Unbiasedness Research Articles

Development of the Aslam-Ahmad estimator for the Cox proportional and hazards regression model with multicollinearity

In the current article, we develop the Aslam-Ahmad estimator i.e. the modified Liu-ridge-type estimator as proposed by Aslam and Ahmad [Aslam M, Ahmad S. The modified Liu-ridge-type estimator: a new class of biased estimators to address multicollinearity. Commun Statist Simul Comput. 2022] for the Cox proportional hazards regression model. It is common to use the maximum partial likelihood approach for the parameter estimation of the Cox proportional hazards model. However, when there is considerable multicollinearity among the regressors, this estimator is unable to give stable estimates for the unknown regression coefficients. To vanquish the problem, the literature suggests many alternative biased estimators. Following this, we propose to tailor the Aslam-Ahmad estimator for the Cox proportional hazards model and define its properties. The performance of the proposed estimator with the available estimators has been evaluated by the Monte Carlo simulations using the scalar mean squared error criterion. A numerical example has also been provided for the illustration.

Revitalizing Agricultural Economy Through Rural E-Commerce? Experience from China’s Revolutionary Old Areas

Many of the world’s less developed regions may not be able to improve the well-being of rural residents through agricultural revitalization because of their remoteness from agricultural markets. Using the county-level data set of China’s underdeveloped old revolutionary base areas from 2010 to 2021, this paper takes the policy planning of rural e-commerce as event intervention to investigate the driving role of the digital product market on agricultural economic development. Empirical results show that rural e-commerce planning policy has significantly promoted the agricultural added value of the pilot counties, and the digital market is the key driving factor of the agricultural economic growth in these underdeveloped areas. Both food production and livestock output have increased significantly as a result of e-commerce policies. Considering the potential bias of the bidirectional fixed effect estimators of staggered differences-in-differences (DID), this study uses heterogeneous robust estimators to verify the growth effect of the agricultural economy. Specifically, digital agricultural markets have significantly promoted agricultural mechanization and significantly improved agricultural total factor productivity. Moreover, empirical evidence does not support transmission mechanisms for off-farm employment and agricultural entrepreneurship. The findings can help less developed countries and regions develop policies to expand the agricultural markets with digital dividends, thereby promoting the development of the agricultural economy.

New biased estimators for the Conway–Maxwell-Poisson Model

Recent studies focus on modelling count data, which often shows overdispersion or underdispersion. The Conway–Maxwell–Poisson (COMP) regression model effectively handles such dispersion. However, multicollinearity can negatively impact the maximum likelihood estimator (MLE) by increasing variance. To address this, biased estimators like the ridge estimator have been suggested to mitigate multicollinearity effects. This research proposes a new COMP hybrid estimator to further address multicollinearity issues. Theoretical comparisons between the COMP hybrid estimator, MLE, and other COMP estimators reveal that the hybrid estimator reduces mean squared error. Monte Carlo simulations and practical applications confirm that these proposed estimators outperform both MLE and existing COMP estimators.

Numerical Realization of Minimum Distance Estimation for Poisson Processes

Abstract The statistical inference for minimum distance parametric estimation has been well developed in recent years, concerning the asymptotic behaviors of the minimum L 1-distance estimator, minimum L 2-distance estimator and minimum Skorohod-distance estimator. The question is how to realize the numerical solution of the minimum Skorohod-distance estimator, due to its complicated analytic structure. This paper aims to discuss the minimum distance estimation problem for Poisson processes. The main contribution includes the consistency and the approximate numerical solution of the minimum Skorohod-distance estimator, accompanied with the study of the minimum L 1-distance estimator and minimum L 2-distance estimator. In the numerical examples, three estimators exhibit the consistency trend. The mean square error of the minimum L 1-distance estimator and minimum L 2-distance estimator are comparable to, or superior to the minimum Skorohod-distance estimator in the regular cases, while the results are reversed in the change-point case. The bias of the minimum Skorohod-distance estimator is either superior or comparable to the others in the regular cases.

Estimation of mean using under-reported and overdispersed count data

Count data arising in various fields of applications are often under-reported. Ignoring undercount naturally leads to biased estimators and inaccurate confidence intervals. Further, overdispersion in count data may arise due to inherent heterogeneity of the data. Negative Binomial distribution is a viable candidate for modeling overdispersed count data. However, in presence of undercount the negative binomial model needs to be adjusted. In this paper, we shall develop likelihood-based methodologies for estimation of mean using validation data after accounting for underreporting and overdispersion. The impact of ignoring undercount on the coverage and length of the confidence intervals is investigated using extensive numerical studies. The study is supplemented with a real-life data analysis.

Modified ridge estimator in the Bell regression model

Abstract The Bell regression model (BRM), a member of the generalized linear models (GLMs), can be used when the dependent variable consists of overdispersed count data. The maximum likelihood estimator (MLE) is generally used to estimate unknown regression coefficients. The major drawback of the MLE is an inflated variance when multicollinearity problems occur. In this study, we proposed a new biased estimator to cope with the multicollinearity in the BRM. The simulation study is conducted to illustrate the performance of the proposed estimator over the MLE and Bell ridge estimator (BRE). Also, we give real data examples to approve the applicability of the proposed estimator in real data problems.

Quantile-based robust Kibria–Lukman estimator for linear regression model to combat multicollinearity and outliers: Real life applications using T20 cricket sports and anthropometric data

The performance of ordinary least squares (OLS) and ridge regression (RR) are influenced when outliers are present in y-direction with multicollinearity among independent variables. The robust RR with ridge parameters provides a biased estimator that has a smaller variance than conventional OLS and RR estimators. The optimal value of the ridge parameter has a vital role in bias-variance tradeoff. This study proposes quantile-based estimation of ridge parameter in robust RR to deal with the joint issue of y-direction outliers and multicollinearity. The effectiveness of the proposed estimators is evaluated using intensive Monte Carlo simulation and two real data sets in terms of mean square error (MSE) and predictions sum of squared error (PSSE) criterion. Simulation findings reveal that the newly developed estimators of ridge parameter in robust RR have better performance than OLS, RR, and existing robust RR estimators when errors are normally and non-normally distributed. The results from two numerical examples of T20 Cricket sports and anthropometric data show that the new estimator with quantile probability 0.50 and 0.99 respectively has winning performance among all competing and proposed estimators.

Bias Mitigation and Representation Optimization for Noise-Robust Cross-modal Retrieval

The remarkable progress in cross-modal retrieval relies on accurately-annotated multimedia datasets. In practice, most existing datasets used for training cross-modal retrieval models are automatically collected from the Internet to reduce data collection costs. However, it inevitably contains mismatched pairs, i.e. , noisy correspondences, thus degrading the model performance. Recent advances utilize the predicted similarity distribution of individual samples for noise validation and correction, which easily faces two challenging dilemmas: 1) confirmation bias and 2) unstable performance with increasing noise. In light of the above, we propose a generalized B ias M itigation and R epresentation O ptimization framework (BMRO). Specifically, we propose a Bias Estimator (BE) to estimate the unbiased confidence factor of a sample by contrasting it against its nearest neighbors. Unbiased confidence factor can precisely adjust sample contribution and enhance accurate sample division. This facilitates the Adaptive Representation Optimizer (ARO) in providing tailored optimization strategies for clean and noisy samples. ARO performs contrastive learning between clean samples and generated hard samples, thus promoting the generalizability and robustness of the representation. Besides, it utilizes complementary learning to reduce incorrect guidance from noisy samples. Extensive experiments on five visual-text benchmarks verify that our BMRO can significantly improve the matching accuracy and performance stability against noisy correspondences.

Multiple imputation using auxiliary imputation variables that only predict missingness can increase bias due to data missing not at random

BackgroundEpidemiological and clinical studies often have missing data, frequently analysed using multiple imputation (MI). In general, MI estimates will be biased if data are missing not at random (MNAR). Bias due to data MNAR can be reduced by including other variables (“auxiliary variables”) in imputation models, in addition to those required for the substantive analysis. Common advice is to take an inclusive approach to auxiliary variable selection (i.e. include all variables thought to be predictive of missingness and/or the missing values). There are no clear guidelines about the impact of this strategy when data may be MNAR.MethodsWe explore the impact of including an auxiliary variable predictive of missingness but, in truth, unrelated to the partially observed variable, when data are MNAR. We quantify, algebraically and by simulation, the magnitude of the additional bias of the MI estimator for the exposure coefficient (fitting either a linear or logistic regression model), when the (continuous or binary) partially observed variable is either the analysis outcome or the exposure. Here, “additional bias” refers to the difference in magnitude of the MI estimator when the imputation model includes (i) the auxiliary variable and the other analysis model variables; (ii) just the other analysis model variables, noting that both will be biased due to data MNAR. We illustrate the extent of this additional bias by re-analysing data from a birth cohort study.ResultsThe additional bias can be relatively large when the outcome is partially observed and missingness is caused by the outcome itself, and even larger if missingness is caused by both the outcome and the exposure (when either the outcome or exposure is partially observed).ConclusionsWhen using MI, the naïve and commonly used strategy of including all available auxiliary variables should be avoided. We recommend including the variables most predictive of the partially observed variable as auxiliary variables, where these can be identified through consideration of the plausible casual diagrams and missingness mechanisms, as well as data exploration (noting that associations with the partially observed variable in the complete records may be distorted due to selection bias).

Except-Extremes Ranked Set Sampling for Estimating the Population Variance with Two Applications of Real Data Sets

The ranked set sampling (RSS) procedure was initially established by McIntyre (1952) for estimating the mean of forage and pasture yield as more precise than simple random sampling (SRS). Recently, Aldrabseh and Ismail (2023) suggested the except extreme RSS (EERSS) approach as a modification to RSS for estimating the population mean. In this paper, a new estimator of the population variance is proposed using the EERSS method. The mean squared error and bias equations of the new estimator are derived. When the underlying distribution is non-symmetric, a simulation study is conducted to evaluate the suggested estimator relative to SRS and RSS, based on the same number of measured units, in terms of the relative precision and bias values for several sample sizes. For symmetric distributions, the exact values of the bias and relative precision of the EERSS variance estimator are evaluated. Two real datasets are utilized to illustrate the performance of the suggested variance estimator. It is found that the EERSS variance estimator is more efficient than the SRS estimator and more precise than RSS in most cases, especially for small set sizes.

120 Cross-validation of breeding values and future phenotypes for heifer pregnancy in Red Angus cattle using the LR method

Abstract Heifer pregnancy (HP) in beef cattle is a heritable and economically relevant trait but is challenging to predict using best linear unbiased prediction (BLUP) methodology due to the binary nature of the phenotypes. The observed categorical responses (e.g., 1 = pregnant; 0 = non-pregnant) are due to an animal either exceeding a particular threshold for pregnancy or not on an underlying genetic distribution which is why this binary trait is commonly evaluated using a threshold model (TM). However, TM are susceptible to scenarios where only 1 category of observation is predominant. In this study we compare genetic evaluations including “partial” and “whole” data to cross-validate methodologies for the prediction of HP. The objectives of this study were then to evaluate estimators of prediction accuracy, bias, and dispersion. Heifer fertility data were obtained from the Red Angus Association of America. Evaluations for HP were performed using ASREML3.0 and a univariate, BLUP, traditional TM; and a linear continuous BLUP animal model (LM) on both reference (whole) and validation (partial) datasets. Reference data included all animals with HP phenotypes, and validation data had censored the most recent 5 yr of HP phenotypes (~16% of HP phenotypes). Reference and validation estimated breeding values (EBV) were then compared using linear regression (LR) methods. Heritability estimates were 0.05 (± 0.007) and 0.15 (± 0.009) for LM and TM respectively. The average BIF accuracy of censored validation animals (n = 10,175) using a LM on whole and partial datasets were 0.07 and 0.03 respectively, and using a TM on whole and partial datasets were 0.09 and 0.04 respectively. Comparing the mean EBV from the partial and whole datasets can be a good estimator of bias in the model as the difference is expected to be 0. The difference between the mean EBV from partial and mean EBV from whole datasets were –0.003 and –0.016 for LM and TM respectively, suggesting that the TM is a slightly more biased evaluation. The regression of EBV obtained with whole data on EBV estimated with partial data has an expected value of 1 if there is no over/under dispersion which can be a useful tool in determining model correctness and gauge bias in an evaluation. The closer a regression coefficient is to 1, the less biased the evaluation is. The slope of the regression of EBV estimated from whole data on partial data for validation animals were 0.98 (P < 0.0001) and 0.91 (P < 0.0001) for LM and TM respectively. Although both regression coefficients were above 0.90 suggesting both evaluations are performing well, these results suggest that TM models may be a more biased predictor of HP than LM despite a small benefit in prediction accuracy for the trait.

An optimal estimation approach in stratified random sampling utilizing two auxiliary attributes with application in agricultural, demography, finance, and education sectors

In the contemporary era of information technology, copious amounts of data are ubiquitous, generated across various sectors on a daily basis. Analyzing every unit of data is impractical due to constraints such as limited resources in terms of time, labor, and cost. In such scenarios, survey sampling becomes a recommended approach for extracting information about population parameters. The primary goal of this study is to devise an estimation method for acquiring information about population parameters. We propose an optimal estimator for an improved estimation of the population mean in stratified random sampling by leveraging the information from two auxiliary attributes. The proposed estimator's bias, mean squared error (MSE), and minimum mean squared error are determined up to the first-order approximation. It is demonstrated that, under the derived conditions, the proposed estimator theoretically outperforms existing estimators. Four population are utilized to evaluate both the performance and applicability of the proposed estimator. The percentage relative efficiency (PRE) of proposed estimator for all the populations is 178.389, 142.881, 181.383, and 152.679 respectively. The suggested estimator superior to existing estimators, as demonstrated by the numerical examples.

Stability of infraslow correlation structure in time-shifted intracranial EEG signals.

It is increasingly understood that the epilepsies are characterized by network pathology that can span multiple spatial and temporal scales. Recent work indicates that infraslow (<0.2Hz) envelope correlations may form a basis for distant spatial coupling in the brain. We speculated that infraslow correlation structure may be preserved even with some time lag between signals. To this end, we studied intracranial EEG (icEEG) data collected from 22 medically refractory epilepsy patients. For each patient, we selected hour-long background, awake icEEG epochs before and after antiseizure medication (ASM) taper. For each epoch, we selected 5,000 random electrode contact pairs and estimated magnitude-squared coherence (MSC) below 0.15Hz of band power time-series in the traditional EEG frequency bands. Using these same contact pairs, we shifted one signal of the pair by random durations in 15-s increments between 0 and 300s. We aggregated these data across all patients to determine how infraslow MSC varies with duration of lag. We further examined the effect of ASM taper on infraslow correlation structure. We also used surrogate data to empirically characterize MSC estimator and to set optimal parameters for estimation specifically for the study of infraslow activity. Our empirical analysis of the MSC estimator showed that hour-long segments with MSC computed using 3-min windows with 50% overlap was sufficient to capture infraslow envelope correlations while minimizing estimator bias and variance. The mean MSC decreased monotonically with increasing time lag until 105s of lag, then plateaued between 106 and 300s. Significantly nonzero infraslow envelope MSC was preserved in all frequency bands until about 1min of time lag, both pre- and post-ASM taper. We also saw a slight, but significant increase in infraslow MSC post-ASM taper, consistent with prior work. These results provide evidence for the feasibility of examining infraslow activity via its modulation of higher-frequency activity in the absence of DC-coupled recordings. The use of surrogate data also provides a general methodology for benchmarking measures used in network neuroscience studies. Finally, our study points to the clinical relevance of infraslow activity in assessing seizure risk.

Development of Motorway Horizontal Alignment Databases for Accurate Accident Prediction Models

The safe and efficient operation of highways minimizes the environmental impact, reduces accidents, and promotes the reliability of the transportation infrastructure, all in support of sustainable transportation. The horizontal alignment of highways holds particular importance as it directly impacts driver behavior, vehicle stability, and overall road safety. In many cases, highway inventory data held by infrastructure operators may contain inaccurate or outdated information. The accuracy of the variables used in crash prediction models eliminates possible bias in the variable estimators. This research proposes a methodology to obtain accurate horizontal geometric features from digital imagery based on the analysis of the planimetry, feature geolocation and centerline azimuth sequence. The reliability of the method is verified by means of numerical and statistical procedures. This methodology is applied to 150 km of motorway segments in Portugal. Although it is found that the geometric characteristics of most of the inventory segments closely matched the extracted alignments, very significant differences are found in some sections. The results of the proposed procedure are illustrated with several examples. Finally, the propagation of error in the determination of the geometric design independent variables in the fitting of the statistical models is discussed based on the results.

Identifying a class of Ridge-type estimators in binary logistic regression models

In the analysis of logistic regression models, various biased estimators have been proposed as an alternative to the maximum likelihood estimator (MLE) for estimating model parameters in the presence of multicollinearity. In this study, a new class of biased estimators called Logistic Ridge-type Estimator (LRTE) is proposed by generalizing the existing biased estimators that include two biasing parameters. The performance of the proposed estimator is compared with the other biased estimators in terms of the Matrix Mean Squared Error (MMSE). Two separate Monte Carlo simulation studies are conducted to investigate the performance of the proposed estimator. A numerical example is provided to demonstrate the performance of the proposed biased estimator. The results revealed that LRTE performed better than other existing biased estimators under the conditions investigated in this study.

Weighted penalized m-estimators in robust ridge regression: an application to gasoline consumption data

ABSTRACT The OLS and ridge regression (RR) estimators are adversely affected, when the problem of multicollinearity and y-direction outliers occur together. The robust ridge regression with penalized parameters offers biased estimators with lower variance than OLS and RR. The optimal penalized parameter value is crucial for balancing variance and bias. This study proposes three new weighted robust penalized M-estimators to address both multicollinearity and y-direction outliers. Their performance is evaluated against OLS, RR and existing penalized M-estimators using Monte Carlo simulations based on mean squared error (MSE). The new estimators exhibit lower MSE in the presence of multicollinearity and y-direction outliers. A real data application on gasoline consumption demonstrates the superior performance of the new estimators.

Testing the Significance of Regression Coefficients in Liu Type Estimators

In the linear regression model, the multicollinearity problem arises when there is a linear relationship between independent variables. This situation causes the variance of the estimations of the model parameters obtained by the Least Squares Estimator method to increase and move away from the true value, resulting in unstable and incorrect results. Biased Estimator methods are developed to eliminate the adverse effects caused by multicollinearity. In this study, a test statistic is obtained to test the significance of the model coefficients for the Liu-Type Estimator using the test statistic method suggested in the study of Halawa and El-Bassiouni (2000). With a simulation study, the significance of the model coefficients of the Ridge, Liu, and Liu type biased estimators in different situations is tested; the type I errors and power values of the estimators are calculated; the results are compared. In addition, a real data application is performed to better understand the test procedure.

AFFECT: an R package for accelerated functional failure time model with error-contaminated survival times and applications to gene expression data

BackgroundSurvival analysis has been used to characterize the time-to-event data. In medical studies, a typical application is to analyze the survival time of specific cancers by using high-dimensional gene expressions. The main challenges include the involvement of non-informaive gene expressions and possibly nonlinear relationship between survival time and gene expressions. Moreover, due to possibly imprecise data collection or wrong record, measurement error might be ubiquitous in the survival time and its censoring status. Ignoring measurement error effects may incur biased estimator and wrong conclusion.ResultsTo tackle those challenges and derive a reliable estimation with efficiently computational implementation, we develop the R package AFFECT, which is referred to Accelerated Functional Failure time model with Error-Contaminated survival Times.ConclusionsThis package aims to correct for measurement error effects in survival times and implements a boosting algorithm under corrected data to determine informative gene expressions as well as derive the corresponding nonlinear functions.

A new general biased estimator in linear measurement error model

Numerous biased estimators are known to circumvent the multicollinearity problem in linear measurement error models. This article proposes a general biased estimator with the ridge regression and the Liu estimators as special cases. The efficiency of the suggested estimator is compared with ridge regression and Liu estimators under the mean squared error matrix criterion. In addition, a Monte Carlo simulation study and a numerical evaluation have been conducted to elucidate the superiority of the new general biased estimator over other estimators.

Impact Force Localization and Reconstruction via ADMM-based Sparse Regularization Method

In practice, simultaneous impact localization and time history reconstruction can hardly be achieved, due to the ill-posed and under-determined problems induced by the constrained and harsh measuring conditions. Although ℓ1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell_{1}$$\\end{document} regularization can be used to obtain sparse solutions, it tends to underestimate solution amplitudes as a biased estimator. To address this issue, a novel impact force identification method with ℓp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell_{p}$$\\end{document} regularization is proposed in this paper, using the alternating direction method of multipliers (ADMM). By decomposing the complex primal problem into sub-problems solvable in parallel via proximal operators, ADMM can address the challenge effectively. To mitigate the sensitivity to regularization parameters, an adaptive regularization parameter is derived based on the K-sparsity strategy. Then, an ADMM-based sparse regularization method is developed, which is capable of handling ℓp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell_{p}$$\\end{document} regularization with arbitrary p values using adaptively-updated parameters. The effectiveness and performance of the proposed method are validated on an aircraft skin-like composite structure. Additionally, an investigation into the optimal p value for achieving high-accuracy solutions via ℓp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell_{p}$$\\end{document} regularization is conducted. It turns out that ℓ0.6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell_{0.6}$$\\end{document} regularization consistently yields sparser and more accurate solutions for impact force identification compared to the classic ℓ1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell_{1}$$\\end{document} regularization method. The impact force identification method proposed in this paper can simultaneously reconstruct impact time history with high accuracy and accurately localize the impact using an under-determined sensor configuration.