements are noise-free. However, unlike in simulations, the LS method is unable to accurately identify the machine’s parameters during the experimental test. On the contrary, the SSA method proves higher efficiency and more precision for IM parameter estimation in both simulations and experimental tests.

After performing a primary identification using the technique of least squares, the initial intention of this study was to apply the SSA for the purpose of identifying all of the machine’s parameters and minimizing errors. These two approaches use the same measurement from a simple running test of an IM, and they offer a quick processing time. Therefore, this combined offline strategy provides a reliable model based on the identified parameters.

Model estimation gives students insights beyond what they can gain from textbook presentations. This paper introduces a way to make doing this easier and more effective. It introduces the program Gnu Regression, Econometrics and Time‐series Library (GRETL) which may be downloaded free of charge, and which students can place on their computers quickly and easily. Using GRETL to produce ordinary least squares (OLS) estimates is an easy, intuitive exercise. Therefore, instructors may assign such exercises without taking a large amount of time to introduce the computer and OLS estimation. GRETL, though designed to facilitate instruction, has grown into a full econometrics package that instructors can use as a research tool as well as an instructional aid.

The paper provides an overview of GRETL's accessibility and its capabilities. Next it addresses the use of GRETL for instructional purposes. Then it shows how GRETL can be used as a research tool.

The paper shows that GRETL can be a useful addition to the instructor who is showing novices how to use regression models. Also, it can be used as a research tool.

Given software like GRETL, instructors no longer need to omit model estimation because of the difficulties in accessing software and showing students how to use it.

This paper introduces a relatively new option, the use of a powerful open‐source software package to instructors in finance and accounting courses.

Real estate market data often contain outliers in the observations. Since outliers have a large influence on least squares estimates, robust regression methods have been recommended for this situation. Compares the performance of least squares and least median of squares, a robust method, in the estimation of price/income relationships for apartment buildings. Multiplicative models with multiplicative errors are estimated by means of natural log transformations. The study confirms the importance of employing robust methods for this application and implies this may well be so for real estate data sets more generally.

With the prosperity of grey extension models, the form and structure of grey forecasting models tend to be complicated. How to select the appropriate model structure according to the data characteristics has become an important topic. The purpose of this paper is to design a structure selection method for the grey multivariate model.

The linear correction term is introduced into the grey model, then the nonhomogeneous grey multivariable model with convolution integral [NGMC(1,N)] is proposed. Then, by incorporating the least absolute shrinkage and selection operator (LASSO), the model parameters are compressed and estimated based on the least angle regression (LARS) algorithm.

By adjusting the values of the parameters, the NGMC(1,N) model can derive various structures of grey models, which shows the structural adaptability of the NGMC(1,N) model. Based on the geometric interpretation of the LASSO method, the structure selection of the grey model can be transformed into sparse parameter estimation, and the structure selection can be realized by LASSO estimation.

This paper not only provides an effective method to identify the key factors of the agricultural drought vulnerability, but also presents a practical model to predict the agricultural drought vulnerability.

Based on the LASSO method, a structure selection algorithm for the NGMC(1,N) model is designed, and the structure selection method is applied to the vulnerability prediction of agricultural drought in Puyang City, Henan Province.