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This article presents a new set of estimators designed to estimate the finite population variance of a study variable in two-phase sampling. These estimators utilize the information about extreme values and ranks of an auxiliary variable. Through a first-order approximation, we investigate the properties of these estimators, including biases and mean squared errors (MSEs). Furthermore, a comprehensive simulation study is conducted to assess their performance and validate our theoretical insights. Results demonstrate that our proposed class of estimators performs better in terms of percent relative efficiency (PRE) across various simulation scenarios compared to existing estimators. In addition, in the application section, we utilize three data sets to further validate the performance of our proposed estimators against conventional unbiased variance estimators, ratio and regression estimators, as well as other existing methods. [ABSTRACT FROM AUTHOR]

This paper presents several nonparametric estimators for the Sharma–Taneja–Mittal entropy measure of a continuous random variable with known support, utilizing spacing, a local linear model, and a kernel function. The properties of these estimators are discussed. Their performance was also examined through real data analysis and Monte Carlo simulations. In the Monte Carlo experiments, the proposed Sharma–Taneja–Mittal entropy estimators were employed to create a test of goodness-of-fit under the standard uniform distribution. The suggested test statistics demonstrate strong performance, as evidenced by a comparison of their power with that of other tests for uniformity. Finally, we examine a classification issue in the recognition of patterns to underscore the significance of these measures. [ABSTRACT FROM AUTHOR]

Hydrogen fuel holds promise for clean energy solutions, particularly in onboard applications such as fuel cell vehicles. However, the development of efficient hydrogen storage systems remains a critical challenge. This study addresses this challenge by exploring the potential of high-strength novel materials, including glass, to maximize onboard hydrogen storage capacity. A mathematical approach was employed to evaluate the feasibility and efficacy of various high-strength materials for hydrogen storage. This study focused on capillary arrays as a promising storage medium and utilized mathematical modeling techniques to estimate the storage capacity enhancement achievable with different materials. The analysis revealed significant variations in storage capacity enhancements in different high-strength novel materials, with glass having promising results. Glass-based materials demonstrated the potential to meet or exceed US Department of Energy (DOE) targets for both gravimetric and volumetric hydrogen storage capacities in capillary arrays. By leveraging a mathematical approach, this study identified high-strength novel materials, including glass and polymers, capable of substantially improving onboard hydrogen storage capacity: 29 wt.% with 40 g/L for quartz glass and 25 wt.% with 38 g/L for Kevlar compared to 5.2 wt.% with 26.3 g/L from a conventional type IV tank. These findings underscore the importance of material selection in optimizing hydrogen storage systems and provide valuable insights for the design and development of next-generation hydrogen storage technologies for onboard applications. [ABSTRACT FROM AUTHOR]

Quickly determining the metal content in plants and subsequently identifying geochemical anomalies can provide clues and guidance for predicting the location and scale of concealed ore bodies in vegetation-covered areas. Although visible, near-infrared and shortwave infrared (VNIR–SWIR) reflectance spectroscopy at wavelengths ranging from 400 to 2500 nm has been proven by many researchers to be a fast, accurate and nondestructive approach for estimating the contents of copper (Cu), lead (Pb), zinc (Zn) and other metal elements in plants, relatively few studies have been conducted on the estimation of lithium (Li) in plants. Therefore, the potential of applying VNIR–SWIR spectroscopy techniques for estimating the Li content in plants was explored in this study. The Jingerquan Li mining area in Hami, Xinjiang, China, was chosen. Three sampling lines were established near a pegmatite deposit and in a background region, canopy reflectance spectra were obtained for desert plants and Li contents were determined in the laboratory; then, quantitative relationships were established between nine different transformed spectra (including both integer and fractional orders) and the Li content was estimated using partial least squares regression (PLSR). The results showed that models constructed using high-order derivative spectra (with an order greater than or equal to 1) significantly outperformed those based on original and low-order derivative spectra (with an order less than 1). Notably, the model based on a 1.1-order derivative spectrum displayed the best performance. Furthermore, the performance of the model based on the two-layer wavelet coefficients of the 1.1-order derivative spectrum was further improved compared with that of the model based on only the 1.1-order derivative spectrum. The coefficient of determination ( R p r e 2 ) and the ratio of performance to deviation (RPD) for the validation set increased from 0.6977 and 1.7656 to 0.7044 and 1.8446, respectively, and the root mean square error (RMSEpre) decreased from 2.5735 to 2.4633 mg/kg. These results indicate that quickly and accurately estimating the Li content in plants via the proposed spectroscopic analysis technique is feasible and effective; however, appropriate spectral preprocessing methods should be selected before hyperspectral estimation models are constructed. Overall, the developed hybrid spectral transformation approach, which combines wavelet coefficients and derivative spectra, displayed excellent application potential for estimating the Li content in plants. [ABSTRACT FROM AUTHOR]

This paper proposes a semiparametric spatial lag model and develops a Bayesian estimation method for this model. In the estimation of the model, the paper combines Reversible Jump Markov Chain Monte Carlo (RJMCMC) algorithm, random walk Metropolis sampler, and Gibbs sampling techniques to sample all the parameters. The paper conducts numerical simulations to validate the proposed Bayesian estimation theory using a numerical example. The simulation results demonstrate satisfactory estimation performance of the parameter part and the fitting performance of the nonparametric function under different spatial weight matrix settings. Furthermore, the paper applies the constructed model and its estimation method to an empirical study on the relationship between economic growth and carbon emissions in China, illustrating the practical application value of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper presents a novel, cost-effective technique for estimating the Doppler effect in the time domain using a single pulse and subsequently leveraging the precise Doppler value to recover the radar waveform. The proposed system offers several key advantages over existing techniques, including the ability to calculate the target speed without any frequency ambiguity and the ability to detect a wide range of target speeds. These two features are not available in any existing techniques, including the conventional moving target detection (MTD) processor. To ensure improved accuracy and robust estimation, the system employs ensemble and iterative techniques by recursively and efficiently reducing the Doppler residues from the signal. Furthermore, the proposed system demonstrates effective signal recovery of a well-known bi-phase code shape at low signal-to-noise ratios in just a few iterations. The performance evaluation of the new algorithm demonstrates its practicability and its superiority over traditional radar systems. Implementation on software-defined radio (SDR) reveals that the proposed system excels in Doppler estimation and signal recovery at low SNRs, demonstrating promising results. [ABSTRACT FROM AUTHOR]

Mesocarnivores are major components of carnivore assemblages, and they play important roles in structuring communities and regulating community dynamics. In Southwest China, many apex predators have been extirpated, and this has potentially resulted in the ecological release of mesocarnivores. Estimating the sizes of mesocarnivore populations is challenging. We used DNA derived from hairs and spatial capture–mark–recapture techniques to estimate the population size of masked palm civets (Paguma larvata) in Laohegou Nature Reserve in the Minshan Mountains of Sichuan Province, China. In the fall of 2014 and the spring of 2015, we collected 144 and 230 hair samples, respectively, at 30 baited stations. We used 16S rRNA fragments, microsatellite genotyping, and sexing to determine that 191 samples were derived from 44 masked palm civet individuals (24 males and 20 females). Using spatially explicit capture–recapture analysis, we estimated that there were 82 ± 13 masked palm civets in the study area, with a density of 1.7 individuals/km2. This is the first study to estimate the population size of masked palm civets in the wild. Our data provide important new information on the density of masked palm civets. [ABSTRACT FROM AUTHOR]

The Kalman filter is an important technique for system state estimation. It requires the exact knowledge of system noise statistics to achieve optimal state estimation. However, in practice, this knowledge is often unknown or inaccurate due to uncertainties and disturbances involved in the dynamic environment, leading to degraded or even divergent filtering solutions. To address this issue, this paper presents a new method by combining the random weighting concept with the limited memory technique to accurately estimate system noise statistics. To avoid the influence of excessive historical information on state estimation, random weighting theories are established based on the limited memory technique to estimate both process noise and measurement noise statistics within a limited memory. Subsequently, the estimated system noise statistics are fed back into the Kalman filtering process for system state estimation. The proposed method improves the Kalman filtering accuracy by adaptively adjusting the weights of system noise statistics within a limited memory to suppress the interference of system noise on system state estimation. Simulations and experiments as well as comparison analysis were conducted, demonstrating that the proposed method can overcome the disadvantage of the traditional limited memory filter, leading to im-proved accuracy for system state estimation. [ABSTRACT FROM AUTHOR]

The sustainability of the transport sector is targeted by various policies adopted by the European Union, and their impact must be constantly monitored in order to maximize the desired objective. This paper, through a two-stage investigation, aims to present a systemic approach of the sustainability dimensions in transport and to introduce an innovative technique to analyze the interdependencies between them. In the first stage, relevant indicators were selected from the Eurostat database for the content of four dimensions: economic, environmental, social and technological. The robustness of the developed dimensions was assessed and validated through a confirmatory factor analysis. In the second stage, a Gaussian graphical model was estimated as a technique integrating graphical and statistical modeling to identify complex structures of linkages between variables (as components of each dimension of sustainability). The structure of the network clearly highlights the dependence of transport on fossil fuel consumption as the main determinant of pollution in the sector (CO2 emissions). In addition, the central role of railways in decarbonizing transport is highlighted, in contrast to the limited, and isolated at one end of the network, role of electric vehicles. The findings support that affordability of this new technology plays an important role in its impact on zero-emission transition. Concentrating on the period 2013–2022, at EU27 level, the results are relevant in the context of decarbonization policies, offering useful insights both for future research and policy makers. [ABSTRACT FROM AUTHOR]

This paper concerns with the existence of radial solutions of the biharmonic elliptic equation ▵ 2 u = f (| x | , u , | ∇ u | , ▵ u) in an annular domain Ω = { x ∈ R N : r 1 < | x | < r 2 } ( N ≥ 2 ) with the boundary conditions u | ∂ Ω = 0 and ▵ u | ∂ Ω = 0 , where f : [ r 1 , r 2 ] × R × R + × R → R is continuous. Under certain inequality conditions on f involving the principal eigenvalue λ 1 of the Laplace operator − ▵ with boundary condition u | ∂ Ω = 0 , an existence result and a uniqueness result are obtained. The inequality conditions allow for f (r , ξ , ζ , η) to be a superlinear growth on ξ , ζ , η as | (ξ , ζ , η) | → ∞ . Our discussion is based on the Leray–Schauder fixed point theorem, spectral theory of linear operators and technique of prior estimates. [ABSTRACT FROM AUTHOR]

First-order algorithms have long dominated the training of deep neural networks, excelling in tasks like image classification and natural language processing. Now there is a compelling opportunity to explore alternatives that could outperform current state-of-the-art results. From the estimation theory, the Extended Kalman Filter (EKF) arose as a viable alternative and has shown advantages over backpropagation methods. Current computational advances offer the opportunity to review algorithms derived from the EKF, almost excluded from the training of convolutional neural networks. This article revisits an approach of the EKF with decoupling and it brings the Fully Decoupled Extended Kalman Filter (FDEKF) for training convolutional neural networks in image classification tasks. The FDEKF is a second-order algorithm with some advantages over the first-order algorithms, so it can lead to faster convergence and higher accuracy, due to a higher probability of finding the global optimum. In this research, experiments are conducted on well-known datasets that include Fashion, Sports, and Handwritten Digits images. The FDEKF shows faster convergence compared to other algorithms such as the popular Adam optimizer, the sKAdam algorithm, and the reduced extended Kalman filter. Finally, motivated by the finding of the highest accuracy of FDEKF with images of natural scenes, we show its effectiveness in another experiment focused on outdoor terrain recognition. [ABSTRACT FROM AUTHOR]

The phenotypic evaluation of root traits in soybeans presents challenges in breeding due to its high cost and the requirement for experimental plot destruction. Establishing relationships between aerial and root traits is crucial, given the relative ease of phenotypic evaluations for aerial traits. Therefore, this study aims to utilize the canonical correlation technique to estimate latent variables, subsequently employing GBLUP for the genomic prediction of the root traits (length, volume, surface area, and dry mass) using phenotypic information from aerial part traits (hypocotyl diameter and dry mass). Our results demonstrate the effectiveness of the technique in predicting the root part, even when not directly evaluated. The agreement observed between the top 10% of individuals selected based on the canonical variable and each root trait individually was considered moderate or substantial. This enables the simultaneous selection of genotypes based on both trait groups, providing a valuable approach for soybean breeding programs. [ABSTRACT FROM AUTHOR]

This paper presents a new technique for estimating the two-dimensional direction of departure (2D-DOD) and direction of arrival (2D-DOA) in bistatic uniform planar array Multiple-Input Multiple-Output (MIMO) radar systems. The method is based on the reduced-dimension (RD) MUSIC algorithm, aiming to achieve improved precision and computational efficiency. Primarily, this pioneering approach efficiently transforms the four-dimensional (4D) estimation problem into two-dimensional (2D) searches, thus reducing the computational complexity typically associated with conventional MUSIC algorithms. Then, exploits the spatial diversity of array response vectors to construct a 4D spatial spectrum function, which is crucial in resolving the complex angular parameters of multiple simultaneous targets. Finally, the objective is to simplify the spatial spectrum to a 2D search within a 4D measurement space to achieve an optimal balance between efficiency and accuracy. Simulation results validate the effectiveness of our proposed algorithm compared to several existing approaches, demonstrating its robustness in accurately estimating 2D-DOD and 2D-DOA across various scenarios. The proposed technique shows significant computational savings and high-resolution estimations and maintains high precision, setting a new benchmark for future explorations in the field. [ABSTRACT FROM AUTHOR]

The determination of a mobile terminal's position with high accuracy and ubiquitous coverage is still challenging. Global satellite navigation systems (GNSSs) provide sufficient accuracy in areas with a clear view to the sky. For GNSS-denied environments like indoors, complementary positioning technologies are required. A promising approach is to use the Earth's magnetic field for positioning. In open areas, the Earth's magnetic field is almost homogeneous, which makes it possible to determine the orientation of a mobile device using a compass. In more complex environments like indoors, ferromagnetic materials cause distortions of the Earth's magnetic field. A compass usually fails in such areas. However, these magnetic distortions are location dependent and therefore can be used for positioning. In this paper, we investigate the influence of elementary structures, in particular a sphere and a cylinder, on the achievable accuracy of magnetic positioning methods. In a first step, we analytically calculate the magnetic field around a sphere and a cylinder in an outer homogeneous magnetic field. Assuming a noisy magnetic field sensor, we investigate the achievable positioning accuracy when observing these resulting fields. For our analysis, we calculate the Cramér–Rao lower bound, which is a fundamental lower bound on the variance of an unbiased estimator. The results of our investigations show the dependency of the positioning error variance on the magnetic sensor properties, in particular the sensor noise variance and the material properties, i.e., the relative permeability of the sphere with respect to the cylinder and the location of the sensor relative to the sphere with respect to the cylinder. The insights provided in this work make it possible to evaluate experimental results from a theoretical perspective. [ABSTRACT FROM AUTHOR]

Gamma-ray spectroscopy (GRS) enables continuous estimation of soil water content (SWC) at the subfield scale with a noninvasive sensor. Hydrological applications, including hyper-resolution land surface models and precision agricultural decision making, could benefit greatly from such SWC information, but a gap exists between established theory and accurate estimation of SWC from GRS in the field. In response, we conducted a robust three-year field validation study at a well-instrumented agricultural site in Nebraska, United States. The study involved 27 gravimetric water content sampling campaigns in maize and soybean and 40K specific activity (Bq kg−1) measurements from a stationary GRS sensor. Our analysis showed that the current method for biomass water content correction is appropriate for our maize and soybean field but that the ratio of soil mass attenuation to water mass attenuation used in the theoretical equation must be adjusted to satisfactorily describe the field data. We propose a calibration equation with two free parameters: the theoretical 40K intensity in dry soil and a, which creates an "effective" mass attenuation ratio. Based on statistical analyses of our data set, we recommend calibrating the GRS sensor for SWC estimation using 10 profiles within the footprint and 5 calibration sampling campaigns to achieve a cross-validation root mean square error below 0.035 g g−1. [ABSTRACT FROM AUTHOR]

The application of statistical estimation theory to Hong–Ou–Mandel interferometry led to enticing results in terms of the detection limit for photon reciprocal delay and polarisation measurement. In the following paper, a fully fibre-coupled setup operating in the telecom wavelength region proves to achieve, for the first time, in common-path Hong–Ou–Mandel-based interferometry, a detection limit for photon phase delay at the zeptosecond scale. The experimental results are then framed in a theoretical model by calculating the Cramer–Rao bound (CRB) and, after comparison with the obtained experimental results, it is shown that our setup attains the optimal measurement, nearly saturating CRB. [ABSTRACT FROM AUTHOR]

Object detection and tracking are pivotal tasks in machine learning, particularly within the domain of computer vision technologies. Despite significant advancements in object detection frameworks, challenges persist in real-world tracking scenarios, including object interactions, occlusions, and background interference. Many algorithms have been proposed to carry out such tasks; however, most struggle to perform well in the face of disturbances and uncertain environments. This research proposes a novel approach by integrating the You Only Look Once (YOLO) architecture for object detection with a robust filter for target tracking, addressing issues of disturbances and uncertainties. The YOLO architecture, known for its real-time object detection capabilities, is employed for initial object detection and centroid location. In combination with the detection framework, the sliding innovation filter, a novel robust filter, is implemented and postulated to improve tracking reliability in the face of disturbances. Specifically, the sliding innovation filter is implemented to enhance tracking performance by estimating the optimal centroid location in each frame and updating the object's trajectory. Target tracking traditionally relies on estimation theory techniques like the Kalman filter, and the sliding innovation filter is introduced as a robust alternative particularly suitable for scenarios where a priori information about system dynamics and noise is limited. Experimental simulations in a surveillance scenario demonstrate that the sliding innovation filter-based tracking approach outperforms existing Kalman-based methods, especially in the presence of disturbances. In all, this research contributes a practical and effective approach to object detection and tracking, addressing challenges in real-world, dynamic environments. The comparative analysis with traditional filters provides practical insights, laying the groundwork for future work aimed at advancing multi-object detection and tracking capabilities in diverse applications. [ABSTRACT FROM AUTHOR]

Sample selection is one of the most important factors in estimating the unknown parameters of distributions, as it saves time, saves effort, and gives the best results. One of the challenges is deciding on a suitable distribution estimate technique and adequate sample selection to provide the best results in comparison with earlier research. The method of moments (MOM) was decided on to estimate the unknown parameters of the Gumbel distribution, but with four changes in the sample selection, which were simple random sample (SRS), ranked set sampling (RSS), maximum ranked set sampling (MRSS), and ordered maximum ranked set sampling (OMRSS) techniques, due to small sample sizes. The MOM is a traditional method for estimation, but it is difficult to use when dealing with RSS modification. RSS modification techniques were used to improve the efficiency of the estimators based on a small sample size compared with the usual SRS estimator. A Monte Carlo simulation study was carried out to compare the estimates based on different sampling. Finally, two datasets were used to demonstrate the adaptability of the Gumbel distribution based on the different sampling techniques. [ABSTRACT FROM AUTHOR]

Each year, numerous tornadoes occur in forested regions of the United States. Due to the substantial number of fallen trees and accessibility issues, many of these tornadoes remain poorly documented and evaluated. The process of documenting tree damage to assess tornado intensity is known as the treefall method, an established and reliable technique for estimating near-surface wind speed. Consequently, the demand for documenting fallen trees has increased in recent years. However, the treefall method proves to be extremely expensive and time-consuming, requiring a laborious assessment of each treefall instance. This research proposes a novel approach to evaluating treefall in large, forested regions using deep learning-based automated detection and advanced image processing techniques. The developed treefall method relies on high-resolution aerial imagery from a damaged forest and involves three main steps: (1) instance segmentation detection, (2) estimating tree taper and predicting fallen tree directions, and (3) obtaining subsampled treefall vector results indicating the predominant flow direction in geospatial coordinates. To demonstrate the method's effectiveness, the algorithm was applied to a tornado track rated EF-4, which occurred on 10 December 2021, cutting through the Land Between the Lakes National Recreation Area in Kentucky. Upon observation of the predicted results, the model is demonstrated to accurately predict the predominant treefall angles. This deep-learning-based treefall algorithm has the potential to speed up data processing and facilitate the application of treefall methods in tornado evaluation. [ABSTRACT FROM AUTHOR]

Parameter estimation is one of the most important tasks in statistics, and is key to helping people understand the distribution behind a sample of observations. Traditionally, parameter estimation is done either by closed-form solutions (e.g., maximum likelihood estimation for Gaussian distribution) or by iterative numerical methods such as the Newton–Raphson method when a closed-form solution does not exist (e.g., for Beta distribution). In this paper, we propose a transformer-based approach to parameter estimation. Compared with existing solutions, our approach does not require a closed-form solution or any mathematical derivations. It does not even require knowing the probability density function, which is needed by numerical methods. After the transformer model is trained, only a single inference is needed to estimate the parameters of the underlying distribution based on a sample of observations. In the empirical study, we compared our approach with maximum likelihood estimation on commonly used distributions such as normal distribution, exponential distribution and beta distribution. It is shown that our approach achieves similar or better accuracy as measured by mean-square-errors. [ABSTRACT FROM AUTHOR]

Ransomware attacks have emerged as a significant threat to critical data and systems, extending beyond traditional computers to mobile and IoT/Cyber–Physical Systems. This study addresses the need to detect early ransomware behavior when only limited data are available. A major step for training such a detection model is choosing a set of relevant and non-redundant features, which is challenging when data are scarce. Therefore, this paper proposes an incremental mutual information-selection technique as a method for selecting the relevant features at the early stages of ransomware attacks. It introduces an adaptive feature-selection technique that processes data in smaller, manageable batches. This approach lessens the computational load and enhances the system's ability to quickly adapt to new data arrival, making it particularly suitable for ongoing attacks during the initial phases of the attack. The experimental results emphasize the importance of the proposed technique in estimating feature significance in limited data scenarios. Such results underscore the significance of the incremental approach as a proactive measure in addressing the escalating challenges posed by ransomware. [ABSTRACT FROM AUTHOR]

Noise removal is a critical stage in the preprocessing of point clouds, exerting a significant impact on subsequent processes such as point cloud classification, segmentation, feature extraction, and 3D reconstruction. The exploration of methods capable of adapting to and effectively handling the noise in point clouds from real-world outdoor scenes remains an open and practically significant issue. Addressing this issue, this study proposes an adaptive kernel approach based on local density and global statistics (AKA-LDGS). This method constructs the overall framework for point cloud denoising using Bayesian estimation theory. It dynamically sets the prior probabilities of real and noise points according to the spatial function relationship, which varies with the distance from the points to the center of the LiDAR. The probability density function (PDF) for real points is constructed using a multivariate Gaussian distribution, while the PDF for noise points is established using a data-driven, non-parametric adaptive kernel density estimation (KDE) approach. Experimental results demonstrate that this method can effectively remove noise from point clouds in real-world outdoor scenes while maintaining the overall structural features of the point cloud. [ABSTRACT FROM AUTHOR]

Estimation of the region of attraction of the power system using sum of squares (SOS) programming theory is investigated in this paper. Firstly, the Taylor expansion formula is applied to explore the inherent polynomial structure of the swing equation. The single machine projection equation for a multi-machine system is proposed based on the amplitude characteristic of the rotor angle response in decoupled space. Secondly, the theory of SOS programming originating from the polynomial system is derived, and the theory about estimation of the region of attraction for the differential algebraic system is summarized. Thirdly, the method for estimating the region of attraction for the polynomial swing equation based on a V-S two-stage iterative procedure is proposed. Finally, a single machine infinite bus power system, an IEEE 3-machine power system, and an IEEE 4-machine power system are employed to validate the effectiveness and accuracy of the proposed method and analysis. [ABSTRACT FROM AUTHOR]

Generative models have recently received a lot of attention. However, a challenge with such models is that it is usually not possible to compute the likelihood function, which makes parameter estimation or training of the models challenging. The most commonly used alternative strategy is called likelihood-free estimation, based on finding values of the model parameters such that a set of selected statistics have similar values in the dataset and in samples generated from the model. However, a challenge is how to select statistics that are efficient in estimating unknown parameters. The most commonly used statistics are the mean vector, variances, and correlations between variables, but they may be less relevant in estimating the unknown parameters. We suggest utilizing Tukey depth contours (TDCs) as statistics in likelihood-free estimation. TDCs are highly flexible and can capture almost any property of multivariate data, in addition, they seem to be as of yet unexplored for likelihood-free estimation. We demonstrate that TDC statistics are able to estimate the unknown parameters more efficiently than mean, variance, and correlation in likelihood-free estimation. We further apply the TDC statistics to estimate the properties of requests to a computer system, demonstrating their real-life applicability. The suggested method is able to efficiently find the unknown parameters of the request distribution and quantify the estimation uncertainty. [ABSTRACT FROM AUTHOR]

We provide a formal statistical theory of consistent estimation of the set of all arbitrage portfolios that meet the description of being a stochastic arbitrage opportunity. Two empirical likelihood ratio tests are developed: one for the null that a given arbitrage portfolio is qualified, and another for the alternative that the portfolio is not qualified. Apart from considering generalized concepts and hypotheses based on multiple host portfolios, the statistical assumption framework is also more general than in earlier studies that focused on special cases with a single benchmark portfolio. Various extensions and generalizations of the theory are discussed. A Monte Carlo simulation study shows promising statistical size and power properties for testing the null, for representative data dimensions. The results of an empirical application illustrate the importance of selecting a proper blocking structure and moment estimation method. [ABSTRACT FROM AUTHOR]

Chlorophyll a and b content (Cab) and leaf area index (LAI) are two key parameters of crops, and their quantitative inversions are important for growth monitoring and the field management of wheat. However, due to the close correlation between the spectral signals of these two parameters and the effects of soil and atmospheric conditions, as well as modeling errors, synchronous retrieval of LAI and Cab from remote sensing data is still a challenging task. In a previous study, we introduced the optimal estimation theory and established the inversion framework by coupling the PROSAIL (PROSPECT + SAIL) model with the unified linearized vector radiative transfer model (UNL-VRTM). The framework fully utilizes the simulated radiance spectra for synchronous retrieval of Cab and LAI at the UAV observation scale and has good convergence and self-consistency. In this study, based on this inversion framework, synchronized retrieval of Cab and LAI was carried out by real wheat UAV observation data and validated with the ground-measured data. By comparing with the empirical statistical model constructed by the PROSAIL model and coupled model, least squares support vector machine (LSSVM), and random forest (RF), the proposed method has the highest accuracy of Cab and LAI estimated from UAV multispectral data (for Cab, R2 = 0.835, RMSE = 14.357; for LAI, R2 = 0.892, RMSE = 0.564). Our proposed method enables the fast and efficient estimation of Cab and LAI in multispectral data without prior measurements and training. [ABSTRACT FROM AUTHOR]