Parameter Estimation Research Articles

Analysing the Symmetric GARCH model across different sample sizes

In the world of econometrics, the GARCH model has the desired ability to model the changing variance (heteroskedasticity) of a financial time series. Therefore, the primary goal of this paper is to investigate changes in volatility, parameter estimates and forecasting error across different window lengths as this may indicate an appropriate sample size to use when fitting an S-GARCH model. After examining the 6489 1-day log-returns on the FTSE/JSE-ALSI between 27 December 1995 and 15 December 2021, an average estimate for volatility of 0.193 670 was calculated. Furthermore, given that the rolling window methodology was applied across 20 different window lengths, a total of 90 000 S-GARCH models were fit to the data. Among others, key results include volatility estimates across most window lengths taking longer to settle after the Global Financial Crisis (GFC) than after the COVID-19 pandemic. In terms of parameter estimates, values for α and β under a window length of 100 trading days were often calculated infinitely close to zero and one respectively, indicating a strong possibility of the optimising algorithm arriving at local maxima of the likelihood function. With the exceptionally low p-values under the Jarque-Bera and Kolmogorov-Smirnov tests, substantial motivation was provided for the use of the Student's t-distribution when fitting GARCH models. Given the results obtained, it is clear that a window length between 100 and 500 can produce fitted models that are unstable and that a window length between 1000 and 2000 may be too large to account for market shocks.

Triaxial behavior and microstructural insights of loose sandy soil stabilized with alkali activated slag

This study investigates the mechanical and microstructural properties of loose sandy soil stabilized with alkali-activated Ground Granulated Blast Furnace Slag (GGBFS). To examine the effects of varying GGBFS contents, curing times, and confining pressures on mechanical behavior, undrained triaxial and unconfined compressive strength (UCS) tests were conducted. Microstructural analyses using FE-SEM, EDX, and FTIR were performed to elucidate the nature and development of cementation. The results of mechanical behavior demonstrate that even with limited GGBFS content (1–6%), the treated samples exhibited significant improvements in strength, stiffness, and energy absorption, underscoring the efficiency of alkali-activated GGBFS as a soil stabilizer. Moreover, mechanical parameters from triaxial tests revealed a nearly constant internal friction angle with increasing GGBFS content and curing duration, while cohesion showed remarkable enhancement. A strong linear correlation between UCS and cohesion was also identified, enabling cost-effective estimation of shear strength parameters. These findings highlight the potential of alkali-activated GGBFS for improving granular soils, offering practical implications for sustainable geotechnical applications, particularly in road construction.

An EM algorithm for fitting matrix-variate normal distributions on interval-censored and missing data

Matrix-variate distributions are powerful tools for modeling three-way datasets that often arise in longitudinal and multidimensional spatio-temporal studies. However, observations in these datasets can be missing or subject to some detection limits because of the restriction of the experimental apparatus. Here, we develop an efficient EM-type algorithm for maximum likelihood estimation of parameters, in the context of interval-censored and/or missing data, utilizing the matrix-variate normal distribution. This algorithm provides closed-form expressions that rely on truncated moments, offering a reliable approach to parameter estimation under these conditions. Results obtained from the analysis of both simulated data and real case studies concerning water quality monitoring are reported to demonstrate the effectiveness of the proposed method.

Dynamic to Static Model Comparison and Hybrid Metaheuristic Optimization in Induction Motor Parameter Estimation

Dynamic to Static Model Comparison and Hybrid Metaheuristic Optimization in Induction Motor Parameter Estimation

Bayesian Fourier coefficient inversion for gravity-induced stress parameters in tilted transversely isotropic gas-bearing reservoirs

Field observations and core data reveal that natural fractures may not be perfectly vertical but are commonly inclined, yielding an effective tilted transversely isotropic (TTI) medium. Neglecting TTI symmetry can lead to erroneous stress prediction results, which are important for hydrocarbon exploration and development. We have developed a Bayesian Fourier coefficient (FC) inversion approach to estimate gravity-induced stress parameters in TTI media, specifically horizontal stress and the differential horizontal stress ratio (DHSR). The gas-bearing reservoir with dipping fractures is modeled as a linearly elastic, homogeneous TTI material. Under the assumption of no lateral strain, we combine fracture-effective medium models with the generalized Hook’s law to establish the relationship between gravity-induced stress parameters and TTI elastic and fracture parameters. Based on seismic scatter theory, we derive a linearized PP-wave reflection coefficient and corresponding FC expressions parameterized by P- and S-wave moduli, density, fracture density, and fracture dip in TTI media. Furthermore, we present a Bayesian FC inversion constrained by a joint multivariable Cauchy prior model to estimate these model parameters, which are then used to calculate gravity-induced stress parameters. A synthetic example demonstrates that Bayesian FC inversion under the TTI model assumption produces more reliable estimates of gravity-induced stress parameters compared to those obtained under the horizontal transversely isotropic (HTI) model assumption. Additionally, a real data set from a gas-bearing reservoir is employed to demonstrate the feasibility of our method. Results indicate that our method yields reasonable estimates of gravity-induced stress parameters with good lateral continuity. The proposed method could aid in identifying optimal zones for hydraulic fracturing of a subterranean formation with TTI symmetry.

A non parametric estimation method using an orthogonal function system

When modeling uncertain systems with uncertain differential equations (UDEs), it is a common thing that the relative function forms are unknown. In such cases, non parametric estimation based on observed data can be used to approximate the relative functions. This article presents a non parametric estimation method for nonautonomous UDEs utilizing an orthogonal function system, which proves to be beneficial in simulating uncertain non autonomous dynamical systems in practical applications. The reliability of the proposed method is validated through various examples. The approximation effects of different orthogonal basis functions are compared. Furthermore, the article illustrates the availability of the proposed method by using the closing price data of four stocks.

Biophysical modeling and experimental analysis of the dynamics of C. elegans body-wall muscle cells.

This study combines experimental techniques and mathematical modeling to investigate the dynamics of C. elegans body-wall muscle cells. Specifically, by conducting voltage clamp and mutant experiments, we identify key ion channels, particularly the L-type voltage-gated calcium channel (EGL-19) and potassium channels (SHK-1, SLO-2), which are crucial for generating action potentials. We develop Hodgkin-Huxley-based models for these channels and integrate them to capture the cells' electrical activity. To ensure the model accurately reflects cellular responses under depolarizing currents, we develop a parallel simulation-based inference method for determining the model's free parameters. This method performs rapid parallel sampling across high-dimensional parameter spaces, fitting the model to the responses of muscle cells to specific stimuli and yielding accurate parameter estimates. We validate our model by comparing its predictions against cellular responses to various current stimuli in experiments and show that our approach effectively determines suitable parameters for accurately modeling the dynamics in mutant cases. Additionally, we discover an optimal response frequency in body-wall muscle cells, which corresponds to a burst firing mode rather than regular firing mode. Our work provides the first experimentally constrained and biophysically detailed muscle cell model of C. elegans, and our analytical framework combined with robust and efficient parametric estimation method can be extended to model construction in other species.

Statistical inferences of reliability and order-restricted nano-droplet rebound by comparative kumaraswamy populations based on balanced joint progressive censoring

Abstract The rebounded nano-droplet (RND) is one of the important issues in creating defective coatings. The RND depends on many factors such as angle of droplet impact and velocity. Reliability model can be considered to determine the probability of surface defect under two impact angles in the RND data. In this paper, we have delved into the application of reliability and order-restricted (ORe) estimation methods for two Kumaraswamy populations in the RND data. The study kicks off by evaluating maximum likelihood and Bayesian estimates of the reliability parameter and order-restricted parameters in presence of balanced joint progressive censored data. Bayes estimations for reliability and ORe parameters under two different loss functions are investigated with the Metropolis-Hastings technique and Lindley’s approach. To evaluate order-restricted Bayesian estimates, ordered Beta-Gamma prior is considered. The asymptotic, Bootstrapping and Bayesian bounds are also computed. A thorough simulation analysis is demonstrated to assess the performance of the supplied approaches across various sample sizes. The usefulness of the techniques is illustrated using RND data to prove their versatility in practical applications.

Assumption-lean regression for non-negative response via variational representation

We present a novel estimator for regression parameters that does not require any assumptions about the conditional distribution family of the response variable, except for non-negativity. This estimator is particularly useful for handling semi-continuous, zero-inflated, and proportional data, eliminating the need for complex models and simplifying the inference process. The estimator is unaffected by over-under dispersion, heavy tails or other problems related to the incorrect assumptions about the response distribution. In addition, the asymptotic properties of the estimator do not depend on the underlying conditional distribution. Apart from that, our method does not involve kernel-based estimation and is, therefore, free from issues related to smoothing parameter selection. The R code for implementing the method and reproducing the results is available in the supplementary materials

A comparative study of the performance of ten metaheuristic algorithms for parameter estimation of solar photovoltaic models

This study conducts a comparative analysis of the performance of ten novel and well-performing metaheuristic algorithms for parameter estimation of solar photovoltaic models. This optimization problem involves accurately identifying parameters that reflect the complex and nonlinear behaviours of photovoltaic cells affected by changing environmental conditions and material inconsistencies. This estimation is challenging due to computational complexity and the risk of optimization errors, which can hinder reliable performance predictions. The algorithms evaluated include the Crayfish Optimization Algorithm, the Golf Optimization Algorithm, the Coati Optimization Algorithm, the Crested Porcupine Optimizer, the Growth Optimizer, the Artificial Protozoa Optimizer, the Secretary Bird Optimization Algorithm, the Mother Optimization Algorithm, the Election Optimizer Algorithm, and the Technical and Vocational Education and Training-Based Optimizer. These algorithms are applied to solve four well-established photovoltaic models: the single-diode model, the double-diode model, the triple-diode model, and different photovoltaic module models. The study focuses on key performance metrics such as execution time, number of function evaluations, and solution optimality. The results reveal significant differences in the efficiency and accuracy of the algorithms, with some algorithms demonstrating superior performance in specific models. The Friedman test was utilized to rank the performance of the various algorithms, revealing the Growth Optimizer as the top performer across all the considered models. This optimizer achieved a root mean square error of 9.8602187789E−04 for the single-diode model, 9.8248487610E−04 for both the double-diode and triple-diode models and 1.2307306856E−02 for the photovoltaic module model. This consistent success indicates that the Growth Optimizer is a strong contender for future enhancements aimed at further boosting its efficiency and effectiveness. Its current performance suggests significant potential for improvement, making it a promising focus for ongoing development efforts. The findings contribute to the understanding of the applicability and performance of metaheuristic algorithms in renewable energy systems, providing valuable insights for optimizing photovoltaic models.

Estimation of stationary and non-stationary moving average processes in the correlation domain.

This paper introduces a novel approach for the offline estimation of stationary moving average processes, further extending it to efficient online estimation of non-stationary processes. The novelty lies in a unique technique to solve the autocorrelation function matching problem leveraging that the autocorrelation function of a colored noise is equal to the autocorrelation function of the coefficients of the moving average process. This enables the derivation of a system of nonlinear equations to be solved for estimating the model parameters. Unlike conventional methods, this approach uses the Newton-Raphson and Levenberg-Marquardt algorithms to efficiently find the solution. A key finding is the demonstration of multiple symmetrical solutions and the provision of necessary conditions for solution feasibility. In the non-stationary case, the estimation complexity is notably reduced, resulting in a triangular system of linear equations solvable by backward substitution. For online parameter estimation of non-stationary processes, a new recursive formula is introduced to update the sample autocorrelation function, integrating exponential forgetting of older samples to enable parameter adaptation. Numerical experiments confirm the method's effectiveness and evaluate its performance compared to existing techniques.

Establishing measurement equivalence of a youth-reported parental monitoring measure across sex, race/ethnicity, and intersectional identity.

Parental monitoring is a robust family-level predictor of youth well-being. Identification of variations by gender and/or race/ethnicity in parental monitoring has important implications for tailoring parenting practices. However, valid comparisons can only be conducted if cross-subpopulation measurement equivalence is established. Although measurement equivalence testing is widely used, it rarely (a) assesses intersectional identity (i.e., identity reflecting multiple factors such as race/ethnicity and gender) or (b) involves generating scores adjusted for nonequivalence. This is the first known study to do both with a parental monitoring measure. Measurement equivalence by sex (proxy for gender), race/ethnicity, and intersectional identity (sex by race/ethnicity) was assessed in the five-item Parental Monitoring Questionnaire administered to middle-school-aged Black, Latinx, and White girls and boys. Data were drawn from the second follow-up of the Adolescent Brain Cognitive Development Study (n = 9,082; 47.5% female, 52.5% male; 15.5% Black, 22.9% Latinx, 61.6% White). Moderated nonlinear factor analysis was used to identify group differences in item-level (intercepts and loadings) and factor-level (mean and variance) parameter estimates for a latent parental monitoring variable and subsequently to generate factor scores accounting for measurement nonequivalence. Intercepts or loadings for four items differed by sex, race/ethnicity, and/or intersectional identity. Factor mean and variance differed by race/ethnicity. Comparisons across the six groups using adjusted (factor) scores differed substantially from comparisons using unadjusted scores, underscoring the impact of systematic measurement bias on the valid assessment of parental monitoring in girls and boys who identify with these racial/ethnic groups. (PsycInfo Database Record (c) 2025 APA, all rights reserved).

Analysis of Spatial Dependence Using the Wave Covariance Structure in Soybean Productivity Associated With Soil Attributes

Objective: The aim of this study is to investigate the interaction between soybean yield and the physical and chemical attributes of the soil, with the goal of developing techniques used in precision agriculture to increase productivity, reduce costs, and minimize environmental impacts. Theoretical Framework: This work is based on the principles of geostatistics, particularly the Wave spatial dependence structure, which is used to model the semivariance function when it exhibits the "hole effect." Method: The research involves a study of soybean yield conducted in a commercial area of 172.04 hectares during the 2022/2023 growing season. Calcium (Ca), copper (Cu), acidity (pH), potassium (K), phosphorus (P), and soil penetration resistance (SPR) levels were used as covariates to explain soybean yield (Prod) through a Gaussian linear spatial model (GLSM). The Thin Plate Spline (TPS) interpolation method was applied to interpolate the physical and chemical soil attributes, considered as fixed covariates, while soybean yield was interpolated using External Drift Kriging (EDK) based on the GLSM. Additionally, techniques for local influence diagnostics were developed and applied to identify observations impacting the results, utilizing the Wave geostatistical model. Results and Discussion: The results revealed that the generated soybean yield map provides important information for defining management zones, optimizing input use, and promoting greater profitability. Furthermore, the removal of locally influential observations alters parameter estimation, the significance of parameters associated with the covariates in the GLSM, and the construction of the interpolated soybean yield map. In the discussion, the results were contextualized in light of the theoretical framework, emphasizing the relevance of the Wave structure and the integration of interpolation techniques in the study of spatial variability. Research Implications: The practical and theoretical implications of this research include improvements in agricultural management by providing support for the delineation of management zones that balance productivity and sustainability. Theoretically, the study contributes to advancing the use of geostatistical models, such as the Wave model, in the analysis of spatial data in precision agriculture. Originality/Value: This study contributes to the literature by exploring the application of the Wave model in an agricultural context, combined with the use of interpolation techniques and local influence diagnostics. Its originality lies in the methodological combination of spatial interpolators and the development of local influence techniques.

A Bayesian Joint Model of Multiple Nonlinear Longitudinal and Competing Risks Outcomes for Dynamic Prediction in Multiple Myeloma: Joint Estimation and Corrected Two-Stage Approaches.

Predicting cancer-associated clinical events is challenging in oncology. In Multiple Myeloma (MM), a cancer of plasma cells, disease progression is determined by changes in biomarkers, such as serum concentration of the paraprotein secreted by plasma cells (M-protein). Therefore, the time-dependent behavior of M-protein and the transition across lines of therapy (LoT), which may be a consequence of disease progression, should be accounted for in statistical models to predict relevant clinical outcomes. Furthermore, it is important to understand the contribution of the patterns of longitudinal biomarkers, upon each LoT initiation, to time-to-death or time-to-next-LoT. Motivated by these challenges, we propose a Bayesian joint model for trajectories of multiple longitudinal biomarkers, such as M-protein, and the competing risks of death and transition to the next LoT. Additionally, we explore two estimation approaches for our joint model: simultaneous estimation of all parameters (joint estimation) and sequential estimation of parameters using a corrected two-stage strategy aiming to reduce computational time. Our proposed model and estimation methods are applied to a retrospective cohort study from a real-world database of patients diagnosed with MM in the US from January 2015 to February 2022. We split the data into training and test sets in order to validate the joint model using both estimation approaches and make dynamic predictions of times until clinical events of interest, informed by longitudinally measured biomarkers and baseline variables available up to the time of prediction.

A phylogenetic approach to delimitate species in a probabilistic way.

Different species concepts and their associated criteria have been used to delimit species boundaries, such as the absence of gene flow for the biological species concept and the presence of morphological distinction for the morphological species concept. The need for different delimitation criteria largely reflects the fact that species are generated under various speciation mechanisms. A key question is how to make species delimitation consistent in a species group, especially when we want to delimit the species boundaries over many newly discovered evolutionary lineages and add these new lineages into a comparative analysis. Instead of forcing a single definition of 'species', we can acknowledge different delimitation criteria by modelling how fast lineages in a species group evolve to meet these criteria along a phylogenetic tree. This study presents such a new model and a new delimitation approach that calculates the probability of each possible species identity of a lineage. We use simulations to show that our likelihood function gives accurate estimates of parameters in the model and our approach have high power to correctly identify species identities. We apply the approach to lineages in two real species groups that already have genomic and morphological evidence for their species identities. Our approach gives consistent inference of species identities with these existing pieces of evidence. We also demonstrate how to use our model to test a popular hypothesis about speciation process across all lineages in a species group and discuss further extension of the model to study speciation.

SA-Net: Leveraging Spatial Correlations Spatial-Aware Net for Multi-Perspective Robust Estimation Algorithm

Robust estimation aims to provide accurate and reliable parameter estimations, particularly when data are affected by noise or outliers. Traditional methods like random sample consensus (RANSAC) struggle with handling outliers because they treat all observations as equally important. A series of advanced deep learning methods have recently emerged, which use deep learning techniques to estimate the probability of each sample being selected, prioritizing higher confidence for observations that are closer to the ground truth model. However, optimizing solely based on proximity to the ground truth model does not guarantee higher-quality estimations. Meanwhile spatial relationships between the data points in the minimum sampled set also influence the accuracy of the final estimated model. To address these issues, we propose Spatial-Aware Net (SA-Net), a dual-branch neural network that integrates both confidence and spatial encodings. SA-Net employs a confidence distribution encoder to learn the confidence distribution and a spatial distribution encoder to capture spatial correlations between point features. By incorporating multi-perspective sampling, the minimum sample set can be selected based on different spatial distributions in the output of the neural network, and applying Chamfer Loss constraints, our approach improves model optimization and effectively mitigates suboptimal solutions. Extensive experiments demonstrate that SA-Net outperforms the state of the art across various real-world robust estimation tasks.

Estimation of gamma distribution parameters

Statements of problems of statistical analysis of data with a gamma distribution are related to classical mathematical statistics. Oddly enough, not all alone were solved within the framework of parametric statistics, which was at the forefront of the development of statistical science in the first third of the 20th century. As with the beta distribution, gaps need to be filled. This is necessary because the gamma distribution is currently widely used in theoretical and applied work. An example is GOST 11.011–83 «Applied statistics. Rules for determining estimates and confidence limits for gamma distribution parameters». The standard gamma distribution is determined by the shape parameter. When switching to a scale-shift family, scale and translation parameters are added. Seven formulations of parameter estimation problems are considered, since each of the three parameters can be either unknown or known. For each of the formulations, the estimates of the method of moments and their asymptotic variances are found. For a known shift parameter, maximum likelihood estimates are obtained. One-step estimates, asymptotically equivalent to maximum likelihood estimates, are used for an unknown shift parameter. The presence of measurement errors affects the accuracy of parameter estimates when applying certain calculation algorithms. In GOST 11.011–83, based on the interval data model, rules are given for choosing an estimation method for unknown shape and scale parameters and a known shift parameter. During the development of GOST 11.011–83, problems were identified, for the solution of which new methods from a scientific point of view were proposed. Further development of new scientific results obtained in the course of solving a practical problem (development of GOST 11.011–83) led to the creation of new scientific directions. We are talking about the statistics of interval data, as well as one-step estimates. To date, the statistics of interval data as a branch of mathematical statistics is quite developed and covers all the main areas of statistical methods. It is an important part of systemic fuzzy interval mathematics.

Transformer Architecture for Micromotion Target Detection Based on Multi-Scale Subaperture Coherent Integration

In recent years, long-time coherent integration techniques have gained significant attention in maneuvering target detection due to their ability to effectively enhance the signal-to-noise ratio (SNR) and improve detection performance. However, for space targets, challenges such as micromotion phenomena and complex scattering characteristics make envelope alignment and phase compensation difficult, thereby limiting integration gain. To address these issues, in this study, we conducted an in-depth analysis of the echo model of cylindrical space targets (CSTs) based on different types of scattering centers. Building on this foundation, the multi-scale subaperture coherent integration Transformer (MsSCIFormer) was proposed, which integrates MsSCI with a Transformer architecture to achieve precise detection and motion parameter estimation of space targets in low-SNR environments. The core of the method lies in the introduction of a convolutional neural network (CNN) feature extractor and a dual-attention mechanism, covering both intra-subaperture attention (Intra-SA) and inter-subaperture attention (Inter-SA). This design efficiently captures the spatial distribution and motion patterns of the scattering centers of space targets. By aggregating multi-scale features, MsSCIFormer significantly enhances the detection performance and improves the accuracy of motion parameter estimation. Simulation experiments demonstrated that MsSCIFormer outperforms traditional moving target detection (MTD) methods and other deep learning-based algorithms in both detection and estimation tasks. Furthermore, each module proposed in this study was proven to contribute positively to the overall performance of the network.

Stability and optimal control of a cholera transmission model with waning vaccine-induced immunity and phage–vibrio interactions

Cholera is still a significant worldwide health concern that continues to affect many regions around the world, posing a persistent threat to human health with its severity unabated. In this paper, a cholera transmission model with waning vaccine-induced immunity and phage–vibrio interactions is investigated. The two important thresholds for distinguishing whether cholera is epidemic or not are obtained, and fundamental properties of the system are studied. The global asymptotic stability of the system is analyzed in detail by constructing suitable Lyapunov functions. To seek the suitable strategies for preventing and controlling cholera infection, we introduced four time-dependent controls into the model to assess the effectiveness of each strategy by applying Pontryagin’s maximum principle. In addition, using the reported cholera case numbers in Yemen, we perform parameter estimation and data fitting, further, a sensitivity analysis of thresholds is conducted.

Second-order skewness of the maximum likelihood estimators in symmetric nonlinear regressions

The symmetric nonlinear regression model encompasses a wide class of models like the nonlinear normal, Student-t, and power exponential regression models, among others. We provide a simple closed-form expression, in matrix form, for the second-order skewness of the maximum likelihood estimators of the regression parameters, as well as a simple expression for the second-order skewness of the maximum likelihood estimator of the scale parameter in the symmetric nonlinear regression model. The matrix formula involves simple operations on matrices and vectors, which is quite suitable for computer implementation. We present Monte Carlo simulations to verify the behaviour of the second-order skewness in small-sized samples in this class of regression models. Real data applications are also considered to show the practical importance of our results.