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This paper presents an estimation approach within the framework of uplink massive machine-type-communications (mMTC) that considers the energy limitations of the devices. We focus on a scenario where a group of sensors observe a set of parameters and send the measured information to a collector node (CN). The CN is responsible for estimating the original observations, which are spatially correlated and corrupted by measurement and quantization noise. Given the use of Gaussian sources, the minimum mean squared error (MSE) estimation is employed and, when considering temporal evolution, the use of Kalman filters is studied. Based on that, we propose a device selection strategy to reduce the number of active sensors and a quantization scheme with adjustable number of bits to minimize the overall payload. The set of selected sensors and quantization levels are, thus, designed to minimize the MSE. For a more realistic analysis, communication errors are also included by averaging the MSE over the error decoding probabilities. We evaluate the performance of our strategy in a practical mMTC system with synthetic and real databases. Simulation results show that the optimization of the payload and the set of active devices can reduce the power consumption without compromising the estimation accuracy. The work presented in this paper has been carried out within the framework of the project ROUTE56 (PID2019-104945GB-I00/ AEI/10.13039/501100011033) funded by the Agencia Estatal de Investigación (Spanish Ministry of Science and Innovation); the FPI grant BES-2017-079994, funded by the Spanish Ministry of Science, Innovation and Universities; and the grant 2017 SGR 578, funded by the Catalan Government (AGAUR, Departament de Rercerca i Universitats, Generalitat de Catalunya).

How to effectively realize the simulation, evaluation, and control of the photovoltaic (PV) system established on the actual measured voltage and current PV cells and module data has attracted widespread attention. The original SE possesses the disadvantages of slow convergence and poor accuracy in the parameter identification of PV cells and modules. This paper proposes an enhanced spherical evolution algorithm (SE) based on a novel dynamic sine-cosine mechanism (DSCSE). The introduction of the dynamic sine-cosine mechanism significantly promotes the information communication of disparate individuals and increases the diversity of diverse populations. To assess the performance of DSCSE, it is compared with ten comparative algorithms to estimate unknown parameters of PV cell and module at fixed and varying temperature and light conditions, including single diode model (SDM), double diode model (DDM), three diode model (TDM) and PV module. The experimental results indicate that the root mean square of the error (RMSE) gained by DSCSE outperforms most competing algorithms. The results of RMSE by DSCSE for SDM, DDM, and TDM of commercial solar cells R.T.C. France and PV module of Photowat-PWP201 is the percentage of improvement of 48.45%, 6.85%, 11.81%, and 4.73% compared to SE, respectively. Furthermore, for three manufacturers, including Mono-crystalline (SM55), Thin-film (ST40), and Multi-crystalline (KC200GT), the results of RMSE by DSCSE harvest the maximum and minimum increase of 96.1% and 31.36%. Therefore, DSCSE is expected to become a novel promising technology to estimate the parameter of PV cells and modules.

In photovoltaic (PV) model, it is an urgent problem to control and optimize the accurate parameters. Hence, many algorithms have been proposed for parameter extraction of different PV models. However, the ability of many optimization algorithms is greatly affected by parameters, and the same parameter is not suitable for different model problems. In recent years, reinforcement learning has achieved competitive results in solving the problem of maximizing returns through learning strategies in the process of interaction with the environment. Therefore, in this paper we propose a new algorithm which combines differential evolution algorithm with reinforcement learning. Specifically, in the iterative process, the fitness function value is evaluated to determine the action reward for adjustment of parameter value, and the parameter value is adjusted through reinforcement learning to obtain the most suitable algorithm parameters for the environment model. The performance of the proposed approach has been verified by extracting single diode model, double diode model and PV module parameters, The simulation results (root mean square error) of single diode model (9.8602E−04), double diode model (9.8248E−04) and 2.4251E−03 for the Photowatt-PWP201, 1.7298E−03 for STM6-40/36 and 1.6601E−02 for the STP6-120/36 comprehensively show that the algorithm has better accuracy and robustness when compared with other advanced algorithms.

Entropy has been widely applied in system identification in the last decade. In this paper, a novel stochastic gradient algorithm based on minimum Shannon entropy is proposed. Though needing less computation than the mean square error algorithm, the traditional stochastic gradient algorithm converges relatively slowly. To make the convergence faster, a multi-error method and a forgetting factor are integrated into the algorithm. The scalar error is replaced by a vector error with stacked errors. Further, a simple step size method is proposed and a forgetting factor is adopted to adjust the step size. The proposed algorithm is utilized to estimate the parameters of an ARX model with random impulse noise. Several numerical solutions and case study indicate that the proposed algorithm can obtain more accurate estimates than the traditional gradient algorithm and has a faster convergence speed.

An approximated expression for the calculated solar cell current is usually used in parameters estimation of the 7-parameter double diode model (DDM) and the 9-parameter triple diode model (TDM) of solar photovoltaic (PV) equivalent circuits. Then the root mean square error (RMSE) is calculated between the measured and estimated values of the output current. In the mathematical sense, the RMSE calculation procedure is not correct. In this work, a novel iterative approach based on the Lambert W function is proposed to calculate the solar cell current in both DDM and TDM. Then, the RMSE values computed using the parameters found by many optimization algorithms presented in the literature are presented and discussed for the RTC France PV cell and Solarex MSX–60 PV module. The results obtained show that RMSE values were not accurately calculated in most of these methods. Further, an improved LSHADE optimization algorithm called Chaotic LSHADE algorithm is proposed to solve the 7-parameter and 9-parameter estimation problem of the PV equivalent circuits. The proposed methodology is also applied to current–voltage characteristics measured in the laboratory for solar modules of Clean Energy Trainer Setup. The 7 and 9 unknown parameters are estimated using the CLSHADE algorithm based on the minimization of the RMSE values calculated. The results obtained show that the proposed algorithm achieves better solutions than the solutions obtained by many optimization algorithms presented in the literature.

When discussing the commercial applications of photovoltaic (PV) systems, one of the most critical problems is to estimate the efficiency of a PV system because current (I) – voltage (V) and power (P) – voltage (V) characteristics are highly non-linear. It should be noted that most of the manufacturer’s datasheets do not have complete information on the electrical equivalent parameters of PV systems that are necessary for simulating an effective PV module. Compared to conventional approaches, computational optimization and global research strategies are more acceptable as an effective alternative to parameter estimation of solar PV modules. Recently, a Gradient-based optimizer (GBO) is reported to solve the engineering design optimization problems. However, the basic GBO algorithm is stuck in local optima when handling complex non-linear problems. In this sense, this paper presents a new optimization technique called the Chaotic-GBO (CGBO) algorithm to derive the parameters of PV modules while offering precise I-V and P-V curves. To this end, the CGBO algorithm is based on a chaotic generator to obtain the PV parameters combined with the GBO algorithm. There are five case studies considered to validate the performance of the proposed CGBO algorithm. A quantitative and qualitative performance evaluation reveals that the proposed CGBO algorithm has improved results than other state-of-the-art algorithms in terms of accuracy and robustness when obtaining PV parameters. The average RMSE values and runtime of five case studies are equal to 9.8427E-04, 2.3700E-04, 2.4251E-03, 4.3524E-03 and 1.8349E-03, and 18.44, 17.78, 18.18, 18.28 and 17.97, respectively. The results proved the superiority of the proposed CGBO algorithm over the different selected algorithms. For future research, this study will be backed up with external support at https://premkumarmanoharan.wixsite.com/mysite.

The direct current (DC) motors are widely used; therefore, they are subject to multiple studies, different control techniques or analyses require a dynamic DC motor model. The parameters are needed to complete the model, which can be challenging to obtain. Therefore, multiple parametric estimation techniques have been developed. This paper presents a metaheuristic cuckoo search algorithm modified for motors as a parametric estimation tool. A cost function is based on the current and velocity error obtained when an input voltage step is applied to the motor. The main difference with similar works is that we used the steady-state equations to determine the parameters. The algorithm proposed is compared with the Steiglitz–McBride and the original cuckoo search algorithms to evaluate its performance objectively. Simulated and experimental results show that the algorithm proposed can calculate the parameters with better accuracy than the original cuckoo search and Steiglitz–McBride. The modifications made to the original algorithm of the cuckoo search allowed finding the values of the parameters motor with a root mean square error of less than 0.1% for signals obtained with simulation and less than 1% for real signals sampled at 0.001 s.

Background Different estimation approaches are frequently used to calibrate mathematical models to epidemiological data, particularly for analyzing infectious disease outbreaks. Here, we use two common methods to estimate parameters that characterize growth patterns using the generalized growth model (GGM) calibrated to real outbreak datasets. Materials and methods Data from 31 outbreaks are used to fit the GGM to the ascending phase of each outbreak and estimate the parameters using both least squares (LSQ) and maximum likelihood estimation (MLE) methods. We utilize parametric bootstrapping to construct confidence intervals for parameter estimates. We compare the results including RMSE, Anscombe residual, and 95% prediction interval coverage. We also evaluate the correlation between the estimates from both methods. Results Comparing LSQ and MLE estimates, most outbreaks have similar parameter estimates, RMSE, Anscombe, and 95% prediction interval coverage. Parameter estimates do not differ across methods when the model yields a good fit to the early growth phase. However, for two outbreaks, there are systematic deviations in model fit to the data that explain differences in parameter estimates (e.g., residuals represent random error rather than systematic deviation). Conclusion Our findings indicate that utilizing LSQ and MLE methods produce similar results in the context of characterizing epidemic growth patterns with the GGM, provided that the model yields a good fit to the data.

This paper presents a new optimal method for model estimation of the unknown parameters of circuit-based proton exchange membrane fuel cells (PEMFCs). The main idea is to minimize the sum of squared error (SSE) value between the actual data and the estimated results. The optimization process here is based on an Improved Fluid Search Optimization Algorithm (IFSO). For verification of the suggested method, it is applied to three practical case studies including Horizon H-12 stacks, NedStack PS6, and Ballard Mark V 5 kW under different operating conditions with temperature variations between 30 o C and 55 o C and pressure variations between 1.0/1.0 Bar and 3.0/3.0 Bar. The results of these case studies are also compared with CGOA, MRFO, and basic FSO algorithm to show the proposed method’s effectiveness. The results show that the minimum value of SSE among different algorithms is 0.7845, 2.15, and 0.084, respectively that are reached by the suggested IFSO algorithm.

This paper presents an optimal technique for parameter estimation of a Solid Oxide Fuel Cell (SOFC) model. The idea is to minimize the Sum of Squared Error (SSE) between the output voltage and the experimental data. To achieve this purpose, a new metaheuristic, called the Converged Grass Fibrous Root Optimization Algorithm (CGRA) is presented and is validated by comparing it with some well-known algorithms. The method is then applied to the optimal parameter estimation of the model To analyze the method accuracy and its robustness, the proposed model is verified under different pressure and temperature operating conditions and the results have been compared with some different methods from the literature. Simulation results indicate a good confirmation between the experimental results and the model designed based on the proposed CGRA. The results for the CGRA show that the SSE results for 3 atm constant pressure and 563.85°C, 649.85°C, 699.85°C, 749.85°C, and 799.85°C are 1.67E−4, 1.84E−4, 9.42E−4, 1.87E−3, and 1.62E−3, respectively and for 799.85°C constant temperature with 1 atm, 2 atm, 3 atm, 4 atm, and 5 atm, are 1.68E−3, 1.84E−3, 9.42E−3, 1.87E−3, and 1.62E−3, respectively that are the minimum values among the other analyzed methods that indicate that the suggested technique gives better efficiency with the highest robustness and convergence speed compared with the other methods.

The problem of parametric estimation in single-phase transformers is addressed in this research from the point of view of metaheuristic optimization. The parameters of interest are the series resistance and reactance as well as the magnetization resistance and reactance. To obtain these parameters considering only the voltage and the currents measured in the terminals of the transformer, a nonlinear optimization model that deals with the minimization of the mean square error among the measured and calculated voltage and current variables is formulated. The nonlinear programming model is solved through the implementation of a simple but efficient metaheuristic optimization technique known as the black-hole optimizer. Numerical simulations demonstrate that the proposed optimization method allows for the reduction in the estimation error among the measured and calculated variables when compared with methods that are well established in the literature such as particle swarm optimization and genetic algorithms, among others. All the simulations were carried out in the MATLAB programming environment.

Thermal conductivity determination of food at temperatures &gt, 100 °C still remains a challenge. The objective of this study was to determine the temperature-dependent thermal conductivity of food using rapid heating (TPCell). The experiments were designed based on scaled sensitivity coefficient (SSC), and the estimated thermal conductivity of potato puree was compared between the constant temperature heating at 121.10 °C (R12B10T1) and the rapid heating (R22B10T1). Temperature-dependent thermal conductivity models along with a constant conductivity were used for estimation. R22B10T1 experiment using the k model provided reliable measurements as compared to R12B10T1 with thermal conductivity values from 0.463 ± 0.011 W m−1 K−1 to 0.450 ± 0.016 W m−1 K−1 for 25–140 °C and root mean squares error (RMSE) of 1.441. In the R12B10T1 experiment, the analysis showed the correlation of residuals, which made the estimation less reliable. The thermal conductivity values were in the range of 0.444 ± 0.012 W m−1 K−1 to 0.510 ± 0.034 W m−1 K−1 for 20–120 °C estimated using the k model. Temperature-dependent models (linear and k models) provided a better estimate than the single parameter thermal conductivity determination with low RMSE for both types of experiments. SSC can provide insight in designing dynamic experiments for the determination of thermal conductivity coefficient.

Accurate and reliable photovoltaic (PV) cell parameter identification is critical to simulation analysis, maximum output power harvest, and optimal control of PV systems. However, inherent high-nonlinear and multi-modal characteristics usually result in thorny obstacles to hinder conventional optimization methods to obtain a fast and satisfactory performance. In this study, a novel bio-inspired grouped beetle antennae search (GBAS) algorithm is devised to effectively identify unknown parameters of three different PV models, i.e., single diode model (SDM), double diode model (DDM), and triple diode model (TDM). Compared against beetle antennae search (BAS) algorithm, optimization efficiency of GBAS algorithm is markedly enhanced based on a cooperative searching group that consists of multiple individuals rather than a single beetle. Besides, a dynamic balance mechanism between local exploitation and global exploration is designed to increase the probability for a higher quality optimum. Comprehensive case studies demonstrate that GBAS algorithm can outperform other advanced meta-heuristic algorithms in both optimization precision and stability for estimating PV cell parameters, e.g., standard deviation (SD) of root mean square error (RMSE) obtained by GBAS algorithm is 64.34% smaller than the best value obtained by other algorithms in SDM, 61.86% smaller than that in DDM.

In this paper, the problem of multidimensional single-tone frequency estimation of sinusoids embedded in white Gaussian noise is investigated. By extracting the two-dimensional (2-D) slice matrices from the multidimensional data, we construct a covariance matrix associated with only one dimension, from which the corresponding frequency is estimated with the utilization of a QR decomposition based iterative method. The frequencies of the remaining dimensions are then obtained following similar procedures. Moreover, the mean square error of the estimated frequencies is devised. The computer simulations are also included to evaluate the performance of the proposed method by comparing with the several state-of-the-art algorithms and Cramér-Rao lower bound.

A novel phenomenological epidemic model is proposed to characterize the state of infectious diseases and predict their behaviors. This model is given by a new stochastic partial differential equation that is derived from foundations of statistical physics. The analytical solution of this equation describes the spatio-temporal evolution of a Gaussian probability density function. Our proposal can be applied to several epidemic variables such as infected, deaths, or admitted-to-the-Intensive Care Unit (ICU). To measure model performance, we quantify the error of the model fit to real time-series datasets and generate forecasts for all the phases of the COVID-19, Ebola, and Zika epidemics. All parameters and model uncertainties are numerically quantified. The new model is compared with other phenomenological models such as Logistic Grow, Original, and Generalized Richards Growth models. When the models are used to describe epidemic trajectories that register infected individuals, this comparison shows that the median RMSE error and standard deviation of the residuals of the new model fit to the data are lower than the best of these growing models by, on average, 19.6% and 35.7%, respectively. Using three forecasting experiments for the COVID-19 outbreak, the median RMSE error and standard deviation of residuals are improved by the performance of our model, on average by 31.0% and 27.9%, respectively, concerning the best performance of the growth models.

Recently, modelling and simulation have been used and applied to understand biological systems better. Therefore, the development of precise computational models of a biological system is essential. This model is a mathematical expression derived from a series of parameters of the system. The measurement of parameter values through experimentation is often expensive and time-consuming. However, if a simulation is used, the manipulation of computational parameters is easy, and thus the behaviour of a biological system model can be altered for a better understanding. The complexity and nonlinearity of a biological system make parameter estimation the most challenging task in modelling. Therefore, this paper proposes a hybrid of Particle Swarm Optimization (PSO) and Harmony Search (HS), also known as PSOHS, designated to determine the kinetic parameter values of essential amino acids, mainly aspartate metabolism, in Arabidopsis thaliana. Three performance measurements are used in this paper to evaluate the proposed PSOHS: the standard deviation, nonlinear least squared error, and computational time. The proposed algorithm outperformed the other two methods, namely Simulated Annealing and the downhill simplex method, and proved that PSOHS is a more suitable algorithm for estimating kinetic parameter values.

Pest in agriculture can raise plant disease and fail to harvest. The pest problem in agriculture can be solved by using pesticide. Pesticide usage must be done proportionally. So, the manufacturer should fix standard pesticide active ingredient in pesticide production. Forecast is a prediction of some future evens. In forecast problem, there are any parameters which should be determined. Parameters can be estimated by exact method or heuristic method. Ant Colony Optimization (ACO) is inspired from the cooperative behavior of ant colonies, which can find the shortest path from their nest to a food source. In this research, we use heuristic method like ACO to estimate exponential smoothing parameter on pesticide active ingredient forecast and pesticide sample weight forecast. From the simulation, on the first iteration, all ants choose parameter randomly. At the optimization process, we update pheromone until all ants choose the similar parameter so that process converges and variance approaches to zero. The optimal exponential smoothing parameter can be applied in forecasting with minimum sum of squared error (SSE).

Estimation methods are generalized in this paper by the idea of “scalar-vector-matrix”. A generalized contraction mapping (GCM) framework is proposed for searching the optimal linear biased estimation. First, based on the latent model and the mean square error criterion, four different biased estimation methods are analyzed. They are the improved principal component estimation (PCE), the improved principal component estimation (IPCE), the ridge estimation (RE), and the generalized ridge estimation (GRE). A suboptimal ridge parameter for the RE is given. Four estimation performance theorems for the four methods are obtained using the traditional contraction mapping (CM) framework. The theoretical results can ease the difficulty of choosing methods for application. Second, we generalize the CM framework into the generalized contraction mapping (GCM) framework, and the optimal linear biased estimation method based GCM is given theoretically by the geometric tools of rotation, contraction, and reflection. Therefore, the GCM framework further improves the estimation performance. Finally, a numerical experiment is designed to validate the correctness of the theorems in the paper.

The estimation of the parameters of a simulation model such that the model’s behaviour matches closely with reality can be a cumbersome task. This is due to the fact that a number of model parameters cannot be directly measured, and such parameters might change during the course of operation in a real system. Friction between different machine components is one example of these parameters. This can be due to a number of reasons, such as wear. Nevertheless, if one is able to accurately define all necessary parameters, essential information about the performance of the system machinery can be acquired. This information can be, in turn, utilised for product-specific tuning or predictive maintenance. To estimate parameters, the augmented discrete extended Kalman filter with a curve fitting method can be used, as demonstrated in this paper. In this study, the proposed estimation algorithm is applied to estimate the characteristic curves of a directional control valve in a four-bar mechanism actuated by a fluid power system. The mechanism is modelled by using the double-step semi-recursive multibody formulation, whereas the fluid power system under study is modelled by employing the lumped fluid theory. In practise, the characteristic curves of a directional control valve is described by three to six data control points of a third-order B-spline curve in the augmented discrete extended Kalman filter. The results demonstrate that the highly non-linear unknown characteristic curves can be estimated by using the proposed parameter estimation algorithm. It is also demonstrated that the root mean square error associated with the estimation of the characteristic curve is 0.08% with respect to the real model. In addition, all the errors in the estimated states and parameters of the system are within the 95% confidence interval. The estimation of the characteristic curve in a hydraulic valve can provide essential information for performance monitoring and maintenance applications. Publishers version

Efficient and accurate estimations of unidentified parameters of photovoltaic (PV) models are essential to their simulation. This study suggests two new variants of the whale optimization algorithm (WOA) for identifying the nine parameters of the three-diode PV model. The first variant abbreviated as RWOA is based on integrating the WOA with ranking methods under a novel updating scheme to utilize each whale within the population as much as possible during the optimization process. The second variant, namely HWOA, has been based on employing a novel cyclic exploration-exploitation operator with the RWOA to promote its local and global search for averting stagnation into local minima and accelerating the convergence speed in the right direction of the near-optimal solution. Experimentally, RWOA and HWOA are validated on a solar cell (RTC France) and two PV modules (Photowatt-PWP201 and Kyocera KC200GT). Further, these proposed variants are compared with five well-known parameter extraction models in order to demonstrate their notable advantages over the other existing competing algorithms for minimizing the root mean squared error (RMSE) between experimentally measured data and estimated one. The experimental findings show that RWOA is superior in some observed cases and superior in the other cases in terms of final accuracy and convergence speed; yet, HWOA is superior in all cases.

Techniques used to analyze exceedances over a high threshold are in great demand for research in economics, environmental science, and other fields. The generalized Pareto distribution (GPD) has been widely used to fit observations exceeding the tail threshold in the peaks over threshold (POT) framework. Parameter estimation and threshold selection are two critical issues for threshold-based GPD inference. In this work, we propose a new GPD-based estimation approach by combining the method of moments and likelihood moment techniques based on the least squares concept, in which the shape and scale parameters of the GPD can be simultaneously estimated. To analyze extreme data, the proposed approach estimates the parameters by minimizing the sum of squared deviations between the theoretical GPD function and its expectation. Additionally, we introduce a recently developed stopping rule to choose the suitable threshold above which the GPD asymptotically fits the exceedances. Simulation studies show that the proposed approach performs better or similar to existing approaches, in terms of bias and the mean square error, in estimating the shape parameter. In addition, the performance of three threshold selection procedures is assessed by estimating the value-at-risk (VaR) of the GPD. Finally, we illustrate the utilization of the proposed method by analyzing air pollution data. In this analysis, we also provide a detailed guide regarding threshold selection.

International audience; Change-point estimation has received much attention in the literature as it plays a significant role in several signal processing applications. However, the study of the optimal estimation performance in such context is a difficult task since the unknown parameter vector of interest may contain both continuous and discrete parameters, namely the parameters associated with the noise distribution and the change-point locations. In this paper, we handle this by deriving a lower bound on the mean square error of these continuous and discrete parameters. Specifically, we propose a Hybrid Cramér-Rao-Weiss-Weinstein bound and derive its associated closed-form expressions. Numerical simulations assess the tightness of the proposed bound in the case of Gaussian and Poisson observations.

In recent years, there has been increased interest in applying data assimilation (DA) methods, originally designed for state estimation, to the model selection problem. In this setting, previous studies introduced the contextual formulation of model evidence, or contextual model evidence (CME), and showed that CME can be efficiently computed using a hierarchy of ensemble‐based DA procedures. Although these studies analysed the DA methods most commonly used for operational atmospheric and oceanic prediction worldwide, they did not study these methods in conjunction with localization to a specific domain. Yet, any application of ensemble DA methods to realistic, very high‐dimensional geophysical models requires the implementation of some form of localization. The present study extends CME estimation to ensemble DA methods with domain localization. Domain‐localized CME (DL‐CME) developed in this article is tested for model selection with two models: (a) the Lorenz 40‐variable midlatitude atmospheric dynamics model (Lorenz‐95); and (b) the simplified global atmospheric SPEEDY model. CME is compared to the root‐mean‐square error (RMSE) as a metric for model selection. The experiments show that CME systematically outperforms RMSE in model selection skill, and that this skill improvement is further enhanced by applying localization to the CME estimate using DL‐CME. The potential use and range of applications of CME and DL‐CME as a model selection metric are also discussed.

Non-linear mixed effects models typically deal with stochasticity in observed processes but models accounting for only observed processes may not be the most appropriate for all data. Hidden Markov models (HMMs) characterize the relationship between observed and hidden variables where the hidden variables can represent an underlying and unmeasurable disease status for example. Adding stochasticity to HMMs results in mixed HMMs (MHMMs) which potentially allow for the characterization of variability in unobservable processes. Further, HMMs can be extended to include more than one observation source and are then multivariate HMMs. In this work MHMMs were developed and applied in a chronic obstructive pulmonary disease example. The two hidden states included in the model were remission and exacerbation and two observation sources were considered, patient reported outcomes (PROs) and forced expiratory volume (FEV1). Estimation properties in the software NONMEM of model parameters were investigated with and without random and covariate effect parameters. The influence of including random and covariate effects of varying magnitudes on the parameters in the model was quantified and a power analysis was performed to compare the power of a single bivariate MHMM with two separate univariate MHMMs. A bivariate MHMM was developed for simulating and analysing hypothetical COPD data consisting of PRO and FEV1 measurements collected every week for 60 weeks. Parameter precision was high for all parameters with the exception of the variance of the transition rate dictating the transition from remission to exacerbation (relative root mean squared error [RRMSE] > 150%). Parameter precision was better with higher magnitudes of the transition probability parameters. A drug effect was included on the transition rate probability and the precision of the drug effect parameter improved with increasing magnitude of the parameter. The power to detect the drug effect was improved by utilizing a bivariate MHMM model over the univariate MHMM models where the number of subject required for 80% power was 25 with the bivariate MHMM model versus 63 in the univariate MHMM FEV1 model and > 100 in the univariate MHMM PRO model. The results advocates for the use of bivariate MHMM models when implementation is possible. Electronic supplementary material The online version of this article (10.1007/s10928-019-09658-z) contains supplementary material, which is available to authorized users.

En este artículo se presentan resultados experimentales sobre la comparación de cinco metodologías para estimar los parámetros de la distribución lognormal con traslado. Los métodos considerados son el método de momentos, el método de máxima verosimilitud local, un método propuesto por Nagatsuka y Balakrishnan, una modificación de este último, y un nuevo método propuesto en este artículo. El método de máxima verosimilitud local proporcionó estimadores que tienen buenas propiedades cuando el tamaño de la muestra no es muy pequeño y el método no falla. Por otro lado, el método de Nagatsuka y Balakrishnan modificado tuvo el mejor desempeño desde el punto de vista de los errores cuadráticos promedio de los estimadores. El nuevo método propuesto en este trabajo mostró el mejor desempeño desde el punto de vista de una medida de bondad de ajuste.

金沢大学理工研究域フロンティア工学系, In parameter estimation, the maximum-likelihood method (ML) does not work for some distributions. In such cases, the maximum product of spacings method (MPS) is used as an alternative. However, the advantages and disadvantages of the MPS, its variants, and the ML are still unclear. These methods are based on the Kullback–Leibler divergence (KLD), and we consider applying the method of weighted residuals (MWR) to it. We prove that, after transforming the KLD to the integral over [0, 1], the application of the collocation method yields the ML, and that of the Galerkin method yields the MPS and Jiang’s modified MPS (JMMPS); and the application of zero boundary conditions yields the ML and JMMPS, and that of non-zero boundary conditions yields the MPS. Additionally, we establish formulas for the approximate difference among the ML, MPS, and JMMPS estimators. Our simulation for seven distributions demonstrates that, for zero boundary condition parameters, for the bias convergence rate, ML and JMMPS are better than the MPS; however, regarding the MSE for small samples, the relative performance of the methods differs according to the distributions and parameters. For non-zero boundary condition parameters, the MPS outperforms the other methods: the MPS yields an unbiased estimator and the smallest MSE among the methods. We demonstrate that from the viewpoint of the MWR, the counterpart of the ML is JMMPS not the MPS. Using this KLD-MWR approach, we introduce a unified view for comparing estimators, and provide a new tool for analyzing and selecting estimators. © 2020, SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional.

Purpose: Biophysical tissue models are increasingly used in the interpretation of diffusion MRI (dMRI) data, with the potential to provide specific biomarkers of brain microstructural changes. However, it has been shown recently that, in the general Standard Model, parameter estimation from dMRI data is ill‐conditioned even when very high b‐values are applied. We analyze this issue for the Neurite Orientation Dispersion and Density Imaging with Diffusivity Assessment (NODDIDA) model and demonstrate that its extension from single diffusion encoding (SDE) to double diffusion encoding (DDE) resolves the ill‐posedness for intermediate diffusion weightings, producing an increase in accuracy and precision of the parameter estimation. Methods: We analyze theoretically the cumulant expansion up to fourth order in b of SDE and DDE signals. Additionally, we perform in silico experiments to compare SDE and DDE capabilities under similar noise conditions. Results: We prove analytically that DDE provides invariant information non‐accessible from SDE, which makes the NODDIDA parameter estimation injective. The in silico experiments show that DDE reduces the bias and mean square error of the estimation along the whole feasible region of 5D model parameter space. Conclusions: DDE adds additional information for estimating the model parameters, unexplored by SDE. We show, as an example, that this is sufficient to solve the previously reported degeneracies in the NODDIDA model parameter estimation.

This paper considers parameter estimation of a hybrid sinusoidal frequency modulated (FM) and polynomial phase signal (PPS) from a finite number of samples. We first show limitations of an existing method, the high-order ambiguity function (HAF), and then propose a new method by adopting the high-order phase function which was originally designed for the pure PPS. The proposed method estimates parameters of interest from peak locations in the time-frequency rate domain, which are less perturbed by the noise than peak values used by the HAF-based method. Numerical evaluation shows the proposed method can handle the hybrid FM-PPS signal with low sinusoidal frequency and improve estimation accuracy in terms of mean squared error for several orders of magnitude.

This paper provides a complete program for the valuation of aggregate non-life insurance liability cash flows based on claims triangle data. The valuation is fully consistent with the principle of valuation by considering the costs associated with a transfer of the liability to a so-called reference undertaking subject to capital requirements throughout the runoff of the liability cash flow. The valuation program includes complete details on parameter estimation, bias correction and conservative estimation of the value of the liability under partial information. The latter is based on a new approach to the estimation of mean squared error of claims reserve prediction.

This letter investigates hybrid lower bounds on the mean square error in order to predict the so-called threshold effect. A new family of tighter hybrid large error bounds based on linear transformations (discrete or integral) of a mixture of the McAulay–Seidman bound and the Weiss–Weinstein bound is provided in multivariate parameters case with multiple test points. For use in applications, we give a closed-form expression of the proposed bound for a set of Gaussian observation models with parameterized mean, including tones estimation which exemplifies the threshold prediction capability of the proposed bound.

The laboratory methods used for the soil water retention curve (SWRC) construction and parameter estimation is time-consuming. A vertical infiltration method was proposed to estimate parameters α and n and to further construct the SWRC. In the present study, the relationships describing the cumulative infiltration and infiltration rate with the depth of the wetting front were established, and simplified expressions for estimating α and n parameters were proposed. The one-dimensional vertical infiltration experiments of four soils were conducted to verify if the proposed method would accurately estimate α and n. The fitted values of α and n, obtained from the RETC software, were consistent with the calculated values obtained from the infiltration method. The comparison between the measured SWRCs obtained from the centrifuge method and the calculated SWRCs that were based on the infiltration method displayed small values of root mean square error (RMSE), mean absolute percentage error (MAPE), and mean absolute error. SWMS_2D-based simulations of cumulative infiltration, based on the calculated α and n, remained consistent with the measured values due to small RMSE and MAPE values. The experiments verified the proposed one-dimensional vertical infiltration method, which has applications in field hydraulic parameter estimation.

The application of Genetic Optimization Algorithm in estimation of the parameters of servo electrical drives is proposed. In comparison with this planned method, least squared error (LSE) estimation method is considered as an expedient method for parameter estimation. Regardless of LSE estimation, Genetic Algorithm method is not restricted to the linear systems with respect to the parameters. GA is imported as an optimization method in comparison with conventional optimization methods because of its power in searching whole solution space with more probability to finding the global optimum. As a condition for convergence, transient excitation is considered instead of persistent excitation. Finally, comparison between LSE and GA based parameter estimation is presented to indicate robustness and resolution of GA identification method. It will be shown that the GA method of estimation has better results in the startup and transients of the system where there is a lack of persistent excitation.

This paper proposes a joint channel-estimation method for the desired and interfering channels for cell edge users in reuse-1 orthogonal frequency-division multiplexing (OFDM) cellular systems. The following assumptions are made in proposing the algorithm: 1) The desired and interferer's channel multipath delays do not overlap; 2) the same pilot sequence is sent from the desired and interfering base stations (BSs); and 3) reuse-3 preamble symbols, as in the preamble structure in IEEE 802.16d/e (Wimax) systems, are used to obtain initial channel estimates without interference. If we make these assumptions, then it is possible to estimate the desired and interfering channels, even with reuse-1 pilots. The proposed pilot-based channel estimation technique exploits the delay subspace structure to reduce the impact of cochannel interference (CCI) on channel estimation. Delay subspace refers to the set of basis vectors spanning the frequency response of the desired and interfering multipath channels. This enables us to jointly estimate and track the desired and interfering channels with a lower mean-squared error (MSE), when compared with the conventional modified least-squares (mLS) technique, which ignores the structure of interference. The significance of accurate channel estimates in symbol detection schemes is demonstrated for systems employing two or more receiver antennas. The proposed channel estimator significantly improves the performance of symbol-detection schemes based on either interference nulling combiner (INC) or minimum MSE diversity combiner (MMSE-DC), when compared with detection schemes using mLS-based channel estimates. Analytical expressions are derived for the MSE of the estimated multipath delays. Simulation results are also provided to show the improved performance for the proposed channel-estimation method compared with the mLS-based channel estimation method, when used in conjunction with INC and MMSE-DC detectors. � 2009 IEEE.

In this letter, we investigate the effect of hopping pilots on the parametric channel estimation in orthogonal frequency-division multiplexing (OFDM) systems. Channel estimation algorithms based on parametric channel modeling require the multipath delays to be estimated at the receiver. The use of a fixed pilot pattern leads to longer training overhead in multipath delay estimation for slow fading channels. However, if hopping pilot patterns are available, then we show that the normalized mean-squared error (NMSE) convergence rate of the channel estimates can be significantly improved. We also show that hopping pilot patterns in OFDM systems effectively allow the eigenvectors of the delay subspace (of the autocorrelation matrix) to be estimated faster. Simulation results are provided to show the faster convergence rate of the NMSE for the hopping pilot pattern over the fixed pilot pattern. ? 2005 IEEE.

In this letter, we analyse the properties of a maximum likelihood channel estimator based on the syndrome of a linear code. For the two examples of a binary symmetric channel and a binary input additive white Gaussian noise channel, we derive expressions for the bias and the mean squared error and compare them to the Cram\'er-Rao bound. The analytical expressions show the relationship between the estimator properties and the parameters of the linear code, i.e., the number of check nodes and the check node degree., Comment: 5 pages, accepted for IEEE Communications Letters