Parameter Estimation Procedure Research Articles

Quantile regression based on the counting process approach under dependent truncated data

This paper focuses on analysing dependent truncated data. To address this, we draw inspiration from some literatures and employ the Archimedean copula model to establish a correlation between the truncation time and the survival time. Building on this, we refer to the U-statistics and the copula-graphic method to estimate the association parameter and the survival function. Subsequently, we proceed to build a quantile regression model and develop an estimation procedure for the quantile regression parameters using the counting process method. To further validate the efficacy of our approach, we conduct simulation experiments with specific settings of quantiles and correlations. In conclusion, we apply our method to analyse two datasets: one pertaining to HIV transfusion infections and the other related to retirement centres.

Parameter characterization of PEM fuel cell mathematical models using an orthogonal learning-based GOOSE algorithm

In this paper, a new method is designed to effectively determine the parameters of proton exchange membrane fuel cells (PEMFCs), i.e., ξ1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\xi }_{1}$$\\end{document}, ξ2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\xi }_{2}$$\\end{document}, ξ3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\xi }_{3}$$\\end{document}, ξ4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\xi }_{4}$$\\end{document}, RC\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${R}_{\ ext{C}}$$\\end{document}, λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda$$\\end{document}, and b\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$b$$\\end{document}. The fuel cells (FCs) involve multiple variable quantities with complex non-linear behaviours, demanding accurate modelling to ensure optimal operation. An accurate model of these FCs is essential to evaluate their performance accurately. Furthermore, the design of the FCs significantly impacts simulation studies, which are crucial for various technological applications. This study proposed an improved parameter estimation procedure for PEMFCs by using the GOOSE algorithm, which was inspired by the adaptive behaviours found in geese during their relaxing and foraging times. The orthogonal learning mechanism improves the performance of the original GOOSE algorithm. This FC model uses the root mean squared error as the objective function for optimizing the unknown parameters. In order to validate the proposed algorithm, a number of experiments using various datasets were conducted and compared the outcomes with different state-of-the-art algorithms. The outcomes indicate that the proposed GOOSE algorithm not only produced promising results but also exhibited superior performance in comparison to other similar algorithms. This approach demonstrates the ability of the GOOSE algorithm to simulate complex systems and enhances the robustness and adaptability of the simulation tool by integrating essential behaviours into the computational framework. The proposed strategy facilitates the development of more accurate and effective advancements in the utilization of FCs.

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This paper investigates a novel category of probability distributions and a specific member within this category. We have formulated a new family of trigonometric distributions by utilizing the odds ratio derived from the distribution function of a base distribution. This newly devised distribution family termed the “Sine pie-power odd-G family” of distributions, is constructed through a transformation involving the sine function. The paper presents an overview of the fundamental characteristics inherent to this proposed distribution family. Using the Weibull distribution as a base reference, we have introduced a member belonging to the proposed distribution family. This member demonstrates various hazard functions such as j, reverse-j, increasing, decreasing, or bathtub shapes. The paper examines essential statistical attributes of this newly introduced distribution. The estimation of the distribution’s parameters is carried out via the maximum likelihood estimation method. The accuracy of the parameter estimation procedure is validated through Monte Carlo simulations. The outcomes of these simulations reveal a reduction in biases and mean square errors as sample sizes increase, even for small samples. Two sets of real-engineering data are considered to demonstrate the proposed distribution’s applicability. The performance of the suggested distribution is evaluated using some model selection criteria and goodness-of-fit test statistics. Empirical evidence from these evaluations substantiates that the proposed model outperforms six existing models.

Cyclohexane dehydrogenation: Critical evaluation of parameter estimation procedures for kinetic modeling

In the present paper a comparison between different parameter estimation procedures commonly used for the kinetic modeling of chemical reaction is performed, based on experimental measurements of the cyclohexane dehydrogenation to benzene. The obtained results show that, when the Arrhenius equation parameters are estimated from estimates of the rate constant taken at different temperatures, larger parameter uncertainties and correlations are obtained, particularly when the variances of the experimental measurements are not considered during the estimation process. It is also observed that an apparent kinetic compensation effect occurs when the experimental data are separated according to the inlet partial pressure and catalyst mass in the reactor, mainly due to the existing and unavoidable experimental uncertainties and parameter correlations. Additionally, it is shown that larger uncertainties and correlations are obtained when the parameter estimates are computed through the differential method, which can also lead to poorer model predictions of the experimental data. Finally, it is shown that the simultaneous one-step estimation of all model parameters through the integral method and considering the available experimental uncertainties can provide the most accurate parameter estimates, making use of mathematical expressions that describe how variances of the experimental measurements depend on the experimental conditions.

Migration and Remittances in Senegal: Effect on Households Members Left Behind

ABSTRACT This article investigates how migration and remittances affect labor market, and how remittances influence human capital in Senegal. Using parametric and nonparametric estimation procedures for the correction of selection bias, the results reveal that migration and remittances reduce labor market participation of household members left behind, and that remittances increase human capital development of the left-behind. The study suggests that both the migration status and the level of remittances are relevant in understanding labor market participation and human capital formation.

Methods for measuring career readiness of high school students: based on multidimensional item response theory and text mining

In contemporary society, career readiness holds paramount significance for individual life, exerting a direct influence on initial employment, job satisfaction, and the sense of career identity. Framed within multidimensional item response theory and text mining, this study embarks on exploring assessment methodologies for high school students’ career readiness by revising the “Career Readiness Questionnaire – Adolescent Version” and employing text mining techniques. Study One collected 1261 valid data points through cluster sampling. With the aid of Bayesian multivariate item response theory parameter estimation procedures and R language, the career readiness measurement tool was revised, yielding a concise scale that aligns with psychometric requirements. The research findings indicated that the concept of “career readiness” is more suitable for the multidimensional graded response model than for the bifactor model. The dataset’s discrimination parameters fell within the range of [1.59, 3.84], the difficulty parameters fell between [−2.91, 2.24], and the peak values of the maximum information functions fell within [0.24, 2.35]. After six items with the lowest peaks were removed (Items 4, 5, 6, 31, 32, and 33), the remaining 30 items composed the Chinese concise version “Career Readiness Questionnaire – Adolescent Version,” with discrimination parameters ranging from [1.45, 3.38], difficulty parameters between [−3.31, 1.76], and maximum information function peaks within [0.50, 2.64]. Building upon the effective participants from Study One, Study Two matched questionnaire data with textual information, resulting in 1012 valid participants. Leveraging text mining, a machine learning model was constructed to predict high school students’ career readiness based on essay texts. The results of Study 2 prove that the revised lexicon was more accurate in feature extraction. Building upon this, the machine learning model for essay text demonstrated excellent performance in predicting career readiness, with random forest outperforming the other algorithms. This study provides a novel approach for schools and parents to comprehend the state of career readiness among high school students, offering a convenient and effective tool for educational activities related to students’ career development.

Capacity Degradation Assessment of Lithium-Ion Battery Considering Coupling Effects of Calendar and Cycling Aging

Capacity degradation of lithium-ion batteries largely determines the cost, performance and environmental impact of various products such as renewable energy production systems, portable electronics, and electric vehicles. Degradation assessment is thus of great importance for prognostic and health management of batteries, which ensures a stable production and operation. There are typically two leading sources contributing to the degradation of a lithium-ion battery, namely, cycling aging during charge/discharge cycles and calendar aging during idle states. However, most existing studies on degradation assessment either only consider a single source or ignore the coupling of these two sources, which makes the evaluation inefficient. A common observation in practice is that a battery tends to degrade faster when it experiences charge/discharge cycles continuously for a longer time. To capture this feature, this paper introduces the concept of the cumulative uninterrupted cycling duration (CUCD), which is defined as the consecutive operation duration since a battery ends the idle state. The CUCD can also help to model the coupling between the calendar and cycling aging. This paper then proposes to model the drift rate of cycling aging as a function of the CUCD and the functional form is determined with the monotonic spline. We estimate the model parameters by maximizing the likelihood function. Hypothesis testings toward the significance of the coupling between two aging sources and the monotonicity of the drift rate function under cycling aging are also provided. The effectiveness and the superiority of the model are validated using numerical and real case studies. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This study aims to characterize the degradation of lithium-ion battery simultaneously considering calendar and cycling agings and the coupling effect. Unlike previous research that only supplied experimental results to qualitatively illustrate the existence of the coupling effect between these two aging sources, this study provides procedures to quantitatively test the significance of such an effect. In addition, previous research ignored the coupling effect in the degradation modeling as it is difficult to capture, this study propose the concept of CUCD to characterize it. The CUCD is also introduced as a stress factor for cycling aging, which is based on the fact that a battery will degrade faster when it experiences charge/discharge cycle continuously for a longer time. Hypothesis testing is also provided to illustrate this monotonicity. To deal with another challenge that the expert knowledge of the functional form between cycling aging and CUCD is unavailable except for the monotonicity, a nonparametric method with the shape-restricted spline is adapted. The estimation procedures for the model parameters are also presented.

Resolution of multiple semi-infinite delaminations using lock-in infrared thermography

Delaminations are flat subsurface defects parallel to the sample surface. Recently we have demonstrated that lock-in infrared thermography, with optical excitation, allows sizing the geometrical parameters (length, depth and thickness) of a semi-infinite delamination. Here, we analyse the ability of this technique to resolve several parallel and semi-infinite delaminations. First, we develop an analytical method (based on the thermal quadrupoles) together with a numerical formulation to calculate the surface temperature of a sample containing several semi-infinite parallel delaminations. We verify that both methods provide the same temperature values, indicating their consistency. Then, we study the ability of lock-in infrared thermography to resolve two close delaminations. In particular we focus on two main configurations: two non-overshadowed delaminations and two superimposed delaminations. Next, after analysing the inverse problem in terms of residual function minimization, we develop a dedicated parametric estimation procedure able to retrieve the geometry of the studied defects. Finally, we test this procedure with synthetic temperature amplitude and phase data to retrieve the geometrical parameters of both delaminations.

Order selection for heterogeneous semiparametric hidden Markov models.

Hidden Markov models (HMMs), which can characterize dynamic heterogeneity, are valuable tools for analyzing longitudinal data. The order of HMMs (ie, the number of hidden states) is typically assumed to be known or predetermined by some model selection criterion in conventional analysis. As prior information about the order frequently lacks, pairwise comparisons under criterion-based methods become computationally expensive with the model space growing. A few studies have conducted order selection and parameter estimation simultaneously, but they only considered homogeneous parametric instances. This study proposes a Bayesian double penalization (BDP) procedure for simultaneous order selection and parameter estimation of heterogeneous semiparametric HMMs. To overcome the difficulties in updating the order, we create a brand-new Markov chain Monte Carlo algorithm coupled with an effective adjust-bound reversible jump strategy. Simulation results reveal that the proposed BDP procedure performs well in estimation and works noticeably better than the conventional criterion-based approaches. Application of the suggested method to the Alzheimer's Disease Neuroimaging Initiative research further supports its usefulness.

Optimal Predictors of General Small Area Parameters Under an Informative Sample Design Using Parametric Sample Distribution Models

Abstract Two challenges in small area estimation occur when (i) the sample selection mechanism depends on the outcome variable and (ii) the parameter of interest is a nonlinear function of the response variable in the assumed model. If, given the values of the model covariates, the sample selection mechanism depends on the model response variable, the design is said to be informative for the model. Pfeffermann and Sverchkov (2007) develop a small area estimation procedure for informative sampling, focusing on the prediction of small area means. Molina and Rao (2010) develop a small area estimation procedure for general parameters that are nonlinear functions of the model response variable. The method of Molina and Rao assumes noninformative sampling. We combine these two approaches to develop a procedure for the estimation of general parameters in small areas under informative sampling. We introduce a parametric bootstrap MSE estimator that is appropriate for an informative sample design. We evaluate the validity of the proposed procedures through extensive simulation studies and illustrate the procedures utilizing Mexico’s income data.

Parameter estimation for strict arcsine distribution

The two-parameter strict arcsine distribution as a member of the natural exponential family with cubic variance function has been shown to be a viable candidate for statistical analysis of count data. Efficient methods of parameter estimation will be essential in practical applications of the distribution. In this paper we examine some methods of parameter estimation. Due to the simple expression of the probability generating function, a probability generating function-based estimation procedure is considered and compared with other estimation procedures. Since the accuracy of the parameter estimation procedure affects the probability of correct selection in choosing the correct probability distribution, we extend the investigation by examining the discrimination between strict arcsine and generalized Poisson distributions in which both have cubic variance functions.

Minimum density power divergence estimation for the generalized exponential distribution

Statistical modeling of rainfall data is an active research area in agro-meteorology. The most common models fitted to such datasets are exponential, gamma, log-normal, and Weibull distributions. As an alternative to some of these models, the generalized exponential (GE) distribution was proposed by Gupta and Kundu (2001a). Rainfall (specifically for short periods) datasets often include outliers, and thus, a proper robust parameter estimation procedure is necessary. Here, we use the popular minimum density power divergence estimation (MDPDE) procedure developed by Basu et al. (1998) for estimating the GE parameters. We derive the analytical expressions for the estimating equations and asymptotic distributions. We analytically compare MDPDE with maximum likelihood estimation in terms of robustness, through an influence function analysis. Besides, we study the asymptotic relative efficiency of MDPDE analytically for different parameter settings. We apply the proposed technique to some simulated datasets and two rainfall datasets from Texas, United States. The results indicate superior performance of MDPDE compared to the other existing estimation techniques in most of the scenarios.

Automated structural parameter estimation of semi-rigid complex joints in a benchmark laboratory steel grid by experimental modal analysis

The mechanical properties of joints may impact a system’s static and dynamic behavior. Since connections are usually complex, modeling their geometric details could take time and effort. Thus, joints of structures are often overlooked in model creation and calibration. Therefore, reliable analytical modeling of in-service structures requires accurate and efficient parameter estimation of the connections in their simplified models. However, joints are physically small parts of a system, and parameter estimation techniques may not be sufficiently sensitive to the variations of connections’ mechanical properties. This paper examines the finite element model updating of a laboratory steel grid focusing on the structural parameter estimation of its complex connections using modal data. The mechanical properties of the joints are parametrized by added mass and reduced rigidity. Therefore, several modified models with different combinations of heavier semi-rigid joints are developed. Each model is updated using two modal-based error functions, and the most representative updated model is selected. The results demonstrate how the grid modal outputs are influenced by updating the mass and stiffness of its connections. Moreover, mass and stiffness interactions of the grid joints in the parameter estimation procedure are illustrated. The updated models can efficiently simulate the structural behavior of the grid with increased confidence and reliability.

The methodology for adaptive modeling and forecasting nonlinear and nonstationary processes

The study is directed towards development of systemic methodology for modeling and forecasting nonlinear and nonstationary processes in economy, finances and other areas of human activities. There exist multiple problems that are to be solved with the data of such type practically in all areas of human activities: such as constructing adequate models including estimation and forecasting state of a system under investigation; technical, economic and medical diagnostics; automatic control in technologies; moving objects control; financial and other risk estimation and management; risk factor interaction; control and monitoring of microclimate in greenhouses and industrial enterprises; decision making support in business; dynamic strategic planning in production; providing stability for critical economic infrastructure etc. The structure and parameter adaptation procedures for the regression and probabilistic models are proposed as well as respective information system architecture and functional layout are developed. The system development is based on the system analysis principles such as hie­rarchical architecture of the system, adaptive approach to model structure estimation, optimization of model parameter estimation procedures, functional completeness of the system providing for autonomous operation of the system, identification and taking into consideration of possible uncertainties available in the process of data processing and mathematical model development, application of appropriate sets of quality criteria that are guarantying high quality of intermediate and final results of data analysis. The possible uncertainties are inherent to data collecting, model constructing and forecasting procedures, and play the role of negative influence factors to the computational procedures of proposed information system. Reduction of their influence is favorable for enhancing the quality of intermediate and final results of computations. The illustrative examples of practical application of the methodology developed proving the system functionality are provided.

Two-Step Parameter Estimation for Read Feature Models

AbstractOver the last two decades, the field of molecular biology has witnessed a revolution due to the development of next generation sequencing (NGS) technologies. NGS enables researchers to routinely generate huge amounts of data that can be used to pursue a large variety of questions in diverse biological systems. The development of these techniques has propelled the emergence of a sub-discipline within computational biology that is concerned with developing methods and statistical models to derive quantitative information from the complex and often indirect data that are generated by NGS. Often, NGS analysis results in particular patterns per biological entity that can be exploited to estimate quantitative parameters of biological interest. Here, I define read feature models (RFMs) as a general framework for such data. RFMs entail global, genome-wide parameters as well as parameters per biological entity, suggesting a two-step procedure for parameter estimation. I describe the analysis of metabolic RNA labeling data as an example of an RFM and analyze and discuss the merits and shortcomings of the two-step estimation.

A Datasheet-Driven Electrothermal Averaged Model of a Diode–MOSFET Switch for Fast Simulations of DC–DC Converters

The design of modern power electronics converters requires accurate electrothermal device models enabling a straightforward parameter estimation and fast, yet accurate, circuit simulations. In this paper, a novel electrothermal averaged model of a diode–MOSFET switch for fast analysis of DC–DC converters is proposed. The model has the form of a SPICE-compatible subcircuit and allows computing in a very short simulation time the DC characteristics of the converter, the waveforms of the terminal voltages and currents of the semiconductor devices, as well as their junction temperatures, both in CCM and DCM.. All the input data required by the parameter estimation procedure can be taken from the datasheets of components. The correctness of the proposed approach is experimentally verified for a buck converter chosen as a case-study. A generally good agreement between measurements and simulations is obtained; as an example, the absolute error in assessing the MOSFET junction temperature does not exceed 12 °C within the whole range of switching frequency of the converter, while the commonly used PLECS model considerably underestimates it.

Population balance model enabled digital design and uncertainty analysis framework for continuous crystallization of pharmaceuticals using an automated platform with full recycle and minimal material use

A systematic digital design framework for the development of a digital twin of a continuous crystallization process was presented using the model compound, diphenhydramine hydrochloride (DPH). The key features of the framework include operating space investigations, kinetic parameter estimation using population balance modeling, and systematic batch-to-continuous crystallization translation of the estimated parameters. An approach that compares experimental uncertainties with model-prediction uncertainties was used to justify the robustness of the parameter estimation procedure. For continuous crystallization development, a continuous configuration with full recycle and dissolution was developed, which enabled rapid process design with minimal material use. The results demonstrated successful model development for both batch and mixed-suspension-mixed-product-removal (MSMPR) crystallization configurations. This experimentally validated model, along with quantified uncertainty space of the kinetic parameters, serves as a digital twin of the process, which was later used to optimize the multistage MSMPR process to produce larger crystals with narrower distributions.

A starch digestion model considering intrinsic granular properties

Starch particle digestion is an important topic in food digestion research. This study has developed a diffusion-reaction model to characterize hindered enzyme diffusion and substrate hydrolysis on the surface and in the interior of porous starch particles. A moving boundary numerical method is applied to account for particle shrinkage caused by surface reaction. This model has been proven to predict the digestion rate of various starch particles of different sizes. The parameter estimation procedure quantifies the properties that are hard to measure by experimental techniques, i.e., diameter, reactive area, and proportion of pores accessible for enzyme as well as susceptibility of starch to enzyme. This work formulates a quantitative procedure for identifying the particle digestion pattern (i.e., outside-in or inside-out) by resorting to the developed model. Computational experiments indicate that in addition to internal architecture, particle size has a significant effect on the digestion pattern.

Sample selection in linear panel data models with heterogeneous coefficients

AbstractWe propose a parametric estimation procedure for linear panel data models with sample selection and heterogeneous coefficients that are present in both outcome model and selection model. Our two‐step estimation procedure accounts for endogeneity from the selection process and endogeneity from correlation between the individual unobserved heterogeneity and the observed covariates using control function like methods. Conditional linear projections are used to establish a tractable approach that builds upon the original Heckman correction to sample selection. Monte Carlo simulations illustrate the finite sample properties of our estimator and demonstrate that our proposed estimator outperforms standard estimators. We apply the proposed approach to estimate gender differences in high‐stakes time‐constrained decisions using Elo ratings data from the World Chess Federation. When addressing both sources of endogeneity, we find a much larger gender skill gap and substantial differences across the genders in strategically selecting into time‐constrained matches.

Improving model-data mismatch for photon-counting detector model using global and local model parameters.

An energy-discriminating capability of a photon counting detector (PCD) can provide many clinical advantages, but several factors, such as charge sharing (CS) and pulse pileup (PP), degrade the capability by distorting the measured x-ray spectrum. To fully exploit the merits of PCDs, it is important to characterize the output of PCDs. Previously proposed PCD output models showed decent agreement with physical PCDs; however, there were still scopes to be improved: a global model-data mismatch and pixel-to-pixel variations. In this study, we improve a PCD model by using count-rate-dependent model parameters to address the issues and evaluate agreement against physical PCDs. The proposed model is based on the cascaded model, and we made model parameters condition-dependent and pixel-specific to deal with the global model-data mismatch and the pixel-to-pixel variation. The parameters are determined by a procedure for model parameter estimation with data acquired from different thicknesses of water or aluminum at different x-ray tube currents. To analyze the effects of having proposed model parameters, we compared three setups of our model: a model with default parameters, a model with global parameters, and a model with global-and-local parameters. For experimental validation, we used CdZnTe-based PCDs, and assessed the performance of the models by calculating the mean absolute percentage errors (MAPEs) between the model outputs and the actual measurements from low count-rates to high count-rates, which have deadtime losses of up to 24%. The outputs of the proposed model visually matched well with the PCD measurements for all test data. For the test data, the MAPEs averaged over all the bins were 49.2-51.1% for a model with default parameters, 8.0-9.8% for a model with the global parameters, and 1.2-2.7% for a model with the global-and-local parameters. The proposed model can estimate the outputs of physical PCDs with high accuracy from low to high count-rates. We expect that our model will be actively utilized in applications where the pixel-by-pixel accuracy of a PCD model is important.