Maximum Likelihood Estimation Research Articles

Behavioral and Psychosocial Dynamics in Diabetes Management: A Path Analysis to Examine the Influence of Acculturation in Arab Immigrant Communities.

Type 2 diabetes mellitus (T2DM) prevalence is rising globally. Arab immigrants with T2DM, one of the least studied ethnic minorities, have a higher diabetes prevalence and more prominent management-related challenges compared with mainstream host societies. Acculturation's impact on self-care activities and diabetes distress (DD) is understudied globally. To examine how acculturation affects self-care practices and DD in first-generation Arab immigrants with T2DM and how health literacy, illness perceptions, and self-efficacy mediate these associations. This multicenter cross-sectional study was conducted in Victoria, Australia. Eligible patients were invited while waiting for their appointments. The questionnaire included validated tools to assess DD, self-care activities, health literacy, self-efficacy, and acculturation. We tested mediation hypothesis using path analysis, with a maximum likelihood estimation to calculate total, direct, and indirect effects and bias-corrected accelerated 95% CI. Overall, 382 Arab immigrants with T2DM participated, with an average age of 57.9 years (SD = 8.0). Half were males, most had low education, and were married. Participants lived in Australia for a mean of 19.1 years (SD = 8.3) and had diabetes for 7.1 years (SD =4.7). Higher acculturation was directly associated with decreased DD. Illness perceptions (p = .002) and self-efficacy (p = .001) mediated the association of acculturation with self-care activities, while health literacy did not. Additionally, self-efficacy fully mediated the relationship between acculturation and DD (p = .001). This research provided valuable insights into the complex interplay between acculturation, diabetes management, and psychosocial factors. Interventions targeting self-efficacy and illness perceptions may improve self-care activities and reduce DD among Arab immigrants with T2DM.

Bayesian estimation of stochastic volatility jump diffusion model parameters using S&P 500 and VIX data

The Stochastic Volatility Jump Diffusion (SVJD) model is a common tool used for option pricing. Existing literature has employed many techniques in order to estimate the parameters of this model, including both Bayesian and frequentist approaches. In 2010, Duan and Yeh [Jump and volatility risk premiums implied by VIX. J Econ Dyn Control. 2010;34(11):2232–2244] used a frequentist approach with maximum likelihood estimation that included the VIX, the Chicago Board Options Exchange (CBOE) Volatility Index, which carries real time S&P 500 option price information in addition to the S&P 500 data. In this paper, we combine the previous Bayesian approach in Cape et al. [Estimating Heston's and Bates' models parameters using Markov Chain Monte Carlo simulation. J Stat Comput Simul. 2015;85(11):2295–2314] with the inclusion of VIX by Duan and Yeh. We provide the derivations of the conditional posterior distributions of the SVJD model's parameters and a guide to a Markov Chain Monte Carlo (MCMC) algorithm used to estimate the parameters. We apply the algorithm to the historical S&P 500 and VIX data and provide the subsequent parameter estimates. We offer these tools for others performing similar research with our R code available upon request.

Agricultural trade liberalization, governance quality, and technical efficiency in the agricultural sector of Southeast Asia

International trade has been regarded as an essential factor in enhancing a country's productivity and efficiency. Nevertheless, developing countries squander money and resources as a result of their deficient institutional quality, impeding their ability to profit from specialization and trade. Therefore, this study intends to investigate the impact of agricultural trade liberalization and governance quality on technical efficiency in Southeast Asia's agricultural sector using balanced panel data spanning from 2002 to 2021. The research utilizes translog stochastic frontier analysis (SFA) with a single-stage maximum likelihood estimation (MLE) to simultaneously calculate the time-varying technical efficiency scores and explore the core factors influencing agricultural inefficiency. The findings reveal that the average output-oriented technical efficiency for ASEAN-8 countries was 94 %. This suggests that there is significant potential to enhance technical efficiency in agricultural production by up to 6 % by addressing the adverse impacts of technical inefficiency. The research findings further point out that Malaysia is the most technically efficient country, having a technical efficiency score of 99.82 %, followed by Vietnam (99.75 %), Thailand (99.70 %), Lao PDR (98.90 %), Myanmar (95.42 %), Indonesia (91.64 %), the Philippines (90.65 %), and Cambodia (76.11 %). The results of disaggregated agricultural trade liberalization demonstrate a significant reduction in agricultural inefficiency in Southeast Asia through agricultural exports and imports. The findings also emphasize that improvements in the rule of law positively contribute to agricultural efficiency, whereas enhancements in terms of voice and accountability and regulatory quality appear to reduce it. Based on these findings, the government should consider enlarging open and liberalized trade policies in order to facilitate the exchange of technology and knowledge within the agriculture sector. Additionally, the government should involve farmers, agricultural cooperatives, local communities, and other relevant stakeholders in the decision-making process to ensure that policies address the specific needs and constraints faced by the sector.

HIGHLY ADAPTIVE LASSO: MACHINE LEARNING THAT PROVIDES VALID NONPARAMETRIC INFERENCE IN REALISTIC MODELS.

Understanding treatment effects on health-related outcomes using real-world data requires defining a causal parameter and imposing relevant identification assumptions to translate it into a statistical estimand. Semiparametric methods, like the targeted maximum likelihood estimator (TMLE), have been developed to construct asymptotically linear estimators of these parameters. To further establish the asymptotic efficiency of these estimators, two conditions must be met: 1) the relevant components of the data likelihood must fall within a Donsker class, and 2) the estimates of nuisance parameters must converge to their true values at a rate faster than . The Highly Adaptive LASSO (HAL) satisfies these criteria by acting as an empirical risk minimizer within a class of càdlàg functions with a bounded sectional variation norm, which is known to be Donsker. HAL achieves the desired rate of convergence, thereby guaranteeing the estimators' asymptotic efficiency. The function class over which HAL minimizes its risk is flexible enough to capture realistic functions while maintaining the conditions for establishing efficiency. Additionally, HAL enables robust inference for non-pathwise differentiable parameters, such as the conditional average treatment effect (CATE) and causal dose-response curve, which are important in precision health. While these parameters are often considered in machine learning literature, these applications typically lack proper statistical inference. HAL addresses this gap by providing reliable statistical uncertainty quantification that is essential for informed decision-making in health research.

Bayesian mixture model for accurate assessment of monthly maximum wind speed: A case study in Gwadar

Assessment of monthly maximum wind speed (MMWS) is essential in various environmental disciplines, including architectural risk assessment, climatology, renewable energy sources, building design, and agricultural activities. The distribution of wind speed is an important module of its development. Presently, several mixing distributions have been suggested for fitting the theoretical maximum wind speed distributions. However, the drawback of various distribution elements is the outcome of numerous fitting presentations, and it is challenging to choose the best form of single distribution to employ when building a hybrid model. In order to solve those difficulties, utilizing the mixtures of Sine-skewed-von Mises distributions (MSS-VM) with various prior parameter distributions is extended in the present study. In this research, the assessment of MMWS employing the maximum-likelihood estimation (MLE) method is taken into consideration for the wind speed data from the Pakistan province of Baluchistan Gwadar station. The results of the Anderson Darling (AD), Chi-square, BIC, and AIC tests, as well as the Kolmogorov Smirnov (KS) test, indicated that MSS-VM was the best distribution for the Gwadar station. The suggested models automatically find the optimum number of elements, in addition to having more appropriate performance. The outcomes demonstrate that MSS-VM performance is more suitable than other heterogeneous and single-distribution models. The design estimations derived using the Bayesian mixture distribution provide a sense of the highest wind speed that will occur across a particular area. It is therefore crucial for designers and policymakers in the planning, designing, and building of various structures.

Estimation of Lifetime Performance Index for Generalized Inverse Lindley Distribution Under Adaptive Progressive Type-II Censored Lifetime Test

The lifetime performance index (LPI) is an important metric for evaluating product quality, and research on the statistical inference of the LPI is of great significance. This paper discusses both the classical and Bayesian estimations of the LPI under an adaptive progressive type-II censored lifetime test, assuming that the product’s lifetime follows a generalized inverse Lindley distribution. At first, the maximum likelihood estimator of the LPI is derived, and the Newton–Raphson iterative method is adopted to solve the numerical solution due to the log-likelihood equations having no analytical solutions. If the exact distribution of the LPI is not available, then the asymptotic confidence interval and bootstrap confidence interval of the LPI are constructed. For the Bayesian estimation, the Bayesian estimators of the LPI are derived under three different loss functions. Due to the complex multiple integrals involved in these estimators, the MCMC method is used to draw samples and further construct the HPD credible interval of the LPI. Finally, Monte Carlo simulations are used to observe the performance of these estimators in terms of the average bias and mean squared error, and two practical examples are used to illustrate the application of the proposed estimation method.

The entropy-transformed Gompertz distribution: Distributional insights and cross-disciplinary utilizations

A novel two-parameter continuous model titled the entropy-transformed Gompertz (ETGPZ) distribution has been developed via the entropy transform. A new framework has been investigated and found to meet the criteria of the probability function. By significantly improving the functional shape and having the ability to model the most likely form of the hazard rate function, this new modification has increased the adaptability of the typical distribution. Some of its core characteristics, such as its statistical and computational features, are clearly presented. A thorough simulation analysis has been done to examine the final behavior of maximum likelihood estimators while estimating model parameters. We assess the performance and practical applicability of the ETGPZ distribution using eight real datasets from engineering and biomedical fields. The results demonstrate that the ETGPZ outperforms the baseline Gompertz (GPZ) distribution, highlighting its superiority and broader potential for various applications.

Fast and Robust Noise Background Modeling and Quasiperiodic Oscillation Detection for Astronomical Time Series

Spectrum with confidence levels is a commonly used method for quasiperiodic oscillation (QPO) detection, but it is prone to yield false positives for two reasons: poor choice and/or biased modeling of the null hypothesis (or noise background). Motivated by this, we propose a new time-domain maximum-likelihood estimation method, which can quickly and accurately estimate the noise background free from background trends, spectra peaks, and even QPOs. Our method provides a wide range of candidate stochastic models (e.g., conventional first-order autoregressive, power law, generalized Gauss–Markov, Matérn, and damped random walk), some of which have not been considered previously. Some pitfalls (e.g., detrending) in previous QPO detections are also correctly processed to minimize the false detections. Along with the multitaper method and wavelet, we revisit QPO detection in the X-ray emission from the active galaxies RE J10341+396 and 1H 0707-495, and point out why the significance levels of the QPO at ∼2.6 × 10−4 Hz would be different in previous detections and reduced if the whole observation duration is considered. Our algorithm can be easily extended to other branches of astrophysics and beyond.

How and why to follow best practices for testing mediation models with missing data.

Mediation models are often conducted in psychology to understand mechanisms and processes of change. However, current best practices for handling missing data in mediation models are not always used by researchers. Missing data methods, such as full information maximum likelihood (FIML) and multiple imputation (MI), are best practice methods of handling missing data. However, FIML or MI are rarely used to handle missing data when testing mediation models, instead analyses used listwise deletion methods, the default in popular software. Compared to listwise deletion, the implementation of FIML or MI to handle missing data reduces parameter estimate bias, while maintaining the sample collected to maximise power and generalizability of results. In this tutorial, we review how to implement full-information maximum likelihood and MI using best practice methods of testing the indirect effect. We demonstrate how to implement these methods using both R and JASP, which are both free, open-source software programmes and provide online supplemental materials for these demonstrations. These methods are demonstrated using two example analyses, one using a cross-sectional mediation model and one using a longitudinal mediation model examining how student-athletes reported worry about COVID predicts their perceived stress, which in turn predicts satisfaction with life.

James-Stein estimator improves accuracy and sample efficiency in human kinematic and metabolic data.

Human biomechanical data are often accompanied with measurement noise and behavioral variability. Errors due to such noise and variability are usually exaggerated by fewer trials or shorter trial durations, and could be reduced using more trials or longer trial durations. Speeding up such data collection by lowering number of trials or trial duration, while improving the accuracy of statistical estimates, would be of particular interest in wearable robotics applications and when the human population studied is vulnerable (e.g., the elderly). Here, we propose the use of the James-Stein estimator (JSE) to improve statistical estimates with a given amount of data, or reduce the amount of data needed for a given accuracy. The JSE is a shrinkage estimator that produces a uniform reduction in the summed squared errors when compared to the more familiar maximum likelihood estimator (MLE), simple averages, or other least squares regressions. When data from multiple human participants are available, an individual participant's JSE can improve upon MLE by incorporating information from all participants, improving overall estimation accuracy on average. Here, we apply the JSE to multiple time-series of kinematic and metabolic data from the following parameter estimation problems: foot placement control during level walking, energy expenditure during circle walking, and energy expenditure during resting. We show that the resulting estimates improve accuracy - that is, the James-Stein estimates have lower summed squared error from the 'true' value compared to more conventional estimates.

Constrained Bayesian Method for Testing Equi-Correlation Coefficient

The problem of testing the equi-correlation coefficient of a standard symmetric multivariate normal distribution is considered. Constrained Bayesian and classical Bayes methods, using the maximum likelihood estimation and Stein’s approach, are examined. For the investigation of the obtained theoretical results and choosing the best among them, different practical examples are analyzed. The simulation results showed that the constrained Bayesian method (CBM) using Stein’s approach has the advantage of making decisions with higher reliability for testing hypotheses concerning the equi-correlation coefficient than the Bayes method. Also, the use of this approach with the probability distribution of linear combinations of chi-square random variables gives better results compared to that of using the integrated probability distributions in terms of providing both the necessary precisions as well as convenience of implementation in practice. Recommendations towards the use of the proposed methods for solving practical problems are given.

Comparison between estimates of beta regression model using MSE

The multiple linear regression analysis shows the effects of explanatory variables on the dependent variable. Its function is to represent data to understand the shape and nature of the relationship between explanatory variables and the response variable. One of the main problems faced by linear regression is the nature of the data, as sometimes it does not follow a normal distribution. This has led to the emergence of different types of linear regression models such as the beta regression model, where the data of the dependent variable is less than one and confined within the period (0,1), and the data is relative and decimal. Non-traditional methods will be used to estimate beta regression parameters because some traditional methods do not provide suitable and accurate results when dealing with one of the main problems encountered in regression, which is multicollinearity. To address this issue, we used some methods include The Maximum Likelihood Estimation (MLE), ridge regression, modified Liu, and Ozkale and Kaciranlar method. Shrinking parameters are proposed for each method, and a comparison between the methods is conducted using the Mean Squared Error comparison criterion through a simulation experiment with two approaches, the simulation results showed that the ridge regression method is the best for the first and second methods of simulation. Paper type Research Paper

A New Extension of Topp-Leone Distribution (NETD) Using Generalized Logarithmic Function

Study’s Excerpt New Extension of Topp-Leone Distribution (NETD), derived using a generalized logarithm function, expanding the Topp-Leone family of distributions, is introduced. Mathematical properties of the NETD, including its quantile function, moments, Renyi entropy, and order statistics were investigated. The model demonstrates superior goodness-of-fit over existing models across four real-world datasets. Full Abstract In this study, we introduce a novel statistical model termed the New Extension of Topp-Leone Distribution (NETD), constructed using a generalized logarithm function. The derivation of the cumulative density function (CDF) and the probability density function (PDF) for this new distribution is thoroughly detailed. A validity test was conducted to confirm the legitimacy of the proposed NETD, and the results affirm that it is indeed a valid probability distribution. We investigate several key mathematical and statistical properties of the NETD, including the quantile function, moments, Renyi entropy, probability-weighted moments, and order statistics. These properties provide a comprehensive understanding of the distribution's behaviour and characteristics. To estimate the parameters of the NETD, we applied the Maximum Likelihood Estimation (MLE) method, which is known for its efficiency and asymptotic properties. The flexibility, versatility, and performance of the NETD were evaluated using four diverse real-world datasets. Through the application of model selection criteria such as the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Corrected Akaike Information Criterion (CAIC), and Hannan-Quinn Information Criterion (HQIC), we demonstrated that the NETD exhibits superior goodness-of-fit compared to existing variants of the Topp-Leone distribution. Our findings suggest that the NETD is a robust and adaptable distribution, capable of effectively modelling a wide range of empirical data. This new extension not only broadens the applicability of the Topp-Leone family of distributions but also enhances the toolkit available for statistical analysis and modelling in various fields.

Optimal Subsampling for Functional Quasi-Mode Regression with Big Data

We propose investigating optimal subsampling for functional regression with massive datasets based on the mode value, which is referred to as functional quasi-mode regression, to reduce data volume and alleviate computational burden. Using data-adaptive weights derived from regression residuals, the suggested regression offers enhanced robustness against nonnormal errors compared to traditional least squares or maximum likelihood estimation methods. To estimate the model, we employ B-spline basis functions to approximate the functional coefficient and include a penalty term in the objective function for enforcing smoothness in the resulting estimator. We adopt a computationally efficient mode-expectation-maximization algorithm, augmented by a Gaussian kernel, for numerical estimation. Under mild regularity conditions, we derive the asymptotic distributions of both full data and subsample quasi-mode estimators. The optimal subsampling probabilities by minimizing the asymptotic variance-covariance matrix under A- and L-optimality criteria are identified. These optimal probabilities rely on the full data estimate, prompting the development of a two-step algorithm to approximate the optimal subsampling procedure. The resultant algorithm is processing-efficient and can significantly reduce computational time compared to the full data approach. We also establish the asymptotic normality of the quasi-mode estimator obtained through this two-step algorithm. To assess finite sample performance, we conduct Monte Carlo simulations and analyze air quality data, showcasing the effectiveness of the developed estimator. Supplemental materials for this article are available online.

Analysis of Reliability for the Electrical Industries Company in Diyala using Modified Extension Weibull Distribution (An Application and Simulation study)

In this paper defining modified extension Weibull distribution, reliability function and hazerd function, we explain the maximum likelihood method under type one censoring sample. The censored samples play an important role in reliability analysis .In this paper we estimate and derived modified extension Weibull distribution whith three parameters under the censored samples type one by maximum likelihood estimation method depend on Newton-Raphson method. Then we applied simulation procedure using Monte-Carlo technique to estimate reliability function under different samples sizes and various initial values for the parameters for all estimated parameters of modified extension Weibull model by used MATLAB program. Finally we find the probability density function f(t), reliability function R(t),and hazard function h(t) for real data which get it from (Diyala province Company) is one of the formations of the Ministry of Industry and Minerals. Paper type: Research paper

Analysis of Reliability for the Electrical Industries Company in Diyala using Modified Extension Weibull Distribution (An Application and Simulation study)

In this paper defining modified extension Weibull distribution, reliability function and hazerd function, we explain the maximum likelihood method under type one censoring sample. The censored samples play an important role in reliability analysis .In this paper we estimate and derived modified extension Weibull distribution whith three parameters under the censored samples type one by maximum likelihood estimation method depend on Newton-Raphson method. Then we applied simulation procedure using Monte-Carlo technique to estimate reliability function under different samples sizes and various initial values for the parameters for all estimated parameters of modified extension Weibull model by used MATLAB program. Finally we find the probability density function f(t), reliability function R(t),and hazard function h(t) for real data which get it from (Diyala province Company) is one of the formations of the Ministry of Industry and Minerals. Paper type: Research paper

Variational Inference based on a Subclass of Closed Skew Normals

Gaussian distributions are widely used in Bayesian variational inference to approximate intractable posterior densities, but the ability to accommodate skewness can improve approximation accuracy significantly, when data or prior information is scarce. We study the properties of a subclass of closed skew normals constructed using affine transformation of independent standardized univariate skew normals as the variational density, and illustrate how it provides increased flexibility and accuracy in approximating the joint posterior in various applications, by overcoming limitations in existing skew normal variational approximations. The evidence lower bound is optimized using stochastic gradient ascent, where analytic natural gradient updates are derived. We also demonstrate how problems in maximum likelihood estimation of skew normal parameters occur similarly in stochastic variational inference, and can be resolved using the centered parameterization. Supplementary materials for this article are available online.

Bayesian inference in arm posture perception.

To configure our limbs in space the brain must compute their position based on sensory information provided by mechanoreceptors in the skin, muscles, and joints. Because this information is corrupted by noise, the brain is thought to process it probabilistically, and integrate it with prior belief about arm posture, following Bayes' rule. Here, we combined computational modeling with behavioral experimentation to test this hypothesis. The model conceives the perception of arm posture as the combination of a probabilistic kinematic chain composed by the shoulder, elbow, and wrist angles, compromised with additive Gaussian noise, with a Gaussian prior about these joint angles. We tested whether the model explains errors in a VR-based posture matching task better than a model that assumes a uniform prior. Human participants were required to align their unseen right arm to a target posture, presented as a visual configuration of the arm in the horizontal plane. Results show idiosyncratic biases in how participants matched their unseen arm to the target posture. We used maximum likelihood estimation to fit the Bayesian model to these observations and estimate key parameters including the prior means and its variance-covariance structure. The Bayesian model including a Gaussian prior explained the response biases and variance much better than a model with a uniform prior. The prior varied across participants, consistent with the idiosyncrasies in arm posture perception, and in alignment with previous behavioral research. Our work clarifies the biases in arm posture perception within a new perspective on the nature of proprioceptive computations.

Deep regression learning with optimal loss function

In this paper, we develop a novel efficient and robust nonparametric regression estimator under a framework of a feedforward neural network (FNN). There are several interesting characteristics for the proposed estimator. First, the loss function is built upon an estimated maximum likelihood function, which integrates the information from observed data as well as the information from the data distribution. Consequently, the resulting estimator has desirable optimal properties, such as efficiency. Second, different from the traditional maximum likelihood estimation (MLE), the proposed method avoids the specification of the distribution, making it adaptable to various distributions such as heavy tails and multimodal or heterogeneous distributions. Third, the proposed loss function relies on probabilities rather than direct observations as in least square loss, contributing to the robustness of the proposed estimator. Finally, the proposed loss function involves a nonparametric regression function only. This enables the direct application of the existing packages, simplifying the computational and programming requirements. We establish the large sample property of the proposed estimator in terms of its excess risk and minimax near-optimal rate. The theoretical results demonstrate that the proposed estimator is equivalent to the true MLE where the density function is known in terms of excess risk. Our simulation studies show that the proposed estimator outperforms the existing methods based on prediction accuracy, efficiency and robustness. Particularly, it is comparable to the MLE with the known density and even gets slightly better as the sample size increases. This implies that the adaptive and data-driven loss function from the estimated density may offer an additional avenue for capturing valuable information. We further apply the proposed method to four real data examples, resulting in significantly reduced out-of-sample prediction errors compared to existing methods.

Bearing remaining life prediction method based on ARAD -ELN and multi-stage wiener process

Abstract Stochastic process-based models are extensively utilized in health assessments and Remaining Useful Life (RUL) predictions of bearings. Nevertheless, bearings in actual operation undergo multiple degradation stages, each characterized by its unique trend of degradation. The application of a singular stochastic process for RUL prediction falls short of achieving optimal performance. Consequently, this paper introduces a multi-stage Wiener process-based approach for the prediction of bearings' RUL. Initially, to tackle the challenge of imbalanced sample sizes across different degradation stages of bearings, an ensemble learning-based neural network (ELN) enhanced by ARIMA Residual Anomaly Detection (ARAD) for the identification of bearing degradation stages is proposed. Subsequently, taking into account the temporal, unit-to-unit, and nonlinear variabilities of the degradation process at each stage, a Wiener process-based multi-stage degradation model for bearings is developed. A method for parameter estimation and updating, utilizing Kalman filtering and Maximum Likelihood Estimation (K-M) is introduced. Finally, the proposed model undergoes validation using both simulated data and the XJTU-SY bearing dataset. Experimental results of three RUL predictions show that the proposed method leads the benchmark model with RMSE values of 3.61, 2.92 and 7.24 respectively, affirming that the proposed model can precisely classify equipment degradation stages and predict RUL with high accuracy and stability.