Aiming to address the issue of low accuracy in model predictions obtained from fitting frequency domain response curves for small unmanned helicopters during the process of modeling their flight dynamics, this study proposes a system identification algorithm based on the combination of weighted least squares and improved grey wolf optimisation algorithm. The algorithm utilises the weighted least squares method to obtain the initial model structure, optimises the initial model parameters using the improved grey wolf optimisation algorithm, and enhances the local search and global optimisation ability of the grey wolf optimisation algorithm by introducing an improved grey wolf subgrouping rule, nonlinear convergence factor and dynamic cooperative rule. Ultimately, this approach establishes a dynamic model for small, unmanned helicopters. The identified model is validated using flight test data, with findings demonstrating that this method achieves higher accuracy in model identification and better fits to frequency domain response curves, thus providing a more accurate reflection of the flight dynamics of small unmanned helicopters.

A maximum likelihood procedure for combining standardized mean differences based on a noncentratt-distribution is proposed. With a proper data augmentation technique, an EM-algorithm is developed. Information and likelihood ratio statistics are discussed in detail for reliable inference. Simulation results favor the proposed procedure over both the existing normal theory maximum likelihood procedure and the commonly used generalized least squares procedure.

A general approach for fitting a model to a data matrix by weighted least squares (WLS) is studied. This approach consists of iteratively performing (steps of) existing algorithms for ordinary least squares (OLS) fitting of the same model. The approach is based on minimizing a function that majorizes the WLS loss function. The generality of the approach implies that, for every model for which an OLS fitting algorithm is available, the present approach yields a WLS fitting algorithm. In the special case where the WLS weight matrix is binary, the approach reduces to missing data imputation.

Several algorithms for covariance structure analysis are considered in addition to the Fletcher-Powell algorithm. These include the Gauss-Newton, Newton-Raphson, Fisher Scoring, and Fletcher-Reeves algorithms. Two methods of estimation are considered, maximum likelihood and weighted least squares. It is shown that the Gauss-Newton algorithm which in standard form produces weighted least squares estimates can, in iteratively reweighted form, produce maximum likelihood estimates as well. Previously unavailable standard error estimates to be used in conjunction with the Fletcher-Reeves algorithm are derived. Finally all the algorithms are applied to a number of maximum likelihood and weighted least squares factor analysis problems to compare the estimates and the standard errors produced. The algorithms appear to give satisfactory estimates but there are serious discrepancies in the standard errors. Because it is robust to poor starting values, converges rapidly and conveniently produces consistent standard errors for both maximum likelihood and weighted least squares problems, the Gauss-Newton algorithm represents an attractive alternative for at least some covariance structure analyses.

The two-way linear fixed effects regression (2FE) has become a default method for estimating causal effects from panel data. Many applied researchers use the 2FE estimator to adjust for unobserved unit-specific and time-specific confounders at the same time. Unfortunately, we demonstrate that the ability of the 2FE model to simultaneously adjust for these two types of unobserved confounders critically relies upon the assumption of linear additive effects. Another common justification for the use of the 2FE estimator is based on its equivalence to the difference-in-differences estimator under the simplest setting with two groups and two time periods. We show that this equivalence does not hold under more general settings commonly encountered in applied research. Instead, we prove that the multi-period difference-in-differences estimator is equivalent to the weighted 2FE estimator with some observations having negative weights. These analytical results imply that in contrast to the popular belief, the 2FE estimator does not represent a design-based, nonparametric estimation strategy for causal inference. Instead, its validity fundamentally rests on the modeling assumptions.

The fluorescence effect induced by Kβ photons is usually so small that it can be neglected. However, in the Fe–Mn system, omitting Kβ fluorescence correction will lead to the overestimation of the Mn content especially when Mn is the minor alloy element. In this study, the error in the Mn concentration induced by Kβ fluorescence was investigated by both Monte Carlo simulation, using the pyPENELOPE program, and systematic electron probe measurements on the Fe–0.53% Mn alloy standard by the aid of CalcZAF software. It is shown that the error caused by Kβ fluorescence exceeds 4% for the Fe–0.53% Mn alloy. The problem can be overcome by utilizing CalcZAF in which β-line fluorescence has been included, or by employing a similar standard Fe–0.85% Mn for Mn in the absence of β-line fluorescence correction. In addition, a modified calibration curve method, using k-values instead of X-ray intensity as a variable, is presented and used to measure the Mn concentration. The accuracy of this method is as good as or better than that of the conventional matrix correction method. Compared with conventional calibration curve methods, it is time-saving because the k-value is not sensitive to instrument fluctuations and the established curve remains valid for a long period.

This article utilizes the 2011 Nielsen scanner data for the Honolulu fresh tomato market to explore the existence of price premium for local food. Hedonic analysis is conducted to delineate the price impact of the local attribute. Contrary to the widely perceived local price premium in the consumer preference literature, mixed results of price premiums and discounts are discovered for local tomato products. Additional investigation suggests that the prices of local tomatoes are likely influenced by seasonal output fluctuation. The limited market distribution capacity facing local producers may have contributed further to the retail discounting.

We establish some explicit expressions for norm-wise, mixed and componentwise condition numbers for the weighted Moore-Penrose inverse of a matrix A ⊗ B and more general matrix function compositions involving Kronecker products. The condition number for the weighted least squares problem (WLS) involving a Kronecker product is also discussed.