Estimation Of Regression Parameters Research Articles

A Hard Re-descending Hybrid Robust Regression Estimation Technique Using Direct Weights

A hybrid approach of M and R estimators using an iterative procedure is proposed to detect outliers and estimation of regression parameters for linear models. We consider the deviation of each residual from its median to measure the likelihood of the corresponding data point to be an outlier. Also, the proposed work develops a reliable algorithm to estimate parameters of regression model that is unaffected by outliers. The significance of the proposed work is a novel hybrid approach of weighing the observations based on the order of residuals. Our proposal is illustrated using Monte Carlo simulation and analysed for few benchmark data sets.

Variable selection and estimation for recurrent event model with covariates subject to measurement error

This article focuses on variable selection in the Andersen–Gill model for recurrent event analysis, particularly when covariates are subject to measurement errors. We propose a comprehensive three-stage procedure that incorporates simulation–extrapolation with various penalty functions. This approach allows for the simultaneous selection of significant covariates, estimation of regression parameters, and adjustment for measurement errors. Through extensive simulation studies, we demonstrate that our method outperforms approaches that fail to account for measurement errors or the need for variable selection. Specifically, our procedure excels in removing unimportant error-prone covariates and accurately estimating the coefficients of important variables. The results also reveal that the magnitude of measurement error has a substantial negative impact on variable selection outcomes. Additionally, we apply our method to a real-world dataset, further illustrating its practical effectiveness and robustness.

Semiparametric varying-coefficient additive hazards model for informatively interval-censored failure time data

The analysis of interval-censored data with informative observation processes has recently attracted much attention and a few methods have been developed. However, all of the existing methods assume that covariate effects are constant and this may not be true sometimes in practice. To address this, in this paper, we propose a varying-coefficient additive hazards model and in the proposed method, frailty variables are used to describe the dependence between the failure time and the informative observation process. For inference, a Bernstein polynomials-based, two-step sieve maximum likelihood method is developed and the proposed method can be easily implemented. Furthermore, the resulting estimators of regression parameters are shown to be consistent and asymptotically normal. An extensive simulation study is conducted and suggests that the proposed approach works well for practical situations. The proposed method is applied to a cardiac allograft vasculopathy (CAV) study that motivated this investigation.

Robust Function-on-Function Regression: A Penalized Tau-based Estimation Approach

This study introduces a novel penalized estimation method tailored for function-on-function regression models, combining the robustness of the Tau estimator with penalization techniques to enhance resistance to outliers. Function-on-function regression is essential for modeling intricate relationships between functional predictors and response variables across diverse fields. However, traditional methods often struggle with outliers, leading to biased estimates and diminished predictive performance. Our proposed approach addresses this challenge by integrating robust Tau estimation with penalization, promoting both robustness and parsimony in parameter estimation. Theoretical foundations of the penalized Tau estimator within function-on-function regression are discussed, along with empirical validations through simulation studies and an empirical data analysis. By incorporating penalization, our method not only ensures robust estimation of regression parameters but also promotes model simplicity, offering enhanced interpretability and generalization capabilities in functional data analysis.

Group inference of high-dimensional single-index models

For the supervised and semi-supervised settings, a group inference method is proposed for regression parameters in high-dimensional semi-parametric single-index models with an unknown random link function. The inference procedure is based on least squares, which can be extended to other general convex loss functions. The proposed test statistics are weighted quadratic forms of the regression parameter estimates, in which the weight could be a non-random matrix or the sample covariance matrix of the covariates. The proposed method could detect dense but weak signals and deal with high correlation of covariates inside the group. A ‘contaminated test statistic’ is established in the semi-supervised regime to decrease the variance. The asymptotic properties of the resulting estimators are established. The finite-sample behaviour of the proposed method is evaluated through extensive simulation studies. Applications to two genomic datasets are provided.

Deep learning-based estimation of time-dependent parameters in Markov models with application to nonlinear regression and SDEs

We present a novel deep-learning method for estimating time-dependent parameters in Markov processes through discrete sampling. Departing from conventional machine learning, our approach reframes parameter approximation as an optimization problem using the maximum likelihood approach. Experimental validation focuses on parameter estimation in multivariate regression and stochastic differential equations (SDEs). Theoretical results show that the real solution is close to SDE with parameters approximated using our neural network derived under specific conditions. Our work contributes to SDE-based model parameter estimation, offering a versatile tool for diverse fields.

Influence of Communication of Team Leadership on Team Effectiveness of Collaborative Partnerships in International Research Organizations in Kenya

The objective of the study was to evaluate the influence of communication by team leadership on the effectiveness of collaborative partnerships in international research organizations in Kenya. The study was grounded on positivist research philosophy. The study adopted the correlational research design. The anticipated respondents from the 12 international research organizations included 164 program leaders, project managers and heads of departments. A census was conducted. Structured questionnaires were used to collect the data. SPSS version 25 was used to organize, code, and analyze information and generate the quantitative report. The data was analyzed using descriptive and inferential statistics. The correlation results showed that communication by team leadership is positively and significantly related to team effectiveness. The regression (R2) showed that 50.1% of the variations of team effectiveness of collaborative partnerships in international research organizations in Kenya were explained by the communication by team leadership R2 = .501. The regression parameter estimates showed that communication by team leadership is positively and significantly related to team effectiveness (β =.743, t (151) = 12.269, p<.05). Thus, communication of team leadership significantly influences the team effectiveness of collaborative partnerships in international research organizations in Kenya. The study recommends effective communication through team leadership is crucial for international research organizations in Kenya to enhance their effectiveness, achieve success, and address various factors influencing collaborative partnerships.

Semiparametric Probit Regression Model with General Interval-Censored Failure Time Data

Interval-censored data frequently arise in various biomedical areas involving periodical follow-ups where the failure or event time of interest cannot be observed exactly but is only known to fall into a time interval. This article considers a semiparametric probit regression model, a valuable alternative to other commonly used semiparametric models in survival analysis, to investigate potential risk factors for the interval-censored failure time of interest. We develop an expectation-maximization (EM) algorithm to conduct the pseudo maximum likelihood estimation (MLE) using the working independence strategy for general or mixed-case interval-censored data. The resulting estimators of regression parameters are shown to be consistent and asymptotically normal with the empirical process techniques. In addition, we propose a novel penalized EM algorithm for simultaneously achieving variable selection and parameter estimation in the case of high-dimensional covariates. The proposed variable selection method can be readily implemented with some existing software and considerably reduces the estimation error of the proposed pseudo-MLE approach. Simulation studies demonstrate the satisfactory performance of the proposed methods. An application to a set of interval-censored data on prostate cancer further confirms the utility of the methodology. Supplementary materials for this article are available online.

Enhanced Model Predictions through Principal Components and Average Least Squares-Centered Penalized Regression

We address the estimation of regression parameters for the ill-conditioned predictive linear model in this study. Traditional least squares methods often encounter challenges in yielding reliable results when there is multicollinearity. Therefore, we employ a better shrinkage method, average least squares-centered penalized regression (ALPR), as it offers a more efficient approach for handling multicollinearity than ridge regression. Additionally, we integrate ALPR with the principal component (PC) dimension reduction method for enhanced performance. We compared the proposed PCALPR estimation technique with existing ones for ill-conditioned problems through comprehensive simulations and real-life data analyses using the mean squared error. This integration results in superior model performance compared to other methods, highlighting the potential of combining dimensionality reduction techniques with penalized regression for enhanced model predictions.

Bayesian relative composite quantile regression approach of ordinal latent regression model with L1/2 regularization

AbstractOrdinal data frequently occur in various fields such as knowledge level assessment, credit rating, clinical disease diagnosis, and psychological evaluation. The classic models including cumulative logistic regression or probit regression are often used to model such ordinal data. But these modeling approaches conditionally depict the mean characteristic of response variable on a cluster of predictive variables, which often results in non‐robust estimation results. As a considerable alternative, composite quantile regression (CQR) approach is usually employed to gain more robust and relatively efficient results. In this paper, we propose a Bayesian CQR modeling approach for ordinal latent regression model. In order to overcome the recognizability problem of the considered model and obtain more robust estimation results, we advocate to using the Bayesian relative CQR approach to estimate regression parameters. Additionally, in regression modeling, it is a highly desirable task to obtain a parsimonious model that retains only important covariates. We incorporate the Bayesian penalty into the ordinal latent CQR regression model to simultaneously conduct parameter estimation and variable selection. Finally, the proposed Bayesian relative CQR approach is illustrated by Monte Carlo simulations and a real data application. Simulation results and real data examples show that the suggested Bayesian relative CQR approach has good performance for the ordinal regression models.

Semiparametric accelerated failure time models under unspecified random effect distributions

Accelerated failure time (AFT) models with random effects, a useful alternative to frailty models, have been widely used for analyzing clustered (or correlated) time-to-event data. In the AFT model, the distribution of the unobserved random effect is conventionally assumed to be parametric, often modeled as a normal distribution. Although it has been known that a misspecfied random-effect distribution has little effect on regression parameter estimates, in some cases, the impact caused by such misspecification is not negligible. Particularly when our focus extends to quantities associated with random effects, the problem could become worse. In this paper, we propose a semi-parametric maximum likelihood approach in which the random-effect distribution under the AFT models is left unspecified. We provide a feasible algorithm to estimate the random-effect distribution as well as model parameters. Through comprehensive simulation studies, our results demonstrate the effectiveness of this proposed method across a range of random-effect distribution types (discrete or continuous) and under conditions of heavy censoring. The efficacy of the approach is further illustrated through simulation studies and real-world data examples.

A new and unified method for regression analysis of interval-censored failure time data under semiparametric transformation models with missing covariates.

This paper discusses regression analysis of interval-censored failure time data arising from semiparametric transformation models in the presence of missing covariates. Although some methods have been developed for the problem, they either apply only to limited situations or may have some computational issues. Corresponding to these, we propose a new and unified two-step inference procedure that can be easily implemented using the existing or standard software. The proposed method makes use of a set of working models to extract partial information from incomplete observations and yields a consistent estimator of regression parameters assuming missing at random. An extensive simulation study is conducted and indicates that it performs well in practical situations. Finally, we apply the proposed approach to an Alzheimer's Disease study that motivated this study.

Joint AFT random-effect modeling approach for clustered competing-risks data

Competing risks data arise when occurrence of an event hinders observation of other types of events, and they are encountered in various research areas including biomedical research. These data have been usually analyzed using the hazard-based models, not survival times themselves. In this paper, we propose a joint accelerated failure time (AFT) modeling approach to model clustered competing risks data. Times to competing events are assumed to be log-linear with normal errors and correlated through a scaled random effect that follows a zero-mean normal distribution. Inference on the model parameters is based on the h-likelihood. Performance of the proposed method is evaluated through extensive simulation studies. The simulation results show that the estimated regression parameters are robust against the violation of the assumed parametric distributions. The proposed method is illustrated with three real competing risks data sets.

Efficient estimation for left-truncated competing risks regression for case-cohort studies.

The case-cohort study design provides a cost-effective study design for a large cohort study with competing risk outcomes. The proportional subdistribution hazards model is widely used to estimate direct covariate effects on the cumulative incidence function for competing risk data. In biomedical studies, left truncation often occurs and brings extra challenges to the analysis. Existing inverse probability weighting methods for case-cohort studies with competing risk data not only have not addressed left truncation, but also are inefficient in regression parameter estimation for fully observed covariates. We propose an augmented inverse probability-weighted estimating equationfor left-truncated competing risk data to address these limitations of the current literature. We further propose a more efficient estimator when extra information from the other causes is available. The proposed estimators are consistent and asymptotically normally distributed. Simulation studies show that the proposed estimator is unbiased and leads to estimation efficiency gain in the regression parameter estimation. We analyze the Atherosclerosis Risk in Communities study data using the proposed methods.

Prediction Penalized Analysis of Stroke Based on New Bayesian Hierarchical Priors Model

The penalized or the regularization methods nowadays are the most statistical popular tools used for model selection and variable selection procedure. The quality of the regression parameter estimates depends on the prediction accuracy of the estimated model and the model interpretability. Penalized operator methods usually produced the most parsimonious model (less number of predictor and more explanation). This paper utilized new scale mixture of Rayleigh mixing with normal density to study the relationship between the stroke size and some predictors. New hierarchical priors model has developed as well new Gibbs sampling algorithm. The results demonstrated that the proposed model is comparable to some exists regularization models.

Empirical likelihood in a partially linear single-index model with censored response data

An empirical likelihood (EL) approach for a partial linear single-index model with censored response data is studied. A bias-corrected EL ratio is proposed, and the asymptotic chi-squared distribution of this ratio is obtained. The result can be directly used to construct the confidence regions of the regression parameters. The estimators of regression parameters and link function are constructed, and their asymptotic distributions are obtained. Also, a confidence band of the link function is constructed. The proposed method has two main features: The first feature is that the EL ratio is calibrated directly from within, instead of multiplying an adjustment factor by an EL ratio, which reflects the nature of EL. The second feature is avoiding undersmoothing of nonparametric functions, thus ensuring that the n-consistency of the parameter estimator. As a byproduct, the EL and estimation of a single-index model with censored response data are studied. The performance of the bias-corrected EL is evaluated by the simulation studies. The proposed method is illustrated with an example of a real data analysis.

Research on the Evaluation and Enhancement Strategies of College Students’ Health Human Capital in “Healthy Hunan” under the Background of Big Data

Abstract This paper precisely explores the structure and characteristics of college students’ healthy human capital and its influencing factors. It aims to enhance students’ positive and healthy mindset and promote optimism in life and learning. A solid analytical framework is constructed by sorting out the ordered multicategorical logistic regression model and parameter estimation methods and the application steps of the propensity score matching model. College students from ten colleges and universities in Hunan Province were selected as research subjects, and a questionnaire was designed to assess their healthy human capital. The specific factors affecting college students’ healthy human capital accumulation were analyzed in depth through the probability density analysis of propensity score matching, standard support hypothesis testing, and the parallel line test and regression results of the ordered multicategorical regression model. The findings show that the curves of the experimental and control groups after propensity score matching almost overlap in the [0.2,0.4] interval, indicating the method’s validity. A more important finding is that the number of college students with poor self-assessed physical health is 8.063 times higher than that of college students with self-assessed mental health as good, which emphasizes the significant impact of mental health on healthy human capital. Therefore, to effectively improve the health human capital of college students, students, families and universities must form a linkage mechanism and work together to cultivate college students’ health awareness.

Biomarker data with measurement error in medical research: A literature review.

A biomarker is a measurable indicator of the severity or presence of a disease or medical condition in biomedical or epidemiological research. Biomarkers may help in early diagnosis and prevention of diseases. Several biomarkers have been identified for many diseases such as carbohydrate antigen 19-9 for pancreatic cancer. However, biomarkers may be measured with errors due to many reasons such as specimen collection or day-to-day within-subject variability of the biomarker, among others. Measurement error in the biomarker leads to bias in the regression parameter estimation for the association of the biomarker with disease in epidemiological studies. In addition, measurement error in the biomarkers may affect standard diagnostic measures to evaluate the performance of biomarkers such as the receiver operating characteristic (ROC) curve, area under the ROC curve, sensitivity, and specificity. Measurement error may also have an effect on how to combine multiple cancer biomarkers as a composite predictor for disease diagnosis. In follow-up studies, biomarkers are often collected intermittently at examination times, which may be sparse and typically biomarkers are not observed at the event times. Joint modeling of longitudinal and time-to-event data is a valid approach to account for measurement error in the analysis of repeatedly measured biomarkers and time-to-event outcomes. In this article, we provide a literature review on existing methods to correct for estimation in regression analysis, diagnostic measures, and joint modeling of longitudinal biomarkers and survival outcomes when the biomarkers are measured with errors. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Robust MethodsStatistical and Graphical Methods of Data Analysis > EM AlgorithmStatistical Models > Survival Models.

REGRESSION ANALYSIS OF ROBUST ESTIMATION-S WITH TUKEY BISQUARE WEIGHTING ON POVERTY LEVEL ON SULAWESI ISLAND

Poverty is a situation where a person experiences difficulty in meeting basic needs. There are several factors that influence poverty, including population, unemployment, gross regional domestic product, human development index, average years of schooling and labor force participation rate. Therefore, it is necessary to carry out regression analysis to determine the relationship between one variable and other variables. One method for estimating regression parameters is the least squares method. Some classic assumptions are not met because there are outlier data. Outliers are data that do not follow the overall distribution pattern, so a method is used that can overcome outliers, namely the S-estimation robust regression method with the Tukey bisquare weighting function. The results of the research show that the best model was obtained from robust S-estimation regression with Tukey bisquare weighting, namely factors that influence the level of poverty on the island of Sulawesi, namely Population Number ), Human Development Index ( ), Average Years of Schooling ( ) and, Force Participation Level. Work .

Subgroup detection based on partially linear additive individualized model with missing data in response

Based on partially linear additive individualized model, a fusion-penalized inverse probability weighted least squares method is proposed to detect the subgroup for missing data in response. Firstly, the B-spline technique is used to approximate the unknown additive individualized functions and then an inverse probability weighted quadratic loss function is established with fusion penalty on the difference of subject-wise B-spline coefficients. Secondly, minimization of such quadratic loss function leads to the estimation of linear regression parameters and individualized B spline coefficients. With a proper tuning parameter, some differences in penalty term are shrunk into zero and thus the corresponding subjects will be clustered into the same subgroup. Thirdly, a clustering method is developed to automatically determine the subgroup membership for the subjects with missing data. Fourthly, large sample properties of resulting estimates are given under some regular conditions. Finally, numerical studies are presented to illustrate the performance of the proposed subgroup detection method.