Maximum Likelihood Estimation Research Articles

Nonparametric estimation of the cumulative incidence function for doubly-truncated and interval-censored competing risks data.

Interval sampling is widely used for collection of disease registry data, which typically report incident cases during a certain time period. Such sampling scheme induces doubly truncated data if the failure time can be observed exactly and doubly truncated and interval censored (DTIC) data if the failure time is known only to lie within an interval. In this article, we consider nonparametric estimation of the cumulative incidence functions (CIF) using doubly-truncated and interval-censored competing risks (DTIC-C) data obtained from interval sampling scheme. Using the approach of Shen (Stat Methods Med Res 31:1157-1170, 2022b), we first obtain the nonparametric maximum likelihood estimator (NPMLE) of the distribution function of failure time ignoring failure types. Using the NPMLE, we proposed nonparametric estimators of the CIF with DTIC-C data and establish consistency of the proposed estimators. Simulation studies show that the proposed estimator performs well for finite sample size.

Gompertz-Weibull {Gompertz} Type I: A Four-Parameter Generalization of the Weibull Family

AbstractIn this paper, we provide a construction method that provides greater flexibility in modeling real-world phenomenon by generalizing univariate probability distributions. The Gompertz distribution is used to provide new classes of models through T-X{Y} construction, in a manner we will define as a “proper” generalization, illustrated by application to the popular Weibull family. We provide moments and other properties of the model, including the necessary equations for maximum likelihood estimation, and we fit a set of real data to the model. A framework for classifying generalizations that includes many previously discovered methods and considerations for the research infrastructure are proposed in our methods and discussion.

Improving power law fitting of root tensile strength–diameter relationships

Abstract Purpose The relationship between root tensile strengths and diameters is often fitted using power law curves. More accurate fitting methodologies were developed, investigating a) the validity of least-squares regression assumptions underlying existing methods, b) how to best quantify intra-diameter variation, and c) whether to fit in terms of tensile strength or tensile force at failure. Methods Regression and maximum likelihood estimation were used to fit various power law models. 6461 tensile strength measurements from 153 existing datasets, covering 103 different plant species, were used to compare models. Results The intra-diameter variation in root strength is proportional to the average strength at each diameter, and is best described using a gamma distribution. When using linear regression on log-transformed measurements, a mathematical correction must be used to avoid underestimating the actual strength (18% on average). Compared to fitting tensile strengths, fitting in terms of root forces at failure was less reliable; the extra emphasis this method places on the effect of large diameters roots was not appropriate because of the typical abundance of thin roots in the field relative to those tested in tension. Average power law fits were proposed for broadleaved trees, conifers, shrubs, grasses and forbs. Conclusion Power law curves should be fitted in terms of root strength rather than root forces at failure, using the newly developed fitting methods that simultaneously fit both the inter-diameter (power law) and intra-diameter variation and can account for fitting bias. This will increase the reliability of future root reinforcement predictions.

Validation, Factor Structure and Measurement Invariance of the Duke University Religion Index Among Puerto Rican Adults.

Religiosity is a determinant of human flourishing and a protective/risk factor on health. In recent years the DUREL has been one of the most used measures in studies of religion and health worldwide. This scale has five items to assess three domains: organizational religiosity (item 1), non-organizational religiosity (item 2), and intrinsic/subjective religiosity (items 3, 4 and 5). Through an online survey, we examined the psychometric properties, factor structure and measurement invariance of the Duke University Religion Index among 411 Spanish-speaking Puerto Rican adults. We found alpha and omega reliability coefficients of .91. In confirmatory factor analysis (CFA) with robust maximum likelihood estimation, best-fit models were those with three factors. We observed adequate convergent/discriminant validity via CFA-related statistics. Using multigroup CFA, the DUREL was gender-invariant. Correlations with external criteria supported its concurrent validity. Our findings support DUREL's utility as a religiosity measure for Puerto Ricans.

Calibration of the Ueno’s Shadow Rate Model of Interest Rates

Shadow rate models of interest rates are based on the assumption that the interest rates are determined by an unobservable shadow rate. This idea dates back to Fischer Black, who understood the interest rate as an option that cannot become negative. Its possible zero values are consequences of negative values of the shadow rate. In recent years, however, the negative interest rates have become a reality. To capture this behavior, shadow rate models need to be adjusted. In this paper, we study Ueno’s model, which uses the Vasicek process for the shadow rate and adjusts its negative values when constructing the short rate. We derive the probability properties of the short rate in this model and apply the maximum likelihood estimation method to obtain the parameters from the real data. The other interest rates are—after a specification of the market price of risk—solutions to a parabolic partial differential equation. We solve the equation numerically and use the long-term rates to fit the market price of risk.

Sieve Maximum Likelihood Estimation of Partially Linear Transformation Models With Interval-Censored Data.

Partially linear models provide a valuable tool for modeling failure time data with nonlinear covariate effects. Their applicability and importance in survival analysis have been widely acknowledged. To date, numerous inference methods for such models have been developed under traditional right censoring. However, the existing studies seldom target interval-censored data, which provide more coarse information and frequently occur in many scientific studies involving periodical follow-up. In this work, we propose a flexible class of partially linear transformation models to examine parametric and nonparametric covariate effects for interval-censored outcomes. We consider the sieve maximum likelihood estimation approach that approximates the cumulative baseline hazard function and nonparametric covariate effect with the monotone splines and -splines, respectively. We develop an easy-to-implement expectation-maximization algorithm coupled with three-stage data augmentation to facilitate maximization. We establish the consistency of the proposed estimators and the asymptotic distribution of parametric components based on the empirical process techniques. Numerical results from extensive simulation studies indicate that our proposed method performs satisfactorily in finite samples. An application to a study on hypobaric decompression sickness suggests that the variable TR360 exhibits a significant dynamic and nonlinear effect on the risk of developing hypobaric decompression sickness.

On the posterior property of the Rician distribution

The Rician distribution, a well-known statistical distribution frequently encountered in fields like magnetic resonance imaging and wireless communications, is particularly useful for describing many real phenomena such as signal process data. In this paper, we introduce objective Bayesian inference for the Rician distribution parameters, specifically the Jeffreys rule and Jeffreys prior are derived. We proved that the obtained posterior for the first priors led to an improper posterior while the Jeffreys prior led to a proper distribution. To evaluate the effectiveness of our proposed Bayesian estimation method, we perform extensive numerical simulations and compare the results with those obtained from traditional moment-based and maximum likelihood estimators. Our simulations illustrate that the Bayesian estimators derived from the Jeffreys prior provide nearly unbiased estimates, showcasing the advantages of our approach over classical techniques. Additionally, our framework incorporates the S.A.F.E. principles – Sustainable, Accurate, Fair, and Explainable – ensuring robustness, fairness, and transparency in predictive modelling.

A spatial stochastic frontier model with fixed effects and endogenous environmental variables

ABSTRACT Stochastic frontier analysis (SFA) models often address fixed effects and endogeneity as separate issues. This study bridges this gap by proposing a unified approach within an ML (maximum likelihood) framework to manage both challenges simultaneously. The ML function is derived in a closed form, but its maximisation requires a numerical solution. To assess the properties of the ML estimator, a Monte Carlo simulation was performed. The simulation shows that the estimator performs reasonably well and gains efficiency asymptotically. The applicability of the estimator was further assessed through an empirical exercise that examined technical efficiency of the production function in a panel of European countries, managing spatiality, endogeneity, and fixed effects.

Aircraft Parameter Estimation Considering Process and Measurement Noise

A practical formulation is proposed for aircraft parameter estimation using the filter-error method, which is a maximum likelihood estimator for dynamic systems with both process noise and measurement noise. The novelty of the proposed formulation is that by accurately estimating the measurement noise covariance matrix using a time series analysis method, the remaining unknowns (which include the unknown parameters in the state-space matrices and the process noise covariance matrix) become decorrelated and can be estimated simultaneously in a straightforward manner. The approach is demonstrated using simulation data and flight test data from a subscale airplane. Results indicate that the proposed algorithm can produce accurate modeling results when both measurement noise and process noise are present in the data.

Efficient non-parametric estimation of variable productivity Hawkes processes

Several approaches to estimating the productivity function for a Hawkes point process with variable productivity are discussed, improved upon, and compared in terms of their root-mean-squared error and computational efficiency for various data sizes, and for binned as well as unbinned data. We find that for unbinned data, a regularized version of the analytic maximum likelihood estimator proposed by Schoenberg is the most accurate but is computationally burdensome. The unregularized version of the estimator is faster to compute but has lower accuracy, though both estimators outperform empirical or binned least squares estimators in terms of root-mean-squared error, especially when the mean productivity is 0.2 or greater. For binned data, binned least squares estimates are highly efficient both in terms of computation time and root-mean-squared error. An extension to estimating transmission time density is discussed, and an application to estimating the productivity of Covid-19 in the United States as a function of time from January 2020 to July 2022 is provided.

Cardiorespiratory fitness, body mass index and mortality: a systematic review and meta-analysis

ObjectiveThe purpose of this review was to assess the joint relationship of cardiorespiratory fitness (CRF) and Body Mass Index (BMI) on both cardiovascular disease (CVD) and all-cause mortality risk.DesignA systematic review and meta-analysis was conducted. Pooled HR and 95% CI were calculated using a three-level restricted maximum likelihood estimation random-effects model with robust variance estimation. The reference group was normal weight-fit and was compared with normal weight-unfit, overweight-unfit and fit, and obese-unfit and fit.Data sourcesElectronic databases (PubMed/MEDLINE, Web of Science and SportDiscus) were searched following registration on PROSPERO.Eligibility criteriaArticles meeting the following criteria were included: (1) published between January 1980 and February 2023, (2) prospective cohort study, (3) CRF assessed using a maximal or VO2peak exercise test, (4) BMI reported and directly measured, (5) joint impact of CRF and BMI on all-cause mortality or CVD mortality were analysed, and (6) the reference group was normal weight, fit individuals.Results20 articles were included in the analysis resulting in a total of 398 716 observations. Compared with the reference group, overweight-fit (CVD HR (95% CI): 1.50 (0.82–2.76), all-cause HR: 0.96 (0.61–1.50)) and obese-fit (CVD: 1.62 (0.87–3.01), all-cause: 1.11 (0.88–1.40)) did not have a statistically different risk of mortality. Normal weight-unfit (CVD: 2.04 (1.32–3.14), all-cause: 1.92 (1.43–2.57)), overweight-unfit (CVD: 2.58 (1.48–4.52), all-cause: 1.82 (1.47–2.24)) and obese-unfit (CVD: 3.35 (1.17–9.61), all-cause: 2.04 (1.54–2.71)) demonstrated 2–3-fold greater mortality risks.ConclusionsCRF is a strong predictor of CVD and all-cause mortality and attenuates risks associated with overweight and obesity. These data have implications for public health and risk mitigation strategies.

Portuguese version of the citizenship fatigue scale: adaptation and evidence of validity.

Citizenship fatigue has been identified as a negative consequence of performing organizational citizenship behaviors and has been studied due to its undesirable effects on employees and organizations. This article aims to present the results of adapting the citizenship fatigue scale to Portuguese language and to provide evidence of its validity. The research methodology involved multiple stages. Initially, the Citizenship Fatigue Scale was translated into Portuguese using a robust back-translation process involving three bilingual translators to ensure semantic accuracy. Subsequently, for psychometric testing, the Citizenship Fatigue Scale and Compulsory Citizenship Behavior Scale were administered to a sample of 406 employees from different economic sectors (103 male; 303 female), aged 18 to 70 years. Reliability and validity indicators were calculated from the CFA structure, employing the maximum likelihood estimation with bootstrapping. Gender invariance was examined at three different levels: [1] configural invariance [2], factor loading invariance and [3] factor loading and intercept invariance. The internal consistency, of the whole scale, measured by Cronbach's alpha, was 0.94. The composite reliability value was also very satisfactory (CF = 0.94). The variance extracted from mean (AVE) value of 0.79 was higher than the required limit of 0.50, indicating an adequate fit of the model. The confirmatory analysis supported a single-factor model and showed good to very good fit indexes (CFI = 1.00; GFI = 0.99; RMSEA ≤ 0.01). The model was successfully replicated with a male and female sample. The results confirm that the Portuguese version of the Citizenship Fatigue Scale is a reliable instrument for research with Portuguese speaking samples and international research.

Machine learning in causal inference for epidemiology.

In causal inference, parametric models are usually employed to address causal questions estimating the effect of interest. However, parametric models rely on the correct model specification assumption that, if not met, leads to biased effect estimates. Correct model specification is challenging, especially in high-dimensional settings. Incorporating Machine Learning (ML) into causal analyses may reduce the bias arising from model misspecification, since ML methods do not require the specification of a functional form of the relationship between variables. However, when ML predictions are directly plugged in a predefined formula of the effect of interest, there is the risk of introducing a "plug-in bias" in the effect measure. To overcome this problem and to achieve useful asymptotic properties, new estimators that combine the predictive potential of ML and the ability of traditional statistical methods to make inference about population parameters have been proposed. For epidemiologists interested in taking advantage of ML for causal inference investigations, we provide an overview of three estimators that represent the current state-of-art, namely Targeted Maximum Likelihood Estimation (TMLE), Augmented Inverse Probability Weighting (AIPW) and Double/Debiased Machine Learning (DML).

Abstract Su902: Ability of Composite Magnetic Resonance Brain Imaging Scores to Predict Functional Outcomes in Survivors of Cardiac Arrest

Background: Brain magnetic resonance imaging (MRI) has been examined for neuroprognostication (NP) after out-of-hospital cardiac arrest (OHCA). However, studies have focused on predicting poor outcomes of non-awakening and/or death. Recommendations for utilization of brain MRI in NP remain weak due to its subjective interpretation. Aim: We modified a previously published brain MRI score and examined our quantitated NP scores’ ability to predict good functional outcomes in OHCA survivors. Methods: We screened OHCA cases (2017-2023, Seattle Medic One registry) for patients who survived to hospital discharge and had brain MRIs performed 25 hours-7 days after arrest. Each MRI was reviewed by two adjudicators; a third reviewer served as tie-breaker. Reviewers were blinded to patient outcomes. Diffusion Weighted Imaging and Fluid Attenuated Inversion Recovery sequences were reviewed to score 35 neuroanatomical regions. Graded severity for estimated affected area (0 = zero; 1= < 25%; 2 = 25-50%; 3 = 50-75%; 4 = >75%) and binary (0 = not affected, 1 = affected) scores were tallied. Points were summed for a composite brain MRI score, “ NP score ”, possible range 0-214. Primary outcome was Cerebral Performance Categories (CPC) at hospital discharge (1-2: “independent”, 3: “dependent”, 4: “vegetative state”). Computational modeling employed folded normal distributions and Maximum Likelihood Estimation. Statistical analyses were Pearson’s, Spearman’s, ANOVA, Fisher LSD, t-tests. Results: Forty-two (42) adult patients were included (74% men, 55% Caucasian). Median NP score was 11.5 (IQR 41.5, n=42) overall, 2 (IQR=10, n=21) for independent versus 25.5 (IQR 36.5, n=10) for dependent patients, and 92 (IQR=81, n=11) for those in a vegetative state. NP scores strongly correlated with CPC [ r s (40) = .69, p< .001 ], and were significantly different between CPC groups [F(2,39) = 32.66, p< 0.001 ]. Interrater concordance for NP score was high (Pearson) r = .88 [r = .96; .95; .90; .71]. Conclusions: Our NP score correlated well with good functional outcomes in OHCA survivors, and (1) identified distinct thresholds that well-separate functional outcome groups and (2) had very strong concordance rate among four pairs of adjudicators. NP score-based predictive modeling differentiates functional outcomes beyond good versus poor dichotomy and may help providers and family anticipate recovery potential.

Reliability analysis of DDV and SPM in BOP-based Weibull model and expand fault dataset using deep learning

The hydraulic systems of deepwater Blowout Preventers (BOPs) are crucial for ensuring the reliability and safety of offshore oil and gas extraction operations. A functional failure can lead to uncontrolled blowouts, resulting in casualties and significant economic losses on the rig. The Direct Drive Valve (DDV) and the Subsea Plated Mounted (SPM) valve are key components that help maintain the proper functioning of the hydraulic system in deepwater BOPs. This study begins by utilizing the Weibull analysis method to assess the reliability of the DDV and SPM valves using limited fault data samples. To enhance the accuracy of predictions, Weibull parameters are estimated through various methods, including Maximum Likelihood Estimation (MLE), Least Squares Estimation (LSE), and a combination of Correlation Coefficient Optimization with Support Vector Regression (CCO + SVR).Given the challenges in gathering extensive fault data for DDV and SPM valves—due to complex subsea environments, cost constraints, time limitations, and other factors—this study proposes a method employing a Back Propagation Neural Network (BPNN) model to augment the limited fault data samples. To ensure the reliable operation of the DDV and SPM valves, preventive maintenance cycles are established at 2840 and 7550 operations, respectively. At the same reliability level, as the number of operational cycles increases, the remaining service life of the valves gradually decreases, leading to a higher probability of failure over a shorter timeframe. The Mean Remaining Life (MRL) of the DDV and SPM valves, corresponding to different operational times, is analyzed, providing essential reference points for their usage and maintenance. When the extended data sample is utilized for reliability evaluation, the reliability characteristics of the small fault data samples are effectively reflected, and the parameter prediction error remains low. This indicates that the extended data sample is more suitable for reliability evaluation.

A novel bounded ℤ-valued autoregressive model with its application on crime data

This paper tackles the challenge of autoregressive modelling for bounded Z -valued count time series, a topic that has been largely overlooked in the existing literature. To bridge this gap, we introduce the trinomial difference bounded Z -valued autoregressive (TDBZAR) model utilizing the trinomial difference thinning operator, and we explore its stochastic properties in detail. Two notable advantages of the TDBZAR model are that the incorporated trinomial difference thinning operator ensures the conditional expectation takes a linear form and allows its 1-step transition probability to be expressed as the convolution of two independent trinomial difference distributions. This significantly simplifies the computation of both the conditional least squares (CLS) and conditional maximum likelihood (CML) estimates, making them more practical and straightforward. Second, we examine the two-step CLS and CML estimates, establishing their asymptotic properties. Third, we compare the performance of these estimators through simulation studies. Finally, we apply the proposed model to a real dataset to investigate which type of crime (rape or sex offense) was more prevalent in police reports from January 1990 to December 1998.

Development of Rainfall Intensity Duration Frequency Curves for Debre Tabor Town, Ethiopia Using Non-stationary Method

Stationary rainfall intensity duration frequency curves have historically influenced urban infrastructure designs. In contrast to the stationary model, which takes constant parameters into account throughout the observation periods, the non-stationary method takes into account changes in the extreme parameters that determine the distribution of precipitation over time. The parameters were estimated using maximum likelihood estimator method. The best model were computed using the R-studio software by comparing information criteria then model parameters, return levels, rainfall intensity are computed. The National Meteorological Agency, situated in Addis Ababa, Ethiopia, provided the essential historical rainfall data of the Debre Tabor rainfall station for this study, Tests and trends were looked for in the rainfall data. Due to its ability to produce the lowest Akaike, corrected Akaike information criteria, and diagnosis test of goodness of fitness Model Type-MV was chosen for Debre Tabor stations. The parameters of the best models were used to forecast the return levels for each of the following return periods: 2, 5, 10, 25, 50, and 100 years. Because the non-stationary technique has varied intensity levels over time, the annual maximum rainfall from the best appropriate model was calculated using its exceedance probability. Using the 95% of exceedance of the return level, the highest rainfall in each fit was determined. In comparison to the stationary model, the non-stationary model produced higher rainfall intensity values. Therefore, when developing IDF curves, the non-stationary approach should be taken into consideration.

Bivariate Generalized Exponential Distribution with Positive Probability at (X = 0, Y = 0) and Estimation of Parameters for a Particular Case

Kundu and Gupta, 2009, J Multivar Anal, 100, 581–593, provided a bivariate generalized exponential distribution (BVGED [Formula: see text]), which is a bivariate continuous lifetime distribution. In practice, however, sometimes both the components may fail instantaneously. Thus, we get a mixture bivariate distribution with positive probability at instantaneous failure of each component. The main aim of this article is to define a BVGED with positive probability at instantaneous failure of each component (BVGEDP [Formula: see text]), where PX=0P(X = 0) and P(Y = 0) is a function of parameter [Formula: see text]. It is observed that the joint probability density function and the cumulative distribution function can be expressed in compact forms. Several properties of the distribution have been discussed. For a particular case (BVGEDP ([Formula: see text] 1, 1, 1)), moment type estimators are obtained which are in closed form and maximum likelihood estimators of parameters ([Formula: see text]) are obtained using an iterative procedure. Also, their finite sample and asymptotic properties are discussed using simulation. A final section presents an application to a real data set on which the proposed BVGEDP ([Formula: see text], 1, 1, 1) distribution is fitted. AMS Subject Classification: 62E99

Statistical analysis of the matrix method for measuring the radar characteristics of objects

The matrix method for measuring the radar characteristics of objects is examined. The method involves irradiating the object with a system of independent test fields, receiving the set of scattered fields, and performing posterior processing of the obtained results based on the superposition principle to determine the required radar characteristics of the object. An analysis of the information capabilities of the matrix method for measuring linear and nonlinear radar characteristics of objects is conducted, considering random errors in the registration of the amplitude and phase of the test signals. The variances of the desired linear and nonlinear radar characteristics of objects are determined, assuming a high signal-to-noise ratio in each test signal reception channel and maximum likelihood estimation of the amplitude and phase of the test signals. It is established that the matrix method for measuring radar characteristics of objects is functional under real conditions involving noise and interference.

Symmetry and Complexity in Gene Association Networks Using the Generalized Correlation Coefficient

High-dimensional gene expression data cause challenges for traditional statistical tools, particularly when dealing with non-linear relationships and outliers. The present study addresses these challenges by employing a generalized correlation coefficient (GCC) that incorporates a flexibility parameter, allowing it to adapt to varying levels of symmetry and asymmetry in the data distribution. This adaptability is crucial for analyzing gene association networks, where the GCC demonstrates advantages over traditional measures such as Kendall, Pearson, and Spearman coefficients. We introduce two novel adaptations of this metric, enhancing its precision and broadening its applicability in the context of complex gene interactions. By applying the GCC to relevance networks, we show how different levels of the flexibility parameter reveal distinct patterns in gene interactions, capturing both linear and non-linear relationships. The maximum likelihood and Spearman-based estimators of the GCC offer a refined approach for disentangling the complexity of biological networks, with potential implications for precision medicine. Our methodology provides a powerful tool for constructing and interpreting relevance networks in biomedicine, supporting advancements in the understanding of biological interactions and healthcare research.