This study aims to evaluate the state of precision livestock farming (PLF)’s spread, utilization, effectiveness, and evolution over the years. PLF includes a plethora of tools, which can aid in a number of laborious and complex tasks. These tools are often used in the monitoring of different animals, with the objective to increase production and improve animal welfare. The most frequently monitored attributes tend to be behavior, welfare, and social interaction. This study focused on the application of three types of technology: wearable sensors, video observation, and smartphones. For the wearable devices, the focus was on accelerometers and global positioning systems. For the video observation, the study addressed drones and cameras. The animals monitored by these tools were the most common ruminants, which are cattle, sheep, and goats. This review involved 108 articles that were believed to be pertinent. Most of the studied papers were very accurate, for most tools, when utilized appropriate; some showed great benefits and potential.

For many years, rare earth elements (REEs) have been part of a wide range of applications (from cell phones and batteries to electric vehicles and wind turbines) needed for daily life all over the world. Moreover, they are often declared to be part of “green technology”. Therefore, the data obtained from the United States Geological Survey (USGS) on the reserve and production of rare earth elements underwent treatment using the multivariate imputation by chained equations (MICE) algorithm to recover missing data. Initially, a simple linear regression model was chosen, which only considered fixed effects (β) and ignored random effects (U_i). However, recognizing the importance of accounting for random effects, the study subsequently employed the multilevel Linear Mixed-Effects (LME) model. This model allows for the simultaneous estimation of both fixed effects and random effects, followed by the estimation of variance parameters (γ, ρ, and σ²). The study demonstrated that the adjusted values closely align with the actual values, as indicated by the p-values being less than 0.05. Moreover, this model effectively captures the sample’s error, fixed, and random components. Also, in this range, the findings indicated two standard deviation measurements for fixed and random effects, along with a variance measurement, which exhibits significant predictive capabilities. Furthermore, within this timeframe, the study provided predictions for world reserves of rare earth elements in various countries until 2053, as well as world production forecasts through 2051. Notably, China is expected to maintain its dominant position in both reserve and production, with an estimated production volume of 101,985.246 tons, followed by the USA with a production volume of 15,850.642 tons. This study also highlights the periodic nature of production, with a specific scale, as well as periodicity in reserve. These insights can be utilized to define and quantify sustainability and to mitigate environmental hazards associated with the use of rare earth materials in the energy industry. Additionally, they can aid in making informed decisions regarding at-risk rare earth reserves, considering potential future trends in electric vehicle (EV) production up to the year 2050.

In the past decade, mixed-effects modeling has received a great deal of attention in the applied and theoretical statistical literature. They are very flexible tools in analyzing repeated measures, panel data, cross-sectional data, and hierarchical data. However, the complex nature of these models has motivated researchers to study different aspects of this problem. One of which is to test the significance of random effects used to model unobserved heterogeneity in the population. The method of likelihood ratio test based on the normality assumption of the error term and random effects has been proposed. However, this assumption does not necessarily hold in practice. In this paper, we propose an optimal test based on the so-called uniform local asymptotic normality to detect the possible presence of random effects in linear mixed models. We show that the proposed test statistic is, consistent, locally asymptotically optimal even for a model that does not require the traditional assumption of normality and is comparable to the classical L.ratio-test when the standard assumptions are met. Finally, simulation studies and real data analysis are also conducted to empirically examine the performance of this procedure.

The Gegenbauer autoregressive moving-average (GARMA) model is pivotal for addressing non-additivity, non-normality, and heteroscedasticity in real-world time-series data. While primarily recognized for its efficacy in various domains, including the health sector for forecasting COVID-19 cases, this study aims to assess its performance using yearly sunspot data. We evaluate the GARMA model’s goodness of fit and parameter estimation specifically within the domain of sunspots. To achieve this, we introduce the random coefficient generalized autoregressive moving-average (RCGARMA) model and develop methodologies utilizing conditional least squares (CLS) and conditional weighted least squares (CWLS) estimators. Employing the ratio of mean squared errors (RMSE) criterion, we compare the efficiency of these methods using simulation data. Notably, our findings highlight the superiority of the conditional weighted least squares method over the conditional least squares method. Finally, we provide an illustrative application using two real data examples, emphasizing the significance of the GARMA model in sunspot research.

The aim of this paper is to assess the significant impact of using quantile analysis in multiple fields of scientific research . Here, we focus on estimating conditional quantile functions when the errors follow a GARMA (Generalized Auto-Regressive Moving Average) model. Our key theoretical contribution involves identifying the Quantile-Regression (QR) coefficients within the context of GARMA errors. We propose a modified maximum-likelihood estimation method using an EM algorithm to estimate the target coefficients and derive their statistical properties. The proposed procedure yields estimators that are strongly consistent and asymptotically normal under mild conditions. In order to evaluate the performance of the proposed estimators, a simulation study is conducted employing the minimum bias and Root Mean Square Error (RMSE) criterion. Furthermore, an empirical application is given to demonstrate the effectiveness of the proposed methodology in practice.