Search Results (24)

The paper presents a statistical model based on the two-weighted exponential distribution (TWED) to examine censored Human Immunodeficiency Virus (HIV) survival information. Identifying HIV as a disability, the study endorses an inclusive and sustainable health policy framework through some predictive findings. The TWED provides an accurate representation of the inherent hazard patterns and also improves the modelling of survival data. The parameter estimation is achieved in both a classical maximum likelihood estimation (MLE) and a Bayesian approach. Bayesian inference can be carried out under general entropy loss conditions and the symmetric squared error loss function through the Markov Chain Monte Carlo (MCMC) method. Based on the symmetric properties of the inverse of the Fisher information matrix, the asymptotic confidence intervals (ACLs) for the MLEs are constructed. Moreover, two-sided symmetric credible intervals (CRIs) of Bayesian estimates are also constructed based on the MCMC results that are based on symmetric normal proposals. The simulation studies are very important for indicating the correctness and probability of a statistical estimator. Implementing the model on actual HIV data illustrates its usefulness. Altogether, the paper supports the idea that statistics play an essential role in promoting disability-friendly and sustainable research in the field of public health in general. Full article

While Forgetting Factor Recursive Least Square (FFRLS) algorithms with evaluation mechanisms have been developed to address SOC-dependent parameter mapping shifts and their efficacy has been proven in Li-ion batteries, their applicability to lithium–sulfur (Li-S) batteries remains uncertain due to different electrochemical characteristics. This study critically evaluates the applicability of a Fisher information matrix-constrained FFRLS framework for online parameter identification in Li-S battery equivalent circuit network (ECN) models. Experimental validation using distinct drive cycles showed that the identification results of polarization-related parameters are significantly biased between different current excitations, and root mean square error (RMSE) variations diverge by 100%, with terminal voltage estimation errors more than 0.05 V. The parametric uncertainty under variable excitation profiles and voltage plateau estimation deficiencies confirms the inadequacy of such approaches, constraining model-based online identification viability for Li-S automotive applications. Future research should therefore prioritize hybrid estimation architectures integrating electrochemical knowledge with data-driven observers, alongside excitation capturing specifically optimized for Li-S online parameter observability requirements and cell nonuniformity and aging condition consideration. Full article

Life testing of products often requires extended observation periods. To shorten the duration of these tests, products can be subjected to more extreme conditions than those encountered in normal use; an approach known as accelerated life testing (ALT) is considered. This study investigates the estimation of unknown parameters and the acceleration factor for the modified Fréchet-Lomax exponential distribution (MFLED), utilizing Type II progressively first-failure censored (PFFC) samples obtained under the framework of constant-stress partially accelerated life testing (CSPALT). Maximum likelihood (ML) estimation is employed to obtain point estimates for the model parameters and the acceleration factor, while the Fisher information matrix is used to construct asymptotic confidence intervals (ACIs) for these estimates. To improve the precision of inference, two parametric bootstrap methods are also implemented. In the Bayesian context, a method for eliciting prior hyperparameters is proposed, and Bayesian estimates are obtained using the Markov Chain Monte Carlo (MCMC) method. These estimates are evaluated under both symmetric and asymmetric loss functions, and the corresponding credible intervals (CRIs) are computed. A comprehensive simulation study is conducted to compare the performance of ML, bootstrap, and Bayesian estimators in terms of mean squared error and coverage probabilities of confidence intervals. Finally, real-world failure time data of light-emitting diodes (LEDs) are analyzed to demonstrate the applicability and efficiency of the proposed methods in practical reliability studies, highlighting their value in modeling the lifetime behavior of electronic components. Full article

Federated learning (FL) enables multiple participants to collaboratively train models while efficiently mitigating the issue of data silos. However, large-scale heterogeneous data distributions result in inconsistent client objectives and catastrophic forgetting, leading to model bias and slow convergence. To address the challenges under non-independent and identically distributed (non-IID) data, we propose DPAO-PFL, a Dynamic Parameter-Aware Optimization framework that leverages continual learning principles to improve Personalized Federated Learning under non-IID conditions. We decomposed the parameters into two components: local personalized parameters tailored to client characteristics, and global shared parameters that capture the accumulated marginal effects of parameter updates over historical rounds. Specifically, we leverage the Fisher information matrix to estimate parameter importance online, integrate the path sensitivity scores within a time-series sliding window to construct a dynamic regularization term, and adaptively adjust the constraint strength to mitigate the conflict overall tasks. We evaluate the effectiveness of DPAO-PFL through extensive experiments on several benchmarks under IID and non-IID data distributions. Comprehensive experimental results indicate that DPAO-PFL outperforms baselines with improvements from $5.41\%$ to $30.42\%$ in average classification accuracy. By decoupling model parameters and incorporating an adaptive regularization mechanism, DPAO-PFL effectively balances generalization and personalization. Furthermore, DPAO-PFL exhibits superior performance in convergence and collaborative optimization compared to state-of-the-art FL methods. Full article

A new method to discover open-loop, unstable, longitudinal aerodynamic parameters, using a ‘two-stage optimization approach’ for designing optimal inputs, and with an application on the fighter aircraft platform, has been presented. System identification of supersonic aircraft requires formulating optimal inputs due to the extremely limited maneuver time, high angles of attack, restricted flight conditions, and the demand for an enhanced computational effect. A pre-requisite of the parametric model identification is to have a priori aerodynamic parameter estimates, which were acquired using linear regression and Least Squares (LS) estimation, based upon simulated time histories of outputs from heuristic inputs, using an F-16 Flight Dynamic Model (FDM). In the ‘first stage’, discrete-time pseudo-random binary signal (PRBS) inputs were optimized using a minimization algorithm, in accordance with aircraft spectral features and aerodynamic constraints. In the ‘second stage’, an innovative concept of integrating the Fisher Informative Matrix with cost function based upon D-optimality criteria and Crest Factor has been utilized to further optimize the PRBS parameters, such as its frequency, amplitude, order, and periodicity. This unique optimum design also solves the problem of non-convexity, model over-parameterization, and misspecification; these are usually caused by the use of traditional heuristic (doublets and multistep) optimal inputs. After completing the optimal input framework, parameter estimation was performed using Maximum Likelihood Estimation. A performance comparison of four different PRBS inputs was made as part of our investigations. The model performance was validated by using statistical metrics, namely the following: residual analysis, standard errors, t statistics, fit error, and coefficient of determination $({\mathrm{R}}^2)$. Results have shown promising model predictions, with an accuracy of more than 95%, by using a Single Sequence Band-limited PRBS optimum input. This research concludes that, for the identification of the decoupled longitudinal Linear Time Invariant (LTI) aerodynamic model of supersonic aircraft, optimum PRBS shows better results than the traditional frequency sweeps, such as multi-sine, doublets, square waves, and impulse inputs. This work also provides the ability to corroborate control and stability derivatives obtained from Computational Fluid Dynamics (CFD) and wind tunnel testing. This further refines control law design, dynamic analysis, flying qualities assessments, accident investigations, and the subsequent design of an effective ground-based training simulator. Full article

Extreme-mass-ratio inspirals (EMRIs) are promising gravitational-wave (GW) sources for space-based GW detectors. EMRI signals typically have long durations, ranging from several months to several years, necessitating highly accurate GW signal templates for detection. In most waveform models, compact objects in EMRIs are treated as test particles without accounting for their spin, mass quadrupole, or tidal deformation. In this study, we simulate GW signals from EMRIs by incorporating the spin and mass quadrupole moments of the compact objects. We evaluate the accuracy of parameter estimation for these simulated waveforms using the Fisher Information Matrix (FIM) and find that the spin, tidal-induced quadruple, and spin-induced quadruple can all be measured with precision ranging from ${10}^{-2}$ to ${10}^{-1}$, particularly for a mass ratio of ∼${10}^{-4}$. Assuming the “true” GW signals originate from an extended body inspiraling into a supermassive black hole, we compute the signal-to-noise ratio (SNR) and Bayes factors between a test-particle waveform template and our model, which includes the spin and quadrupole of the compact object. Our results show that the spin of compact objects can produce detectable deviations in the waveforms across all object types, while tidal-induced quadrupoles are only significant for white dwarfs, especially in cases approaching an intermediate-mass ratio. Spin-induced quadrupoles, however, have negligible effects on the waveforms. Therefore, our findings suggest that it is possible to distinguish primordial black holes from white dwarfs, and, under certain conditions, neutron stars can also be differentiated from primordial black holes. Full article

Several authors have attempted to compute the asymptotic Fisher information matrix for a univariate or multivariate time-series model to check for its identifiability. This has the form of a contour integral of a matrix of rational functions. A recent paper has proposed a short Wolfram Mathematica notebook for VARMAX models that makes use of symbolic integration. It cannot be used in open-source symbolic computation software like GNU Octave and GNU Maxima. It was based on symbolic integration but the integrand lacked symmetry characteristics in the appearance of polynomial roots smaller or greater than 1 in modulus. A more symmetric form of the integrand is proposed for VARMA models that first allows a simpler approach to symbolic integration. Second, the computation of the integral through Cauchy residues is also possible. Third, an old numerical algorithm by Söderström is used symbolically. These three approaches are investigated and compared on a pair of examples, not only for the Wolfram Language in Mathematica but also for GNU Octave and GNU Maxima. As a consequence, there are now sufficient conditions for exact model identifiability with fast procedures. Full article

In this work, we introduce an extension of the so-called beta autoregressive moving average ($\beta$ARMA) models. $\beta$ARMA models consider a linear dynamic structure for the conditional mean of a beta distributed variable. The conditional mean is connected to the linear predictor via a suitable link function. We propose modeling the relationship between the conditional mean and the linear predictor by means of the asymmetric Aranda-Ordaz parametric link function. The link function contains a parameter estimated along with the other parameters via partial maximum likelihood. We derive the partial score vector and Fisher’s information matrix and consider hypothesis testing, diagnostic analysis, and forecasting for the proposed model. The finite sample performance of the partial maximum likelihood estimation is studied through a Monte Carlo simulation study. An application to the proportion of stocked hydroelectric energy in the south of Brazil is presented. Full article

The length-biased lognormal distribution is a length-biased version of lognormal distribution, which is developed to model the length-biased lifetime data from, for example, biological investigation, medical research, and engineering fields. Owing to the existence of censoring phenomena in lifetime data, we study the change-point-testing problem of length-biased lognormal distribution under random censoring in this paper. A procedure based on the modified information criterion is developed to detect changes in parameters of this distribution. Under the sufficient condition of the Fisher information matrix being positive definite, it is proven that the null asymptotic distribution of the test statistic follows a chi-square distribution. In order to evaluate the uncertainty of change point location estimation, a way of calculating the coverage probabilities and average lengths of confidence sets of change point location based on the profile likelihood and deviation function is proposed. The simulations are conducted, under the scenarios of uniform censoring and exponential censoring, to investigate the validity of the proposed method. And the results indicate that the proposed approach performs better in terms of test power, coverage probabilities, and average lengths of confidence sets compared to the method based on the likelihood ratio test. Subsequently, the proposed approach is applied to the analysis of survival data from heart transplant patients, and the results show that there are differences in the median survival time post-heart transplantation among patients of different ages. Full article

In estimating logistic regression models, convergence of the maximization algorithm is critical; however, this may fail. Numerous bias correction methods for maximum likelihood estimates of parameters have been conducted for cases of complete data sets, and also for longitudinal models. Balanced data sets yield consistent estimates from conditional logit estimators for binary response panel data models. When faced with a missing covariates problem, researchers adopt various imputation techniques to complete the data and without loss of generality; consistent estimates still suffice asymptotically. For maximum likelihood estimates of the parameters for logistic regression in cases of imputed covariates, the optimal choice of an imputation technique that yields the best estimates with minimum variance is still elusive. This paper aims to examine the behaviour of the Hessian matrix with optimal values of the imputed covariates vector, which will make the Newton–Raphson algorithm converge faster through a reduced absolute value of the product of the score function and the inverse fisher information component. We focus on a method used to modify the conditional likelihood function through the partitioning of the covariate matrix. We also confirm that the positive moduli of the Hessian for conditional estimators are sufficient for the concavity of the log-likelihood function, resulting in optimum parameter estimates. An increased Hessian modulus ensures the faster convergence of the parameter estimates. Simulation results reveal that model-based imputations perform better than classical imputation techniques, yielding estimates with smaller bias and higher precision for the conditional maximum likelihood estimation of nonlinear panel models. Full article

This work discusses the issues of estimation and prediction when lifespan data following alpha-power Weibull distribution are observed under Type II hybrid censoring. We calculate point and related interval estimates for both issues using both non-Bayesian and Bayesian methods. Using the Newton–Raphson technique under the classical approach, we compute maximum likelihood estimates for point estimates in the estimation problem. Under the Bayesian approach, we compute Bayes estimates under informative and non-informative priors using the symmetric loss function. Using the Fisher information matrix under classical and Bayesian techniques, the corresponding interval estimates are derived. Additionally, using the best unbiased and conditional median predictors under the classical approach, as well as Bayesian predictive and associated Bayesian predictive interval estimates in the prediction approach, the predictive point estimates and associated predictive interval estimates are computed. We compare several suggested approaches of estimation and prediction using real data sets and Monte Carlo simulation studies. A conclusion is provided. Full article

There are many degradation models that are used in reliability analyses. The Wiener degradation model is the most popular across different applications. In this paper, we propose an approach for searching for an optimal design on the basis of the Wiener degradation model. The distinguishing feature of the approach is that the condition that the degradation index cannot exceed a critical level has been taken into account. The elements of the conditional Fisher information matrix have been obtained. This enables us to calculate the optimal stress levels by maximizing the functional of the conditional Fisher information matrix. Moreover, a degradation analysis of light-emitting diodes (LEDs) has been considered. Full article

In this paper, an algorithm for Mathematica is proposed for the computation of the asymptotic Fisher information matrix for a multivariate time series, more precisely for a controlled vector autoregressive moving average stationary process, or VARMAX process. Meanwhile, we present briefly several algorithms published in the literature and discuss the sufficient condition of invertibility of that matrix based on the eigenvalues of the process operators. The results are illustrated by numerical computations. Full article

Hellinger information as a local characteristic of parametric distribution families was first introduced in 2011. It is related to the much older concept of the Hellinger distance between two points in a parametric set. Under certain regularity conditions, the local behavior of the Hellinger distance is closely connected to Fisher information and the geometry of Riemann manifolds. Nonregular distributions (non-differentiable distribution densities, undefined Fisher information or denisities with support depending on the parameter), including uniform, require using analogues or extensions of Fisher information. Hellinger information may serve to construct information inequalities of the Cramer–Rao type, extending the lower bounds of the Bayes risk to the nonregular case. A construction of non-informative priors based on Hellinger information was also suggested by the author in 2011. Hellinger priors extend the Jeffreys rule to nonregular cases. For many examples, they are identical or close to the reference priors or probability matching priors. Most of the paper was dedicated to the one-dimensional case, but the matrix definition of Hellinger information was also introduced for higher dimensions. Conditions of existence and the nonnegative definite property of Hellinger information matrix were not discussed. Hellinger information for the vector parameter was applied by Yin et al. to problems of optimal experimental design. A special class of parametric problems was considered, requiring the directional definition of Hellinger information, but not a full construction of Hellinger information matrix. In the present paper, a general definition, the existence and nonnegative definite property of Hellinger information matrix is considered for nonregular settings. Full article

The optimal subsampling is an statistical methodology for generalized linear models (GLMs) to make inference quickly about parameter estimation in massive data regression. Existing literature only considers bounded covariates. In this paper, the asymptotic normality of the subsampling M-estimator based on the Fisher information matrix is obtained. Then, we study the asymptotic properties of subsampling estimators of unbounded GLMs with nonnatural links, including conditional asymptotic properties and unconditional asymptotic properties. Full article