Maximum Likelihood Estimation Research Articles

Gen Z Tourism Employees’ Adaptive Performance During a Major Cultural Shift: The Impact of Leadership and Employee Voice Behavior

Based on social exchange theory and the norm of reciprocity, the current study proposes a mediation model to assess the role of employee voice behavior (promotive and prohibitive) on the relationship between leadership (i.e., transformational, inclusive, and adaptive) and Gen Z employees’ adaptive performance (AP). Research data were obtained from 195 Gen Z employees and their supervisors from a group of luxury hotels located in Greece that had experienced a major cultural shift. The research model was examined using the structural equation modeling technique (SEM) with maximum likelihood estimation using the analysis of moment structures program (AMOS version 24). The research findings indicate that (a) all three leadership approaches positively influence Gen Z employees’ AP, (b) promotive voice behavior mediates the relationship between all leadership approaches and Gen Z employees’ AP, and (c) prohibitive voice behavior mediates the relationship between inclusive leadership and Gen Z employees’ AP. The results suggest that by implementing human-centered practices and procedures to positively influence Gen Z employees’ voice behavior, tourism leaders/managers can increase their AP.

Parameter Estimation of a Partially Observed Hypoelliptic Stochastic Linear System

In this article, we address the problem of the parameter estimation of a partially observed linear hypoelliptic stochastic system in continuous time, a relevant problem in various fields, including mechanical and structural engineering. We propose an online approach which is an approximation to the expectation–maximization (EM) algorithm. This approach combines the Kalman–Bucy filter, to deal with partial observations, with the maximum likelihood estimator for a degenerate n-dimensional system under complete observation. The performance of the proposed approach is illustrated by means of a simulation study undertaken on a harmonic oscillator that describes the dynamic behavior of an elementary engineering structure subject to random vibrations. The unknown parameters represent the oscillator’s stiffness and damping coefficients. The simulation results indicate that, as the variance of the observation error vanishes, the proposed approach remains reasonably close to the output of the EM algorithm, with the advantage of a significant reduction in computing time.

Optimal limits of continuously monitored thermometers and their Hamiltonian structure

We investigate the fundamental and practical precision limits of thermometry in bosonic and fermionic environments by coupling an N-level probe to them and continuously monitoring it. Our findings show that the ultimate precision limit, quantified by the Fisher information, scales linearly with N, offering an exponential improvement over equilibrium thermometry, where the scaling is only log2N. For a fixed Hamiltonian structure, we develop a maximum-likelihood estimation strategy that maps the observed continuously monitored trajectories of the probe into temperature estimates with minimal error. By optimizing over all possible Hamiltonian structures, we discover that the optimal configuration is an effective two-level system, with both levels exhibiting degeneracy that increases with N—a stark contrast to equilibrium thermometry, where the ground state remains nondegenerate. Our results have practical implications. First, continuous monitoring is experimentally feasible on several platforms and accounts for the preparation time of the probe, which is often overlooked in other approaches such as prepare and reset. Second, the linear scaling is robust against deviations from the effective two-level structure of the optimal Hamiltonian. Additionally, this robustness extends to cases of initial ignorance about the temperature. Thus, in global estimation problems, the linear scaling remains intact even without adaptive strategies. Published by the American Physical Society 2025

Weighted past and paired dynamic varentropy measures, their properties, usefulness and inferences

We introduce two uncertainty measures, say weighted past varentropy (WPVE) and weighted paired dynamic varentropy (WPDVE). Several properties of these proposed measures, including their effect under the monotone transformations are studied. An upper bound of the WPVE using the weighted past Shannon entropy and a lower bound of the WPVE are obtained. Further, the WPVE is studied for the proportional reversed hazard rate (PRHR) models. Upper and lower bounds of the WPDVE are derived. In addition, the non-parametric kernel estimates of the WPVE and WPDVE are proposed. Furthermore, the maximum likelihood estimation technique is employed to estimate WPVE and WPDVE for an exponential population. A numerical simulation is provided to observe the behaviour of the proposed estimates. A real data set is analysed, and then the estimated values of WPVE are obtained. Based on the bootstrap samples generated from the real data set, the performance of the non-parametric and parametric estimators of the WPVE and WPDVE is compared in terms of the absolute bias and mean squared error (MSE). Finally, we have reported an application of WPVE. Abbreviations RV: Random variable; PDF: Probability density function; IC: Information content; SE: Shannon entropy; VE: Varentropy; MSE: Mean squared error; RVE: Residual varentropy; CDF: Cumulative distribution function; PVE: Past varentropy; WVE: Weighted varentropy; WPSE: Weighted past Shannon entropy; WRVE: Weighted residual varentropy; WPVE: Weighted past varentropy; WPRE: Weighted past Rényi entropy; PRHR: Proportional reversed hazard rate; WPDE: Weighted paired dynamic entropy; WPDVE: Weighted paired dynamic varentropy entropy; AB: Absolute bias; CRHR: Cumulative reversed hazard rate; VPL: Variance past lifetime; MPL: Mean past lifetime; MRL: Mean residual lifetime; VRL: Variance residual lifetime; GMB-II: Gumbel-II; GXE: Generalised X-exponential; EXP: Exponential; lnL: Log-likelihood criterion; AIC: Akaikes information criterion; BIC: Bayesian information criterion; MLE: Maximum likelihood estimate

Pulse characterization at the single-photon level through chronocyclic Q-function measurements

The characterization of the complex spectral amplitude, that is, the spectrum and spectral phase, of single-photon-level light fields is a crucial capability for modern photonic quantum technologies. Since established pulse characterization techniques are not applicable at low intensities, alternative approaches are required. Here, we demonstrate the retrieval of the complex spectral amplitude of single-photon-level light pulses through measuring their chronocyclic Q −function. Our approach draws inspiration from quantum state tomography by exploiting the analogy between quadrature phase space and time-frequency phase space. In the experiment, we perform time-frequency projections with a quantum pulse gate (QPG), which directly yield the chronocyclic Q −function. We evaluate the complex spectral amplitude from the measured chronocyclic Q −function data with maximum likelihood estimation (MLE), which is the established technique for quantum state tomography. The MLE yields not only an unambigious estimate of the complex spectral amplitude of the state under test that does not require any a priori information, but also allows for, in principle, estimating the spectral-temporal coherence properties of the state. Our method accurately recovers features such as jumps in the spectral phase and is resistant against regions with zero spectral intensity, which makes it immediately beneficial for classical pulse characterization problems.

Bayesian inferences for an accelerated degradation model based on tweedie exponential dispersion process

Tweedie exponential dispersion (TED) process is a large class of generalized stochastic process, which includes the commonly used Wiener process, Gamma process and inverse Gausssian process as special cases. In this paper, we propose an accelerated degradation model based on the TED process, and then apply the objective Bayesian method to make inferences on the model. The Jeffreys prior and reference priors under different group orderings are derived, and the posterior property based on each prior is then validated. A simulation study is carried out to assess the performance of the proposed Bayesian method in comparison with the maximum-likelihood estimation (MLE), and finally the method is applied to analyse a real degradation dataset.

Static-Aperture Synthesis Method in Remote Sensing and Non-Destructive Testing Applications

The study is dedicated to the statistical optimization of radar imaging of surfaces with the synthetic aperture radar (SAR) technique, assuming a static surface area and applying the ability to move a sensor along a nonlinear trajectory via developing a new method and validating its operability for remote sensing and non-destructive testing. The developed models address the sensing geometry for signals reflected from a surface along with the observation signal–noise equation, including correlation properties. Moreover, the optimal procedures for coherent radar imaging of surfaces with the static SAR technology are synthesized according to the maximum likelihood estimation (MLE). The features of the synthesized algorithm are the decoherence of the received oscillations, the matched filtering of the received signals, and the possibility of using continuous signal coherence. Furthermore, the developed optimal and quasi-optimal algorithms derived from the proposed MLE have been investigated. The novel framework for radio imaging has demonstrated good overall operability and efficiency during simulation modeling (using the MATLAB environment) for real sensing scenes. The developed algorithms of spatio–temporal signal processing in systems with a synthesized antenna with nonlinear carrier trajectories open a promising direction for creating new methods of high-precision radio imaging from UAVs and helicopters.

Examination of nonlinear longitudinal processes with latent variables, latent processes, latent changes, and latent classes in the structural equation modeling framework: The R package nlpsem.

We introduce the R package nlpsem (Liu, 2023), a comprehensive toolkit for analyzing longitudinal processes within the structural equation modeling (SEM) framework, incorporating individual measurement occasions. This package emphasizes nonlinear longitudinal models, especially intrinsic ones, across four key scenarios: (1) univariate longitudinal processes with latent variables, optionally including covariates such as time-invariant covariates (TICs) and time-varying covariates (TVCs); (2) multivariate longitudinal analyses to explore correlations or unidirectional relationships between longitudinal variables; (3) multiple-group frameworks for comparing manifest classes in scenarios (1) and (2); and (4) mixture models for scenarios (1) and (2), accommodating latent class heterogeneity. Built on the OpenMx R package, nlpsem supports flexible model designs and uses the full information maximum likelihood method for parameter estimation. A notable feature is its algorithm for determining initial values directly from raw data, improving computational efficiency and convergence. Furthermore, nlpsem provides tools for goodness-of-fit tests, cluster analyses, visualization, derivation of pvalues and three types of confidence intervals, as well as model selection for nested models using likelihood-ratio tests and for non-nested models based on criteria such as Akaike information criterion and Bayesian information criterion. This article serves as a companion document to the nlpsem R package, providing a comprehensive guide to its modeling capabilities, estimation methods, implementation features, and application examples using synthetic intelligence growth data.

Estimation and Bayesian Prediction for the Generalized Exponential Distribution Under Type-II Censoring

This research focuses on the prediction and estimation problems for the generalized exponential distribution under Type-II censoring. Firstly, maximum likelihood estimations for the parameters of the generalized exponential distribution are computed using the EM algorithm. Additionally, confidence intervals derived from the Fisher information matrix are developed and analyzed alongside two bootstrap confidence intervals for comparison. Compared to classical maximum likelihood estimation, Bayesian inference proves to be highly effective in handling censored data. This study explores Bayesian inference for estimating the unknown parameters, considering both symmetrical and asymmetrical loss functions. Utilizing Gibbs sampling to produce Markov Chain Monte Carlo samples, we employ an importance sampling approach to obtain Bayesian estimates and compute the corresponding highest posterior density (HPD) intervals. Furthermore, for one-sample prediction and, separately, for the two-sample case, we provide the corresponding posterior distributions, along with methods for computing point predictions and predictive intervals. Through Monte Carlo simulations, we evaluate the performance of Bayesian estimation in contrast to maximum likelihood estimation. Finally, we conduct an analysis of a real dataset derived from deep groove ball bearings, calculating Bayesian point predictions and predictive intervals for future samples.

Bivariate Latent Change Score Models in Small Sample Contexts: Comparison of Maximum Likelihood and Bayesian Estimation

This study examines the performance of fitting bivariate latent change score (BLCS) models under small sample sizes (i.e., N ≤ 100) and limited numbers of repeated measures (i.e., t ≤ 5). Under these realistic conditions, we compared the performance of two estimation methods: maximum likelihood (ML) and Bayesian methods with various priors (i.e., non-informative priors and data-dependent priors). Results indicate that, in general, the Bayesian estimation method, especially with non-informative priors, achieved higher convergence rates and smaller empirical standard deviations for parameter estimates, whereas the ML method exhibited lower relative biases for parameter estimates. When the proportional and coupling coefficients are positive, the Bayesian method with non-informative priors provides accurate and stable parameter estimates for a sample size of ≥50 and ≥5 waves. When negative coefficients are included, either the ML or Bayesian method can be recommended, provided there are ≥4 waves, substantial coefficient effects, and minimal measurement error.

Seismic Fragility Assessment of Base-Isolated Nuclear Power Plant Structures

Base isolators constitute solutions for improving the seismic performance of civil and nuclear engineering structures. This paper evaluates the seismic fragility of based-isolated nuclear power plant structures using the proposed fragility curves. A finite element model of the structures is developed deploying SAP2000, a structural analysis program. For constructing fragility curves, a set of ground motions is employed to perform nonlinear time-history analyses associated with Incremental Dynamic Analyses (IDA). Three Damage States (DS) are defined based on the shear deformation of base isolators. Finally, the maximum likelihood estimation technique generates a set of fragility curves for DS. Additionally, a comparison of fragility curves between IDA and Cloud Analysis (CA) is presented.

Monte Carlo method for constructing confidence intervals with unconstrained and constrained nuisance parameters in the NOvA experiment

Abstract Measuring observables to constrain models using maximum-likelihood estimation is fundamental to many physics experiments. Wilks' theorem provides a simple way to construct confidence intervals on model parameters, but it only applies under certain conditions. These conditions, such as nested hypotheses and unbounded parameters, are often violated in neutrino oscillation measurements and other experimental scenarios. Monte Carlo methods can address these issues, albeit at increased computational cost. In the presence of nuisance parameters, however, the best way to implement a Monte Carlo method is ambiguous. This paper documents the method selected by the NOvA experiment, the profile construction. It presents the toy studies that informed the choice of method, details of its implementation, and tests performed to validate it. It also includes some practical considerations which may be of use to others choosing to use the profile construction.

Noisy Non‐Negative Tucker Decomposition With Sparse Factors and Missing Data

ABSTRACTTensor decomposition is a powerful tool for extracting physically meaningful latent factors from multi‐dimensional non‐negative data, and has been an increasing interest in a variety of fields such as image processing, machine learning, and computer vision. In this paper, we propose a sparse non‐negative Tucker decomposition and completion approach for the recovery of underlying non‐negative data under incompleted and generally noisy observations. Here the underlying non‐negative tensor data is decomposed into a core tensor and several factor matrices with all entries being non‐negative and the factor matrices being sparse. The loss function is derived by the maximum likelihood estimation of the noisy observations, and the norm is employed to enhance the sparsity of the factor matrices. We establish the error bound of the estimator of the proposed model under generic noise scenarios, which is then specified to the observations with additive Gaussian noise, additive Laplace noise, and Poisson observations, respectively. Our theoretical results are better than those by existing tensor‐based or matrix‐based methods. Moreover, the minimax lower bounds are shown to be matched with the derived upper bounds up to logarithmic factors. Numerical experiments on both synthetic data and real‐world data sets demonstrate the superiority of the proposed method for non‐negative tensor data completion.

Maximum likelihood estimation for small noise multi-scale McKean-Vlasov stochastic differential equations

Maximum likelihood estimation for small noise multi-scale McKean-Vlasov stochastic differential equations

Statistical Inference Based on Censored Data of Entropy for Lomax Distribution

The current research centers around entropy, which is officially defined as an indicator of the possible amount of information of the Lomax (Lo) distribution that quantifies the uncertainty of random variables. When the parameters are unknown under adaptive progressive Using type-II censored data, the entropy maximum likelihood estimate (MLE) is computed and the bootstrap confidence intervals of entropy is displayed. The Bayes estimator of entropy is demonstrated using both the symmetric and asymmetric loss functions. In the meantime, the posterior is also computed to assess how well the entropy estimators perform in relation to various loss functions. The Bayesian estimates were obtained in a numerical simulation applying the method of Markov Chain Monte Carlo (MCMC). Then, using Monte Carlo simulations, various approaches are compared to identify the believable intervals of the entropy's highest posterior density (HPD). Lastly, the recommended methods are illustrated using a numerical example.

Quantification of albumin and γ-globulin concentrations by multivariate regression based on admittance relaxation time distribution (mrARTD)

Albumin andγ-globulin concentrations in subcutaneous adipose tissues (SAT) have been quantified by multivariate regression based on admittance relaxation time distribution (mrARTD) under the fluctuated background of sodium electrolyte concentration. ThemrARTD formulatesP=Ac+Ξ(P: peak matrix of distribution function magnitudeγˆand relaxation timesτˆ,c: concentration matrix of albumincAlb,γ-globulinGloc, and sodium electrolyteNac,A: coefficient matrix of a multivariate regression model, andΞ: error matrix). ThemrARTD is implemented by two processes which are: (1) the training process ofAthrough the maximum likelihood estimation ofPand (2) the quantification process ofcAlb,Gloc, andNacthrough the model prediction. In the training process, a positive correlation is present betweencAlb,Gloc, andNactoγˆ1atτˆ1= 0.1 as well asγˆ2atτˆ2= 1.40 μs as under a fixed concentration of proteins solution into a porcine SAT (cAlb= 0.800-2.400 g/dL,Gloc= 0.400-1.200 g dl-1andNac= 0.700-0.750 g dl-1). ThemrARTD method quantifiescAlb,Gloc, andNacin SAT with an absolute error of 33.79%, 44.60%, and 2.18%, respectively.

An Extension of Some Truncated Distributions Family With Application

This paper represents a suggested a combination of continuous distributions based on Truncated Gompertz-G (tgo-gd[0,1]) and Truncated Gompertz-Weibull (tgo-wd) distributions. Some of the main properties of the suggested combination such as the distribution function (cdf), the probability function (pdf), survival function (Sf), hazard function (Hrf), quintile function (Qf), moment generating function (mgf), skewness ,, kurtosis , entropy, and maximum likelihood estimator (MLE) for the proposed combination of tgo-wd[0,1] have been presented. As well, an experimentally estimation for the parameters of the distributions using MLE have been studied. After the application, the potentiality of the proposed family by means of one real data sets are shown more flexibility in compare with the other models.

Jointly modeling responses and omitted items by a competing risk model: A survival analysis approach.

Item response theory models are commonly adopted in educational assessment and psychological measurement. Such models need to be modified to accommodate practical situations when statistical sampling assumptions are violated. Omission is a common phenomenon in educational testing. In modern computer-based testing, we have not only examinees' responses but also their response times. This paper utilizes response time and develops a joint model of responses and response times. The new approach is analogous to those developed in survival analysis for dealing with right-censored data. In particular, a key ingredient is the introduction of the omission time (OT), which corresponds to the censoring time in survival analysis. By competing risk formulation, the proposed method provides an alternative narrative to how an item becomes answered versus omitted, depending on the competing relationship of response time and OT, so that the likelihood function can be constructed properly. The maximum likelihood estimator can be computed via the expectation-maximization algorithm. Simulation studies were conducted to evaluate the performance of the proposed method and its robustness against various mis-specifications. The method was applied to a dataset from the PISA 2015 Science Test.

The impact of computerized adaptive test termination rules on accuracy across different ability estimation methods

The study aimed to compare the termination rules of computerized adaptive testing (CAT), specifically the rule of termination after a fixed number of items versus the rule of termination based on the minimum standard error (SE), using the methods of maximum likelihood estimation (MLE) and maximum a posteriori. The goal was to assess the relative accuracy of each rule to determine which method provides the highest measurement accuracy. In order to address the objectives of the study, the researcher developed a mathematics item bank for the 6<sup>th</sup> and 7<sup>th</sup> grades consisting of 275 items. This bank was used to develop 6 achievement tests, three for 6th grade and three for 7<sup>th</sup> grade, with each test comprising 46 items. In addition, 10 items were common to all the tests and were used as a common core. The tests were conducted with 2612 students of class six and seven. For data and information analysis and processing, BILOG-MG-3.0, SPSS, and Fast Test Web v3.80.26 applications were used. Four different applications were performed on another sample of 403 students in order to evaluate the precision of the CAT procedure through several terminating criteria–a fixed criterion of 25 administered items and a criterion based on a SE of no larger than 0.25. From the results obtained, the accuracy of examinations is independent of the method used in estimating the parameters and that the determination of the fixed period is superior to the determination relating to SE. Moreover, the results revealed that adopting Bayes’ theorem and a termination rule determined by standard deviation improves precision of the estimation, though in a case where 25 items are used, MLE is the best.

Neonatal outcomes and resuscitation practices following the addition of heart rate-guidance to basic resuscitation.

To evaluate the impact of heart rate-guided basic resuscitation compared to Helping Babies Breathe on neonatal outcomes and resuscitation practices in the Democratic Republic of the Congo. We conducted a pre-post clinical trial comparing heart rate-guided basic resuscitation to Helping Babies Breathe in three facilities, enrolling in-born neonates ≥28 weeks gestation. We collected observational data during a convenience sample of resuscitations and extracted clinical data from the medical record for all participants. We evaluated our primary outcome of effective breathing at three minutes after birth among newborns not breathing well at 30 seconds after birth employing generalized linear models using maximum likelihood estimation. Among 1,284 newborns with observational data, there was no difference in the proportion effectively breathing at three minutes (adjusted relative risk 1.08 [95% CI 0.81, 1.45]). Among 145 receiving bag mask ventilation, time to bag mask ventilation decreased 64.3 seconds during heart rate-guided resuscitation (p<0.001). Among 10,906 enrolled in the trial, perinatal mortality was unchanged (adjusted relative risk 1.19 [95% CI 0.96, 1.48]) and death before discharge increased (adjusted relative risk 1.43 [95% CI 1.03, 1.99]). Expert review of stillborn cases demonstrated a stillbirth misclassification rate of 33.3% during Helping Babies Breathe versus 5.9% in heart rate-guided resuscitation. During heart rate-guided basic resuscitation, time to bag mask ventilation was reduced by greater than one minute. The increase in death before discharge and unchanged perinatal mortality may be due to resuscitation of newborns with a higher risk of mortality who were previously presumed stillborn. A cluster-randomized trial of heart rate-guided basic resuscitation is needed to evaluate its impact on neonatal mortality in low-resource settings.