Estimation Of Regression Parameters Research Articles

Weighted rank estimation for nonparametric transformation models with doubly truncated data

Doubly truncated data often arise when event times are observed only if they fall within subject-specific intervals. We analyze doubly truncated data using nonparametric transformation models, where an unknown monotonically increasing transformation of the response variable is equal to an unknown monotonically increasing function of a linear combination of the covariates plus a random error with an unspecified log-concave probability density function. Furthermore, we assume that the truncation variables are conditionally independent of the response variable given the covariates and leave the conditional distributions of truncation variables given the covariates unspecified. For estimation of regression parameters, we propose a weighted rank (WR) estimation procedure and establish the consistency and asymptotic normality of the resulting estimator. The limiting covariance matrix of the WR estimator can be estimated by a resampling technique, which does not involve nonparametric density estimation or numerical derivatives. A numerical study is conducted and suggests that the proposed methodology works well in practice, and an illustration based on real data is provided.

Tools for Selecting Working Correlation Structures When Using Weighted GEE to Model Longitudinal Survey Data.

Weighted generalized estimating equations (GEE) are popular for the marginal analysis of longitudinal survey data. This popularity is due to the ability of these estimating equations to provide consistent regression parameter estimates and corresponding standard error estimates as long as the population mean and survey weights are correctly specified. Although the data analyst must incorporate a working correlation structure within the weighted GEE, this structure need not be correctly specified. However, accurate modeling of this structure has the potential to improve regression parameter estimation, i.e. reduce standard errors, and therefore the selection of a working correlation structure for use within GEE has received considerable attention in standard longitudinal data analysis settings. In this manuscript, we describe how correlation selection criteria can be extended for use with weighted GEE in the context of analyzing longitudinal survey data. Importantly, we provide and demonstrate an R function that we have created for such analyses. Furthermore, we discuss correlation selection in the context of using existing software which does not have this explicit capability. The methods are demonstrated via the use of data from a real survey in which we are interested in the mean number of falls that elderly individuals in a specific subpopulation experience over time.

ANALISIS SURVIVAL MODEL REGRESI SEMIPARAMETRIK PADA LAMA STUDI MAHASISWA

In survival analysis to determine the relationship between variables is used a regression model, one of which uses the semiparametric regression model. The semiparametric regression model is a model that does not require assumptions or information on survival data distribution. That way, this model is more flexible in its use. In this study, the semiparametric regression model used the Cox Proportional Hazard (Cox PH) regression model. Estimation of Cox PH regression parameters can be done without determining the function baseline hazard. The purpose of this study is to determine the factors that influence the duration of student studies. If there are many students whose studies have not been on time, it shows that there is a lack of professionalism in the academic field of the educator. Thus, the community will assess the low quality of the university, resulting in a decrease in the number of students who want to study at the university. The samples in this study were students of class 2014 Universitas Islam Darul Ulum Lamongan. The variables have used the length of study for students, gender, GPA, school origin, organization, and work. Based on the results of the assumption Proportional Hazard (PH) conducted, all independent variables have fulfilled these assumptions, so that these variables can be used in Cox PH regression. After parameter estimation by Cox PH regression, the GPA and organizational factors significantly influence the duration of student study. Students with high GPA and participating in organizations more quickly complete their studies.

Loss Reserving Estimation With Correlated Run-Off Triangles in a Quantile Longitudinal Model

In this paper, we consider a loss reserving model for a general insurance portfolio consisting of a number of correlated run-off triangles that can be embedded within the quantile regression model for longitudinal data. The model proposes a combination of the between- and within-subportfolios (run-off triangles) estimating functions for regression parameter estimation, which take into account the correlation and variation of the run-off triangles. The proposed method is robust to the error correlation structure, improves the efficiency of parameter estimators, and is useful for the estimation of the reserve risk margin and value at risk (VaR) in actuarial and finance applications.

Regression analysis of case II interval-censored data with auxiliary covariates

The effect of some exposures on a survival time is often of interest in many epidemiological and biomedical studies. Due to budget constraints or technical difficulties, some exposures of interest may not be measured for the whole study cohort but only available in a subset of them. While the exposure of interest is not fully observed, there could exist an auxiliary covariate related to it that is cheaper or more convenient to observe. Given such situations, statistical methods that take advantage of existing auxiliary information about an expensive exposure variable are desirable in practice. Such methods should improve the study efficiency and increase the statistical power for a definite quantities of assays. In this paper, we discusses regression analysis of case II interval-censored data with continuous auxiliary covariates. An estimator of regression parameters was proposed by maximizing the estimated partial likelihood function which makes use of the available auxiliary information. Asymptotic properties of the resulting estimator are established. An extensive simulation study was conducted to assess the finite sample performance of the proposed method. The proposed method was also illustrated through an application to a HIV-1 infection example.

Bayesian empirical likelihood for ridge and lasso regressions

Ridge and lasso regression models, which are also known as regularization methods, are widely used methods in machine learning and inverse problems that introduce additional information to solve ill-posed problems and/or perform feature selection. The ridge and lasso estimates for linear regression parameters can be interpreted as Bayesian posterior estimates when the regression parameters have Normal and independent Laplace (i.e., double-exponential) priors, respectively. A significant challenge in regularization problems is that these approaches assume that data are normally distributed, which makes them not robust to model misspecification. A Bayesian approach for ridge and lasso models based on empirical likelihood is proposed. This method is semiparametric because it combines a nonparametric model and a parametric model. Hence, problems with model misspecification are avoided. Under the Bayesian empirical likelihood approach, the resulting posterior distribution lacks a closed form and has a nonconvex support, which makes the implementation of traditional Markov chain Monte Carlo (MCMC) methods such as Gibbs sampling and Metropolis–Hastings very challenging. To solve the nonconvex optimization and nonconvergence problems, the tailored Metropolis–Hastings approach is implemented. The asymptotic Bayesian credible intervals are derived.

Predictive validation and forecasts of short-term changes in healthcare expenditure associated with changes in smoking behavior in the United States.

ObjectivesOut-of-sample forecasts are used to evaluate the predictive adequacy of a previously published national model of the relationship between smoking behavior and real per capita health care expenditure using state level aggregate data. In the previously published analysis, the elasticities between changes in state adult current smoking prevalence and mean cigarette consumption per adult current smoker and healthcare expenditures were 0.118 and 0.108 This new analysis provides evidence that the model forecasts out-of-sample well.MethodsOut-of-sample predictive performance was used to find the best specification of trend variables and the best model to bridge a break in survey data used in the analysis. Monte-Carlo simulation was used to calculate forecast intervals for the effect of changes in smoking behavior on expected real per capita healthcare expenditures.ResultsThe model specification produced good-out-of-sample forecasts and stable recursive regression parameter estimates spanning the break in survey methodology. In 2014, a 1% relative reduction in adult current smoking prevalence and mean cigarette consumption per adult current smoker decreased real per capita healthcare expenditure by 0.104% and 0.113% the following year, respectively (elasticity). A permanent relative reduction of 5% reduces expected real per capita healthcare expenditures $99 (95% CI $44, $154) in the next year and $31.5 billion for the entire US (in 2014 dollars), holding other factors constant. The reductions accumulate linearly for at least five years following annual permanent decreases of 5% each year. Given the limitations of time series modelling in a relatively short time series, the effect of changes in smoking behavior may occur over several years, even though the model contains only one lag for the explanatory variables.ConclusionReductions in smoking produce substantial savings in real per capita healthcare expenditure in short to medium term. A 5% relative drop in smoking prevalence (about a 0.87% reduction in absolute prevalence) combined with a 5% drop in consumption per remaining smoker (about 16 packs/year) would be followed by a $31.5 billion reduction in healthcare expenditure (in 2014 dollars).

On a global measure of nonlinearity and its application in parameter estimation in nonlinear regression

On a global measure of nonlinearity and its application in parameter estimation in nonlinear regression

Multiple imputation methods for handling incomplete longitudinal and clustered data where the target analysis is a linear mixed effects model.

Multiple imputation (MI) is increasingly popular for handling multivariate missing data. Two general approaches are available in standard computer packages: MI based on the posterior distribution of incomplete variables under a multivariate (joint) model, and fully conditional specification (FCS), which imputes missing values using univariate conditional distributions for each incomplete variable given all the others, cycling iteratively through the univariate imputation models. In the context of longitudinal or clustered data, it is not clear whether these approaches result in consistent estimates of regression coefficient and variance component parameters when the analysis model of interest is a linear mixed effects model (LMM) that includes both random intercepts and slopes with either covariates or both covariates and outcome contain missing information. In the current paper, we compared the performance of seven different MI methods for handling missing values in longitudinal and clustered data in the context of fitting LMMs with both random intercepts and slopes. We study the theoretical compatibility between specific imputation models fitted under each of these approaches and the LMM, and also conduct simulation studies in both the longitudinal and clustered data settings. Simulations were motivated by analyses of the association between body mass index (BMI) and quality of life (QoL) in the Longitudinal Study of Australian Children (LSAC). Our findings showed that the relative performance of MI methods vary according to whether the incomplete covariate has fixed or random effects and whether there is missingnesss in the outcome variable. We showed that compatible imputation and analysis models resulted in consistent estimation of both regression parameters and variance components via simulation. We illustrate our findings with the analysis of LSACdata.

Life Satisfaction and mobility: Their associations with career attitudes, and health-related factors among postgraduates having studied in universities intra EU and outside EU

BackgroundUniversity postgraduates’ mobility towards, and outside the EU is continuously increasing, creating a competitive context in which maintaining a high life satisfaction (LS) is a public health challenge. However, the relationship between LS and its determinants among this population are under-documented. Our aims were to measure LS indicators of mobile postgraduates (Intra EU: Who pursue part of their studies in Europe; Outside EU: Who study outside of Europe) versus non-mobile (pursue their studies in Luxembourg), and to analyze the associations between LS and career attitudes, socioeconomic characteristics, and health-related factors for each group.MethodSix hundred and sixty-four (644) students obtained financial aid from the Luxembourgish government independent of their family’s socioeconomic situation. Contacted by post, they completed an online questionnaire. Analyses included a multiple linear regression model in which only significant relationships (p < 0.05) were used.ResultsThree groups were created: Mobile intra EU (n = 381), mobile outside EU (n = 43) and non-mobile (n = 66) postgraduates. Health satisfaction was positively linked to LS, in all groups. Among the mobile outside EU group, majority (63.2%) were men and 57.9% did not live alone - health was the only determinant which contributed to their LS. Among the mobile intra EU, majority (57.8%) were women, and 64.3% not living alone. Autonomy and career adaptability attitudes were positively associated with their LS (b: 0.210 and 0.119, respectively), whereas the worry factor was negatively (b: − 0.153 and -0.159) associated. The non-mobile, were the oldest of the three groups. Majority (51.6%) were women, and 93.7% did not live alone. Career optimism and planning attitudes were positively correlated to their LS (regression parameter estimates (b: 0.400 and 0.212, respectively).ConclusionsAttention should be devoted to the LS of local and cosmopolitan students, as it seems to be a relevant health indicator. Overall, the farther the mobility was, the higher the postgraduates’ general LS (8.5/10) was; this indicator was higher than the LS indicator for the age group 25–34 years 7.53/10 (EU-28, in 2013). University’ services could promote the development of career projects and the promotion of health to enhance postgraduates’ LS. University policy makers need to ensure this for all students.

A vine copula approach for regression analysis of bivariate current status data with informative censoring

ABSTRACTBivariate current status data occur in many areas and many authors have discussed their analysis and proposed many inference procedures [Jewell, N.P., van der Laan, M.J., and Lei, X. (2005), ‘Bivariate Current Status Data with Univariate Monitoring Times’, Biometrika, 92, 847–862; Wang, N., Wang, L., and McMahan, C.S. (2015), ‘Regression Analysis of Bivariate Current Status Data Under the Gammafrailty Proportional Hazards Model Using the Em Algorithm’, Computational Statistics & Data Analysis, 83, 140–150; Hu, T., Zhou, Q., and Sun, J. (2017), ‘Regression Analysis of Bivariate Current Status Data Under the Proportional Hazards Model’, The Canadian Journal of Statistics, 45, 410–424]. However, most of these methods are for the situation where the observation or censoring is non-informative and sometimes one may face informative censoring [Zhang, Z., Sun, J., and Sun, L. (2005), ‘Statistical Analysis of Current Data with Informative Observation Times’, Statistics in Medicine, 24, 1399–1407; Chen, C.M., Lu, T.F.C., Chen, M.H., and Hsu, C.M. (2012), ‘Semiparametric Transformation Models for Current Status Data with Informative Censoring’, Biometrical Journal, 19, 641–656; Ma, L., Hu, T., and Sun, J. (2015), ‘Sieve Maximum Likelihood Regression Analysis of Dependent Current Status Data’, Biometrika, 85, 649–658], where one has to deal with three correlated random variables. In this paper, a vine copula approach is developed for regression analysis of bivariate current status data in the presence of informative censoring. The proposed estimators are shown to be strongly consistent and the asymptotic normality and efficiency of the estimated regression parameter are also established. Numerical results suggest that the proposed method works well in practice.

Prediction in polynomial errors-in-variables models

A multivariate errors-in-variables (EIV) model with an intercept term, and a polynomial EIV model are considered. Focus is made on a structural homoskedastic case, where vectors of covariates are i.i.d. and measurement errors are i.i.d. as well. The covariates contaminated with errors are normally distributed and the corresponding classical errors are also assumed normal. In both models, it is shown that (inconsistent) ordinary least squares estimators of regression parameters yield an a.s. approximation to the best prediction of response given the values of observable covariates. Thus, not only in the linear EIV, but in the polynomial EIV models as well, consistent estimators of regression parameters are useless in the prediction problem, provided the size and covariance structure of observation errors for the predicted subject do not differ from those in the data used for the model fitting.

НЕЛИНЕЙНОЕ ОЦЕНИВАНИЕ ПАРНОЙ ОДНОПАРАМЕТРИЧЕСКОЙ РЕГРЕССИИ В УСЛОВИЯХ НЕДОСТАТКА СТАТИСТИКИ

Parametric regression is a mathematical model of a phenomenon in the form of functional dependence between the parameters of this phenomenon, one of which is a dependent variable and independent arguments of a function, and the other is its unknown estimated parameters. Since measurements are often burdened with errors, the construction of the model is carried out in the probabilistic scheme of the problem statement, and the estimates of unknown parameters are carried out by statistical methods using evaluation equations. For a nonlinear regression that is not intrinsically linear, the estimated equations with respect to the estimated parameter are not analytically solved. In this case, iteration methods are used, the effectiveness of which depends on the initial approximation. There is an iterative formula for generalized minimal-contrast estimation of non-linear one-parameter pair (one argument) regression. Its components are the implementations of the estimated regression parameter found analytically or numerically by the regression function at measured values of the dependent variable and the independent argument without taking into account the measurement errors. The average of these realizations with a certain approximation accuracy is a consistent estimate, which was previously proved by the numerical characteristics of the realizations found. This estimate can be used as an initial estimate in an iterative parametric regression estimation formula. In this paper, the implementation of the estimated parameter with approximately zero variance is considered not only as an initial approximation, but also as a self-sufficient estimate, if its accuracy is satisfactory. It is an approximation of the estimated parameter of known accuracy proportional to the cube of the standard deviation of the initial data. The results of the simulation experiment for estimating regression parameters by the proposed approximation method and by means of a consistent assessment are consistent with the theoretical descriptions of the methods. Their comparison is in favor of approximation, if the volume of the original data is less than ten. In this case, the deviation from the true value of the estimated parameter is less than the deviation of the compared state estimate by a maximum of two orders of magnitude (188 times) by at least 1.5 times. Conditions of optimality of the method assumes its use in studies of rare phenomena, as well as in expensive experiments in the broad (economic and humanitarian) sense of the word, he effectiveness of the evaluation method can be anticipated by checking to experience the fulfillment of the conditions of evaluation formation, which depend on the range of values of the argument of the regression function.

On the correspondence of deviances and maximum-likelihood and interval estimates from log-linear to logistic regression modelling.

Consider a set of categorical variables where at least one, denoted by Y, is binary. The log-linear model that describes the contingency table counts implies a logistic regression model, with outcome Y. Extending results from Christensen (1997, Log-linear models and logistic regression, 2nd edn. New York, NY, Springer), we prove that the maximum-likelihood estimates (MLE) of the logistic regression parameters equals the MLE for the corresponding log-linear model parameters, also considering the case where contingency table factors are not present in the corresponding logistic regression and some of the contingency table cells are collapsed together. We prove that, asymptotically, standard errors are also equal. These results demonstrate the extent to which inferences from the log-linear framework translate to inferences within the logistic regression framework, on the magnitude of main effects and interactions. Finally, we prove that the deviance of the log-linear model is equal to the deviance of the corresponding logistic regression, provided that no cell observations are collapsed together when one or more factors in become obsolete. We illustrate the derived results with the analysis of a real dataset.

Continuous-Time Switching Regression Method with Unknown Switching Points

Linear regression with switching in continuous time is considered. A method for estimation of switching points and switching regression parameters is described. Examples of its use are given.

Robust Risk Minimization for Statistical Learning From Corrupted Data

We consider a general statistical learning problem where an unknown fraction of the training data is corrupted. We develop a robust learning method that only requires specifying an upper bound on the corrupted data fraction. The method minimizes a risk function defined by a non-parametric distribution with unknown probability weights. We derive and analyse the optimal weights and show how they provide robustness against corrupted data. Furthermore, we give a computationally efficient coordinate descent algorithm to solve the risk minimization problem. We demonstrate the wide range applicability of the method, including regression, classification, unsupervised learning and classic parameter estimation, with state-of-the-art performance.

Triangular angles parameterization for the correlation matrix of bivariate longitudinal data

Multivariate longitudinal data is often encountered in the jobs of statisticians and practitioners. It is challenging to model the covariance matrix due to the complex structure of correlations among multiple responses. For this modeling task, several effective Cholesky decomposition based methods have been studied. However, direct interpretation of the covariation structure among multiple responses is still less well investigated to the best of our knowledge. In this paper, we propose a joint mean-variance correlation modeling method based on the triangular angles parameterization (TAP) for the correlation matrix of bivariate longitudinal data. The proposed unconstrained parameterization is able to automatically eliminate the positive definiteness constraint of the correlation matrix and leads to the aforementioned direct interpretation. Furthermore, the variance matrix is diagonal rather than block-diagonal, so the positive-definiteness constraint of this matrix can be easily satisfied. The entries of the proposed decomposition are modeled by regression models, and the maximum likelihood estimators of regression parameters are obtained. The resulting estimators are shown to be consistent and asymptotically normal. Simulations and a study of poplar growth illustrate that the proposed method performs well.

Machine learning model to characterize seizure development in traumatic brain injury patients.

Traumatic brain injury (TBI) occurs in 69 million people annually and many patients go on to develop disabling disorders such as post-traumatic epilepsy (PTE). This work focuses on data modeling and analysis for TBI patients who develop seizures. We investigated and analyzed MRI scans using voxel-based morphometry (VBM) to characterize gray level intensity differences between TBI patients who developed seizures and TBI patients who have not developed seizures. We used MRI scans from the Epilepsy Bioinformatics Study for Antiepileptogenic Therapy, which aims to identify epileptogenic biomarkers through an international project involving multiple species, modalities, and research institutions. Using the VBM approach, statistically significant voxel changes were identified between the two clinical groups in different brain regions. Stochastic modeling and statistical analysis of the data in terms of interesting, confounding factors (age and total intracranial volume) and residual variability applied to each voxel independently, are presented. Statistical inference is used to test hypotheses that are expressed as functions of the General Linear Model estimated regression parameters. In addition, we used significant voxels to train a Neural Network (NN) classifier and evaluate the informative power of the proposed approach. The NN was able to distinguish the two clinical groups with an Area Under the receiver operating characteristics Curve of 62%.

Robust ridge regression for estimating the effects of correlated gene expressions on phenotypic traits

Statistical packages such as edgeR and DESeq are intended to detect genes that are relevant to phenotypic traits and diseases. A few studies have also modeled the relationships between gene expressions and traits. In the presence of multicollinearity and outliers, which are unavoidable in genetic data, the robust ridge regression estimator can be applied with the trait value as the response variable and the gene expressions as explanatory variables. In some simulation scenarios, the robust ridge estimator is resistant to outliers and less susceptible to multicollinearity than the ordinary least-squares (OLS) estimator. This study investigated the reliability of the robust ridge estimator, in a scenario where the explanatory variables have tail-dependence and negative binomial distributions, by comparing its performance to that of OLS using vine copula to model the tail-dependence among gene expressions. The robust ridge estimator and OLS were both applied to an ecological dataset. First, statistical analysis was used to compare RNA sequencing data between two treatments; then, 15 differentially expressed genes were selected. Next, the regression parameter estimates of robust ridge and OLS for the effects of the 15 contigs (explanatory variables) on trait values (response variables) were compared. Robust ridge regression was found to detect fewer positive and negative slopes than OLS regression. These results indicate that robust ridge regression can be successfully applied for RNA sequencing analysis to estimate the effect of trait-associated genes using real data, and holds great promise as a tool for modeling the association between RNA expression and phenotypic traits.

Self-excited hysteretic negative binomial autoregression

This paper studies an observation-driven model for time series of counts, in which the observations are supposed to follow a negative binomial distribution conditioned on past information with the form of the hysteretic autoregression. As an extension of the classical two-regime threshold process, the hysteretic autoregression enjoys a more flexible regime-switching mechanism. Stability properties of the model are established by the e-chain and Lyapunov’s method. The estimator for regression parameters is obtained by the quasi-maximum likelihood with Poisson-based score estimating function, and the corresponding asymptotic properties are established. Moreover, a reasonable method for selecting search ranges for thresholds is also proposed and simulation studies are considered. As an application, we bring attention to some features of the daily number of trades of Siparex Croissance which have been overlooked in previous studies.