Efficient Parameter Estimation Research Articles

Extreme Values Approach in Food Risk Modeling

In this paper we estimate the incubation period of a possible pathology following exposure to dioxins during a poor diet. The tools developed for this purpose include the probabilistic extremal model and the stochastic behavior of the distribution tails of the contamination. We propose a cumulative distribution function for a random variable that follows both a Gaussian distribution and a GPD. A global optimization method is also explored for the efficient estimation of parameters of GPD.

Modeling serially correlated heavy-tailed data with some missing response values using stochastic EM algorithm

The linear regression model is a popular tool used by almost all in different areas of research. The model relies mainly on the assumption of uncorrelated errors from a Gaussian distribution. However, many datasets in practice violate this basic assumption, making inference in such cases invalid. Therefore, the linear regression model with structured errors driven by heavy-tailed innovations are preferred in practice. Another issue that occur frequently with real-life data is missing values, due to some reasons such as system breakdown and labor unrest. Despite the challenge these two issues pose to practitioners, there is scarcity of literature where they have jointly been studied. Hence, this article considers these two issues jointly, for the first time, and develops an efficient parameter estimation procedure for Student’s-t autoregressive regression model for time series with missing values of the response variable. The procedure is based on a stochastic approximation expectation–maximization algorithm coupled with a Markov chain Monte Carlo technique. The procedure gives efficient closed-form expressions for the parameters of the model, which are very easy to compute. Simulations and real-life data analysis show that the method is efficient for use with incomplete time series data.

Partial Effects for Binary Outcome Models with Unobserved Heterogeneity

Unobserved heterogeneity is ubiquitous in empirical research. In this article, I propose a method for estimating binary outcome models with panel data in the presence of unobserved heterogeneity, called the Penalized Flexible Correlated Random Effects (PF-CRE) estimator. I show that this estimator produces consistent and efficient estimates of the model parameters. PF-CRE also provides consistent estimates of partial effects, which cannot be calculated with existing consistent estimators. Using Monte Carlo simulations, I show that PF-CRE performs well in finite samples. I also illustrate the performance of PF-CRE in two real-data applications: a small T study on party contacts and tactical voting during the 2015 UK general election and a large T panel dealing with the effect of economic sanctions on government stability. In both cases I find that PF-CRE is a valid approach that reduces bias or generates efficiency gains in the estimation.

Multivariate control charts for monitoring process mean vector of individual observations under regularized covariance estimation

ABSTRACT Multivariate control charts are generally used in industries for monitoring and diagnosing processes characterized by several process variables. The applications of charts assume that the in-control process parameters are known and the charts’ limits are obtained from the known parameters. The parameters are typically unknown in practice, and the charts’ limits are usually based on estimated parameters from some historical in-control datasets in the Phase I study. The performance of the charts for monitoring future observation depends on efficient estimates of the process parameters from the historical in-control process. When only a few historical observations are available, the performance of the charts based on the empirical estimates of the process mean vector and covariance matrix have been shown to deviate from the desired performance of the charts based on the true parameters. We investigate the performance of the multivariate Shewhart control charts based on several shrinkage estimates of the covariance matrix when only a few in-control observations are available to estimate the parameters. Simulation results show that the control charts based on the shrinkage estimators outperform the charts based on existing classical estimators. An example involving high-dimensional monitoring is provided to illustrate the performance of the proposed Shrinkage-based Shewhart chart.

Evaluating the relative efficiency among robust estimation methods for multilevel factor analysis with categorical data

Multilevel measurement models are more frequently applied to help answer questions when data arise from hierarchically structured multivariate data. In this simulation study of multilevel factor models, we evaluated the relative efficiency among three estimation methods: robust maximum likelihood, unweighted least squares, and weighted least squares. We found that weighted least squares yielded more or equally efficient parameter estimates under all sample size conditions for all model parameters. The relative efficiency of standard errors was less straightforward where maximum likelihood was more efficient for loadings and residual variances, but weighted least squares was more efficient for the factor covariance matrices. Finally, we give recommendations for estimating multilevel confirmatory factor analysis models and directions for future research.

Joint frailty modeling of time-to-event data to elicit the evolution pathway of events: a generalized linear mixed model approach.

Multimorbidity constitutes a serious challenge on the healthcare systems in the world, due to its association with poorer health-related outcomes, more complex clinical management, increases in health service utilization and costs, but a decrease in productivity. However, to date, most evidence on multimorbidity is derived from cross-sectional studies that have limited capacity to understand the pathway of multimorbid conditions. In this article, we present an innovative perspective on analyzing longitudinal data within a statistical framework of survival analysis of time-to-event recurrent data. The proposed methodology is based on a joint frailty modeling approach with multivariate random effects to account for the heterogeneous risk of failure and the presence of informative censoring due to a terminal event. We develop a generalized linear mixed model method for the efficient estimation of parameters. We demonstrate the capacity of our approach using a real cancer registry data set on the multimorbidity of melanoma patients and document the relative performance of the proposed joint frailty model to the natural competitor of a standard frailty model via extensive simulation studies. Our new approach is timely to advance evidence-based knowledge to address increasingly complex needs related to multimorbidity and develop interventions that are most effective and viable to better help a large number of individuals with multiple conditions.

Using Bayesian optimization to automate the calibration of complex hydrological models: Framework and application

A framework that integrates Bayesian optimization (BO) and high-performance computing was developed, to automate calibration of complex hydrological models. It adopts a loosely coupled web architecture, integrating Tornado and SpringBoot, to facilitate bidirectional transfer of variables between BO and model evaluation. Extensive model evaluations were implemented on a Hadoop cluster, to wrap the model into the calculation flexibly and separate the calculation process from the algorithm execution effectively. A case study, calibrating a SWAT model in the Meichuan Basin (Jiangxi Province, China), indicated that the framework provides an ideal environment for assessment of the capability of BO to quantify the efficient estimation of SWAT parameters. Compared with that of the built-in SWAT-CUP tool, the number of executions was reduced from 1500 to 150, while maintaining similar accuracy. The framework also allows evaluation of the performance of different surrogate models and acquisition functions and provides instant visualization for searching for optimal parameters.

A novel hybrid robust tapering approach for nonlinear regression in the presence of autocorrelation and outliers

Nonlinear models are commonly used for analyzing real-life data such as in medicine, engineering, and economics. To make efficient inferences about model parameter estimations and statistical results in nonlinear regression, assumptions related to error term are needed to be satisfied. Ordinary least squares and some modified least squares methods fail to give efficient parameter estimates when there are the problems of autocorrelation and outlier together in nonlinear regression. In this study, a novel hybrid robust tapering approach called as robust modified two-stage least squares is proposed to overcome the problems for obtaining more efficient parameter estimates in nonlinear regression. Two numerical examples and a comprehensive Monte–Carlo simulation study are given in order to examine the performance of robust modified two-stage least squares.

Detection and fast motion parameter estimation for target with range walk effect based on new axis rotation moving target detection

In order to address the range walk (RW) effect in the field of radar high speed target detection, the axis rotation MTD (AR-MTD) class algorithms based on long-time coherent integration, i.e., AR-MTD, improved axis rotation MTD (IAR-MTD), and modified location rotation transform (MLRT) have been proposed in recent works. However, they are faced with detection performance loss and large computational complexity. In this paper, a new axis rotation MTD (NAR-MTD) algorithm is proposed. Different from the previous AR-MTD class algorithms, NAR-MTD first selects the image center of 2-D compressed signal as the coordinate system origin, and then simplifies the axis rotation relationship to reduce the rotation error caused by the coordinate transformation and correct the RW to the initial range location. Furthermore, by exploiting the geometrical information of mismatched NAR-MTD, the adaptive AR-MTD (AAR-MTD) is proposed to realize efficient motion parameter estimation of the moving target in different SNR environments. Numerical simulations and real data process indicate that NAR-MTD has a better detection ability than that of AR-MTD class algorithms. Meanwhile, the computational efficiency of AAR-MTD is about two orders of magnitude higher than that of direct 2-D search of NAR-MTD.

Cluster Gauss-Newton and CellNOpt Parameter Estimation in a Small Protein Signaling Network of Vorinostat and Bortezomib Pharmacodynamics.

Ordinary differential equation (ODE)-based models of signal transduction pathways often contain parameters that are unidentifiable or unmeasurable by experimental data, and calibrating such models to data remains challenging. Here, two efficient parameter estimation methods, cluster Gauss-Newton (CGN) and CellNOpt (CNO), were applied to fit a signaling network model of U266 multiple myeloma cells to the activity dynamics of key proteins in response to vorinostat and/or bortezomib. A logic-based network model was constructed and transformed to 17 ODEs with 79 parameters estimated within broad ranges of biologically plausible values. The top 10% best-fit parameters by both methods had high uncertainties with CV > 50% for the majority of parameters. The root mean square and prediction errors were comparable without statistically significant differences between the two methods. Despite uncertain parameter estimation, protein dynamics after the sequential combination of bortezomib and vorinostat was predicted with reasonable accuracy and precision. Global sensitivity analyses of partial rank correlation coefficients and Sobol sensitivity demonstrated that apoptosis induction was most sensitive to parameters governing the activity of the proteasome-JNK-caspase-8 axis. Simulations revealed that the greatest magnitude of pharmacodynamic drug interactions between bortezomib and vorinostat occurred at caspase-9, AKT, and Bcl-2. Two sequential combinations were explored in silico, and the outcome matched qualitatively with an empirical evaluation of the pharmacodynamic interaction based on cell viability. Overall, the CGN and CNO algorithms performed similarly for this ODE-based network model calibration, and the calibrated model provided meaningful insights into cellular signaling mechanisms in response to pharmacological perturbations.

Consistent one-bay frame simplified model for efficient seismic evaluation of steel moment frame buildings with equal and unequal bay lengths

A Consistent One-Bay Frame (COBF) simplified model for the efficient estimation of Engineering Demand Parameters (EDPs) in Steel Moment Resisting Frames (SMRFs) with equal and unequal bay lengths is proposed. The geometry of the Substitute One-Bay Frame (SOBF) simplified model has been used, and the elastic and inelastic properties of the beams and columns in this model are determined using an energy consistent approach in a way that the energy balance is established between the members of the original SMRF and the SOBF simplified model. This way, the SOBF simplified model, which originally could only be used for MRFs with equal bay lengths, can now be used for MRFs with any geometric arrangement for bay lengths. Two 9- and 20-story SMRFs with equal bay lengths and two others with unequal bay lengths have been employed as structural models. The concentrated plastic hinges with modified Ibarra-Medina-Krawinkler (IMK) deterioration model have been used to apply strength and stiffness deterioration in numerical models. The accuracy of the proposed simplified model in estimating the EDPs along the height of the structure has been evaluated using Nonlinear Time History Analysis (NLTHA) under 22 pairs of FEMA P-695 earthquake records at the three seismic intensity levels of SLE, DBE, and MCE. The proposed simplified model has been compared with the Consistent Generic (CG) simplified model previously developed for SMRFs. This comparison suggests that the proposed simplified model is more efficient and reliable. Evaluating the seismic performance of the proposed simplified model using the conventional Incremental Dynamic Analysis (IDA) method and the Endurance Time Analysis (ETA) method at all of the seismic intensity levels reveals that using the COBF simplified model along with the ETA simplified method not only reduces the Degrees of Freedom (DOFs) of the original SMRF and the number of the NLTHAs but also leads to a proper estimation of the EDPs of the original SMRF from low seismic intensity level to collapse intensity level. Therefore, it is very helpful to use it for reducing the complexities of the new generation of Performance-Based Earthquake Evaluation.

Modified ridge-type estimator for the inverse Gaussian regression model

This paper considers the parameter estimation for the inverse Gaussian regression model (IGRM) in the presence of multicollinearity. The inverse Gaussian modified ridge-type estimator (IGMRTE) is developed for efficient parameter estimation and compared with other estimation methods such as the maximum likelihood estimator (MLE), ridge and Liu estimator. We derived the properties of the proposed estimator and conducted a theoretical comparison with some of the existing estimators using the matrix mean squared error and mean squared error criterions. Furthermore, the statistical properties of these estimators are systematically scrutinized via a Monte Carlo simulation study under different conditions. The findings of the simulation study demonstrate that the proposed IGMRTE showed a much more robust behavior in the presence of severe multicollinearity. A real life example is also analyzed to evaluate the effectiveness of the estimators under study. Both the simulation and the application results confirm the use of IGMRTE for the estimation of unknown regression coefficients of the IGRM when the explanatory variables are highly correlated.

Rank-Based Inference for Survey Sampling Data

Abstract For regression models where data are obtained from sampling surveies, the statistical analysis is often based on approaches that are either non-robust or inefficient. The handling of survey data requires more appropriate techniques, as the classical methods usually result in biased and inefficient estimates of the underlying model parameters. This article is concerned with the development of a new approach of obtaining robust and efficient estimates of regression model parameters when dealing with survey sampling data. Asymptotic properties of such estimators are established under mild regularity conditions. To demonstrate the performance of the proposed method, Monte Carlo simulation experiments are carried out and show that the estimators obtained from the proposed methodology are robust and more efficient than many of those obtained from existing approaches, mainly if the survey data tend to result in residuals with heavy-tailed or skewed distributions and/or when there are few gross outliers. Finally, the proposed approach is illustrated with a real data example.

A robust and efficient variable selection method for linear regression

Variable selection is fundamental to high dimensional statistical modeling, and many approaches have been proposed. However, existing variable selection methods do not perform well in presence of outliers in response variable or/and covariates. In order to ensure a high probability of correct selection and efficient parameter estimation, we investigate a robust variable selection method based on a modified Huber's function with an exponential squared loss tail. We also prove that the proposed method has oracle properties. Furthermore, we carry out simulation studies to evaluate the performance of the proposed method for both p<n and p>n. Our simulation results indicate that the proposed method is efficient and robust against outliers and heavy-tailed distributions. Finally, a real dataset from an air pollution mortality study is used to illustrate the proposed method.

Survey design and analysis considerations when utilizing misclassified sampling strata

BackgroundA large multi-center survey was conducted to understand patients’ perspectives on biobank study participation with particular focus on racial and ethnic minorities. In order to enrich the study sample with racial and ethnic minorities, disproportionate stratified sampling was implemented with strata defined by electronic health records (EHR) that are known to be inaccurate. We investigate the effect of sampling strata misclassification in complex survey design.MethodsUnder non-differential and differential misclassification in the sampling strata, we compare the validity and precision of three simple and common analysis approaches for settings in which the primary exposure is used to define the sampling strata. We also compare the precision gains/losses observed from using a disproportionate stratified sampling scheme compared to using a simple random sample under varying degrees of strata misclassification.ResultsDisproportionate stratified sampling can result in more efficient parameter estimates of the rare subgroups (race/ethnic minorities) in the sampling strata compared to simple random sampling. When sampling strata misclassification is non-differential with respect to the outcome, a design-agnostic analysis was preferred over model-based and design-based analyses. All methods yielded unbiased parameter estimates but standard error estimates were lowest from the design-agnostic analysis. However, when misclassification is differential, only the design-based method produced valid parameter estimates of the variables included in the sampling strata.ConclusionsIn complex survey design, when the interest is in making inference on rare subgroups, we recommend implementing disproportionate stratified sampling over simple random sampling even if the sampling strata are misclassified. If the misclassification is non-differential, we recommend a design-agnostic analysis. However, if the misclassification is differential, we recommend using design-based analyses.

High-Frequency Modeling of a Three-Winding Power Transformer Using Sweep Frequency Response Analysis

A power transformer is an essential device for stable and reliable power transfer to customers. Therefore, accurate modeling of transformers is required for simulation-based analysis with the model. The paper proposes an efficient and straightforward parameter estimation of power transformers based on sweep frequency response analysis (SFRA) test data. The method first develops a transformer model consisting of repetitive RLC sections and mutual inductances and then aligns the simulated SFRA curve with the measured one by adjusting parameters. Note that this adjustment is based on individual parameter impacts on the SFRA curve. After aligning the two curves, the final transformer model can be obtained. In this paper, actual single-phase, three-winding transformer model parameters were estimated based on field SFRA data, showing that SFRA curves simulated from the estimated model are consistent with the measured data.

Stratified sampling in highly polluted data as an effective and reliable alternative to high breakdown point estimators

Observations on certain real-life cases include units that are incompatible with other data sets. Values that are extreme in nature do influence estimates obtained by conventional estimators. Robust estimators are therefore necessary for efficient estimation of parameters. This paper uses stratification with simple random sampling without replacement to optimize sample allocation in stratum for efficient parameter estimation as an alternative method of handling highly contaminated samples. Our proposed method stratifies the highly contaminated population into two non-overlapping sub-populations, and stratified samples of sizes 50, 200, and 500 was drawn. We estimate the model parameters form the contaminated sampled data using ordinary least squares under the proposed method, and using the two high breakdown point estimators; the Least Median of Squares and Least Trimmed Squares. Our findings shows that the proposed method did not perform well for low contamination levels (⩽ 30%) but outperformed Least Median of Squares and Least Trimmed Squares for higher contamination rates (⩾ 40%). This indicates that our proposed method compares well and compete favorably with the two high breakdown point estimators.

Modeling lifetime of parallel components system with covariate, right and interval censored data

This research aims to model the lifetime of parallel components system with covariates, right, and interval censored data. The lifetimes of the components are assumed to follow the exponential distribution, with constant failure rates. A simulation study is conducted to assess the performance of the maximum likelihood estimates, without and with midpoint imputation method at various sample sizes, censoring proportions, and number of components in the system. The combination which produces the best parameter estimates is then identified by comparing the bias, standard error and root mean square error of these estimates. The simulation results indicate that the midpoint imputation method produces more efficient and accurate parameter estimates with smaller bias, standard error and root mean square error. Also, in general, better estimates are obtained at low censoring levels, large sample sizes, and a high number of parallel components in the system. The proposed model is then fitted to a modified real data of diabetic retinopathy patients. Following that, the non-parametric log-rank test and Wald hypothesis test are carried out to check the significance of the covariate, age in the model. The results show that the model fits the data rather well and the age of patients has no significant effect on the survival time of the patients’ eyes.

Optimal model for weaning-weight of Bunaji Bulls at NAPRI Farm, Shika, Nigeria

Empirical models have over the years been commonly established by animal research centers for the study of weight-age profiles in order to understand the metabolic processes of growth. They provide efficient parameter estimates for mature weight and rate of maturing, but were found to consistently either over-or-under estimate the mature weight. estimate the mature weight. They also perform poorly in predicting weight in early life or beyond the range of input data. At the National Animal Production Research Institute (NAPRI) farm, Shika, Brody was established as the model that provides efficient parameter estimates of weight-age profiles for Bunaji bulls. However, a major drawback of the model is its consistent underestimation of weight prior to six months of age, leading to poor prediction of weaning weight. To address this shortcoming, we propose in this article a joint mean-covariance model that provide optimal parameter estimates for the weaning weight of Bunaji bulls

Robust regression with asymmetric loss functions.

In robust regression, it is usually assumed that the distribution of the error term is symmetric or the data are symmetrically contaminated by outliers. However, this assumption is usually not satisfied in practical problems, and thus if the traditional robust methods, such as Tukey's biweight and Huber's method, are used to estimate the regression parameters, the efficiency of the parameter estimation can be lost. In this paper, we construct an asymmetric Tukey's biweight loss function with two tuning parameters and propose a data-driven method to find the most appropriate tuning parameters. Furthermore, we provide an adaptive algorithm to obtain robust and efficient parameter estimates. Our extensive simulation studies suggest that the proposed method performs better than the symmetric methods when error terms follow an asymmetric distribution or are asymmetrically contaminated. Finally, a cardiovascular risk factors dataset is analyzed to illustrate the proposed method.