Estimation Of Regression Parameters Research Articles

A study on group lasso for grouped variable selection in regression model

Estimation of regression parameters using the Least Squares (LS) method could not be performed when the number of explanatory variables exceeds the number of observations. An approach that can solve the problem is the LASSO (Least Absolute Shrinkage and Selection Operator) method. This method produces a stable model but with slight bias as the trade-off. Yuan and Lin [6] introduced the Group LASSO method which can be used when there are grouped structure in the variables. This current paper provided a study of the performance of the Group LASSO method through a simulation with several different scenarios. Furthermore, the Group LASSO method was applied to the Human Development Index (HDI) data of Bengkulu Province in 2019. The simulation yieled that the Group LASSO analysis was better than LASSO in term of its Mean Squared Error of Prediction (MSEP), False Negative Rate (FNR) and R-Squared. In the application of the approach to the HDI data, our result was in line with the simulation results that the analysis of Group LASSO was better than LASSO with MSEP Group LASSO of 0.25 and R-Squared of 98%.

METODE MODIFIED JACKKNIFE RIDGE REGRESSION DALAM PENANGANAN MULTIKOLINIERITAS (STUDI KASUS INDEKS PEMBANGUNAN MANUSIA DI JAWA TENGAH)

The human development index is a value where the value showed the measure of living standards comparison in a region. The Human Development Index is influenced by several factors, one of them is the education factor that is the average years of schooling and expected years of schooling. A statistical method to find the correlation between the independent variable and the dependent variable can be conducted using the linear regression method. Linear regression requires several assumptions, one of which is the multicollinearity assumption. If the multicollinearity assumption is not fulfilled, another alternative is needed to estimate the regression parameters. One method that can be used to estimate regression parameters is the ridge regression method with an ordinary ridge regression estimator. Ordinary ridge regression then developed more into several methods, such as generalized ridge regression, jackknife ridge regression, and modified jackknife ridge regression method. The generalized Ridge Regression method causes a reduction to variance in linear regression, while the jackknife ridge regression method is obtained by resampling jackknife process on the generalized ridge regression method. Modified jackknife ridge regression is a combination of generalized ridge regression and jackknife ridge regression method. In this journal, the three ridge regression methods will be compared based on the Mean Squared Error obtained in each method. The results of this study indicate that the jackknife ridge regression method has the smallest MSE value. Keywords: Generalized Ridge Regression, Jackknife Ridge Regression, Modified Jackknife Ridge Regression, Multicolinearity

An Interval-Censored Proportional Hazards Model

We fit a Cox proportional hazards (PH) model to interval-censored survival data by first subdividing each individual's failure interval into nonoverlapping sub-intervals. Using the set of all interval endpoints in the data set, those that fall into the individual's interval are then used as the cut points for the sub-intervals. Each sub-interval has an accompanying weight calculated from a parametric Weibull model based on the current parameter estimates. A weighted PH model is then fit with multiple lines of observations corresponding to the sub-intervals for each individual, where the lower end of each sub-interval is used as the observed failure time with the accompanying weights incorporated. Right-censored observations are handled in the usual manner. We iterate between estimating the baseline Weibull distribution and fitting the weighted PH model until the regression parameters of interest converge. The regression parameter estimates are fixed as an offset when we update the estimates of the Weibull distribution and recalculate the weights. Our approach is similar to Satten et al.'s (1998) method for interval-censored survival analysis that used imputed failure times generated from a parametric model in a PH model. Simulation results demonstrate apparently unbiased parameter estimation for the correctly specified Weibull model and little to no bias for a mis-specified log-logistic model. Breast cosmetic deterioration data and ICU hyperlactemia data are analyzed.

Semiparametric analysis of case K interval-censored failure time data in the presence of a cured subgroup and informative censoring

Interval censoring and the existence of a cured subgroup occur quite often in survival studies and many procedures have been developed for dealing with each of the two issues individually or them together. In this paper, we discuss the situation where both issues exist and furthermore, interval censoring may be informative, for which there exists relatively much less literature. For the problem, we present a frailty-based joint model approach in which a frailty term is employed to describe the correlation between the failure time of interest and the censoring mechanism. For inference, a two-step estimation procedure is developed and in particular, the sieve maximum-likelihood estimation approach is used for estimation of the unknown function. The proposed estimators of regression parameters are shown to be consistent and asymptotically normal, and an extensive simulation study conducted suggests that the proposed procedure works well for practical situations. In addition, an application is provided.

A Fixed Effect Panel Spatial Error Model in Identifying Factors of Poverty in West Java Province

In the last five years, poverty had been a major problem in West Java Province (WJP). Hence, it becomes a strategic development issue for the next five years. To contribute in eradicating the poverty, we aimed this study at identifying poverty factors and measuring their effects. There are two issues in modelling poverty in WJP. First, there was spatial dependency in poverty among regions. Second, due to data limitation, some important factors were not included in the empirical model. Both might lead to bias in regression parameter estimates. Accordingly, we applied a fixed effect panel spatial error model on the poverty rate in WJP. We found that health and economic welfare effected poverty.

Unified approach for regression models with nonmonotone missing at random data

Unified approach (Chen and Chen in J R Stat Soc B 62(3):449–460, 2000) uses a working regression model to extract information from auxiliary variables in two-stage study for computing an efficient estimator of regression parameter. As far as we know, the method is limited to deal with missing complete at random data in a simple monotone missing data pattern. In this research, we extend the unified approach to estimate regression models with nonmonotone missing at random data. We describe an inverse probability weighting estimator condition on estimators from a set of working regression models which contains information from incomplete data and auxiliary variables. The proposed method is flexible and can easily accommodate incomplete data and auxiliary variables. We investigate the finite-sample performance of the proposed estimators using simulation studies and further illustrate the estimation method on a case–control study investigating the risk factors of hip fractures.

On the Use of Regression Calibration in a Complex Sampling Design With Application to the Hispanic Community Health Study/Study of Latinos.

Regression calibration is the most widely used method to adjust regression parameter estimates for covariate measurement error. Yet its application in the context of a complex sampling design, for which the common bootstrap variance estimator can be less straightforward, has been less studied. We propose 2 variance estimators for a multistage probability-based sampling design, a parametric and a resampling-based multiple imputation approach, where a latent mean exposure needed for regression calibration is the target of imputation. This work was motivated by the Hispanic Community Health Study/Study of Latinos (HCHS/SOL) data from 2008 to 2011, for which relationships between several outcomes and diet, an error-prone self-reported exposure, are of interest. We assessed the relative performance of these variance estimation strategies in an extensive simulation study built on the HCHS/SOL data. We further illustrate the proposed estimators with an analysis of the cross-sectional association of dietary sodium intake with hypertension-related outcomes in a subsample of the HCHS/SOL cohort. We have provided guidelines for the application of regression models with regression-calibrated exposures. Practical considerations for implementation of these 2 variance estimators in the setting of a large multicenter study are also discussed. Code to replicate the presented results is available online.

Generalized quasi-likelihood estimation procedure for non-stationary over-dispersed longitudinal counts

Poisson log-linear regression model is commonly used for analysing count data. Valid inference based on this model can be drawn when the mean and variance of the data are equal. However, in practice variance of responses is often much greater than the mean of the responses, known as over-dispersion. Also, non-stationarity, i.e. non-constant mean, or/and non-constant variance, and/or covariance that is not solely the function of elapsed time between responses over the period of study, is another issue in the longitudinal study. It has been found that ignoring such departures may arise bias and provide misleading conclusions. As a remedy, negative binomial (NB) regression was suggested by the researcher for modelling longitudinal count. For longitudinal non-stationary count with over-dispersion, there is no established observation-driven model in the literature. Although there exists a non-stationary NB type model in the time series context, this type of observation-driven model has never been used in longitudinal data. In this paper, we have extended the non-stationary model to the longitudinal set-up and proposed a GQL estimation procedure for estimating regression parameters. An extensive simulation study has been carried out through which it has been shown that GQL provides unbiased estimates of the regression parameters. Performance of the method of moment approach for estimating correlation and over-dispersion parameter has also found to be consistent. The proposed model and estimation technique, thereafter, was applied to analyse longitudinal epileptic seizure count data.

Estimation of parameters of logistic regression for two-stage randomized response technique

When a survey study is related to sensitive issues such as political orientation, sexual orientation, and income, respondents may not be willing to reply truthfully, which leads to bias results. To protect the respondents’ privacy and improve their willingness to provide true answers, Warner (J Am Stat Assoc 60:63–69, 1965) proposed the randomized response (RR) technique in which respondents select a question by means of a random device in order to ensure that they maintain privacy. Huang (Stat Neerl 58:75–82, 2004) extended the RR design of Warner (1965) to propose a two-stage RR design. Not only can this method be used to estimate the population proportion of persons with a sensitive characteristic, but also estimate the honest answer rate in the first stage. This work develops a covariate extension of the two-stage RR design of Huang (2004) by applying logistic regression to investigate the effects of covariates on a sensitive characteristic and an honest response. Simulation experiments are conducted to study the finite-sample performance of the maximum likelihood estimators of the logistic regression parameters. The proposed methodology is applied to analyze the survey data of sexuality of freshmen at Feng Chia University in Taiwan in 2016.

Uniform moment bounds for the standard estimators in the Cox proportional hazard model

We consider the Cox regression model and show that the regression parameter estimator and the Breslow estimator for the cumulative hazard have uniformly bounded moments of any order if we restrict to a sequence of events with probability converging to one. These results are needed, for example, when studying global errors of shape restricted estimators of the baseline hazard function.

Regression analysis of asynchronous longitudinal data with informative observation processes

A great deal of literature has been established for regression analysis of longitudinal data but most of the existing methods assume that covariates can be observed completely or at the same observation times for the response variable, and the observation process is independent of the response variable completely or given covariates. As pointed out by many authors, in practice, one may face the situation where the response variable and covariates are observed intermittently at different time points, leading to sparse asynchronous longitudinal data, or the observation process may be related to the response variable even given covariates. It is apparent that sometimes both issues can occur in the same time and although some literature has been developed to address each of the two issues, it does not seem to exist an established approach that can deal with both together. To address this, in this paper, a flexible semiparametric transformation conditional model is presented and for estimation, a kernel-weighted estimating equation-based approach is proposed. The proposed estimators of regression parameters are shown to be consistent and asymptotically follow the normal distribution. For the assessment of the finite sample performance of the method, an extensive simulation study is carried out and suggests that it performs well for practical situations. The approach is applied to a prospective HIV study that motivated this investigation.

Fitting a shared frailty illness-death model to left-truncated semi-competing risks data to examine the impact of education level on incident dementia

BackgroundSemi-competing risks arise when interest lies in the time-to-event for some non-terminal event, the observation of which is subject to some terminal event. One approach to assessing the impact of covariates on semi-competing risks data is through the illness-death model with shared frailty, where hazard regression models are used to model the effect of covariates on the endpoints. The shared frailty term, which can be viewed as an individual-specific random effect, acknowledges dependence between the events that is not accounted for by covariates. Although methods exist for fitting such a model to right-censored semi-competing risks data, there is currently a gap in the literature for fitting such models when a flexible baseline hazard specification is desired and the data are left-truncated, for example when time is on the age scale. We provide a modeling framework and openly available code for implementation.MethodsWe specified the model and the likelihood function that accounts for left-truncated data, and provided an approach to estimation and inference via maximum likelihood. Our model was fully parametric, specifying baseline hazards via Weibull or B-splines. Using simulated data we examined the operating characteristics of the implementation in terms of bias and coverage. We applied our methods to a dataset of 33,117 Kaiser Permanente Northern California members aged 65 or older examining the relationship between educational level (categorized as: high school or less; trade school, some college or college graduate; post-graduate) and incident dementia and death.ResultsA simulation study showed that our implementation provided regression parameter estimates with negligible bias and good coverage. In our data application, we found higher levels of education are associated with a lower risk of incident dementia, after adjusting for sex and race/ethnicity.ConclusionsAs illustrated by our analysis of Kaiser data, our proposed modeling framework allows the analyst to assess the impact of covariates on semi-competing risks data, such as incident dementia and death, while accounting for dependence between the outcomes when data are left-truncated, as is common in studies of aging and dementia.

Application of autoregressive dynamic adaptive (ARDA) model in real-time wind power forecasting

Wind prediction technology has been the focus on the national research with the basis of the power system planning, a reference for power dispatch, and the optimal power flow distribution. Prediction technology is moving into the direction of controlling refinement with the development of the information technology, the artificial intelligence technology, and the improvement of edge computing devices. The wind farms can use real-time wind power prediction to improve their overall efficiency through advanced planning of the wind turbine adjustment and the pre-setting of the yaw, pitch, and generation excitation control systems. This paper proposes an innovative autoregressive dynamic adaptive (ARDA) model based on the improvement of the autoregressive (AR) model. The fixed parameter estimation method of the AR model is improved in the proposed model to a dynamically adaptive stepwise parameter estimation method. Meanwhile, the coefficients of the model are updated adaptively based on the characteristics of wind power data, which improves the accuracy of the proposed model. The prediction accuracy of the proposed model is further improved by the residual function. It was observed that the model adapts well to wind power data with different degrees of volatility. The ARDA model and two other models were tested by using stationary and fluctuating wind power data (unit: seconds), and the wind power prediction results at different forecasting step lengths were compared. It was observed that the ARDA model is more accurate, with faster calculation rate, and better dynamic adaptability to data fluctuations than the ARIMA and LSTM models. This paper proposes an important method for real-time power prediction that can be employed for the advanced control and improved the power generation of wind farms.

Швидкi розрахунки оцiнок коварiацiйних матриць методом складаного ножа

We consider data in which each observed subject belongs to one of different subpopulations (components). The true number of component which a subject belongs to is unknown, but the researcher knows the probabilities that a subject belongs to a given component (concentration of the component in the mixture). The concentrations are different for different observations. So the distribution of the observed data is a mixture of components’ distributions with varying concentrations. A set of variables is observed for each subject. Dependence between these variables is described by a nonlinear regression model. The coefficients of this model are different for different components. Normality of estimator for nonlinear regression parameters is demonstrated under general assumptions. A mixture of logistic regression models with continuous response is considered as an example. In the paper we construct confidence ellipsoids for the regression parameters based on the modified least squares estimators. The covariances of these estimators are estimated by the multiple modifications of jackknife technique. Performance of the obtained confidence ellipsoids is assessed by simulations.

A penalized likelihood approach for efficiently estimating a partially linear additive transformation model with current status data

Current status data are commonly encountered in medical and epidemiological studies in which the failure time for study units is the outcome variable of interest. Data of this form are characterized by the fact that the failure time is not directly observed but rather is known relative to an observation time, i.e., the failure times are either left- or right-censored. Due to its structure, the analysis of such data can be challenging. To circumvent these challenges and to provide for a flexible modeling construct which can be used to analyze current status data, herein a partially linear additive transformation model is proposed. In the formulation of this model, constrained B-splines are employed to model the monotone transformation function and nonparametric covariate effects. To provide for more efficient estimators, a penalization technique is used to regularize the estimation of all unknown functions. An easy to implement hybrid algorithm is developed for model fitting, and a simple and consistent estimator of the large-sample variance-covariance matrix for regression parameter estimators is proposed. It is shown theoretically that the proposed estimators of the finite-dimensional regression coefficients are root-n consistent, asymptotically normal, and achieve the semiparametric information bound, while the estimators of the nonparametric components attain the optimal rate of convergence. The finite-sample performance of the proposed methodology is evaluated through extensive numerical studies and is further demonstrated through the analysis of human papillomavirus (HPV) data.

Linear Bayesian estimators for linear models with constraints

The paper employs a linear Bayesian procedure to simultaneously estimate regression parameters and variance parameter in a linear model with equality constraints. We obtain the expression of the linear Bayesian estimator (LBE) for the parameter vector, which consists of the regression parameters and the variance parameter, without specifying the specific form of the prior. The superiorities of the proposed LBE over some classical estimators are established in terms of mean squared error matrix criterion. Monte Carlo simulations and a numerical example are presented to compare its performances with those of the usual Bayesian estimator and the Lindley approximation as well.

Темп прироста ВВП как регрессия от внутренних и внешних факторов.

The internal and external factors influencing the economic growth of the countries, in particular, Russia, are analyzed. A macro model is proposed in the form of a regression, where on the left the GDP growth rate, and on the right the regressors –the main control effects: the employment growth rate, the product of the share of gross savings in GDP on the number of employed specialists in R & D, the growth rate of oil prices on the world market. Computational experiments are carried out to estimate regression parameters on the statistics of Russia. The contributions of various factors to the economic growth rate are estimated. Conclusions are given.

Two-phase analysis and study design for survival models with error-prone exposures.

Increasingly, medical research is dependent on data collected for non-research purposes, such as electronic health records data. Health records data and other large databases can be prone to measurement error in key exposures, and unadjusted analyses of error-prone data can bias study results. Validating a subset of records is a cost-effective way of gaining information on the error structure, which in turn can be used to adjust analyses for this error and improve inference. We extend the mean score method for the two-phase analysis of discrete-time survival models, which uses the unvalidated covariates as auxiliary variables that act as surrogates for the unobserved true exposures. This method relies on a two-phase sampling design and an estimation approach that preserves the consistency of complete case regression parameter estimates in the validated subset, with increased precision leveraged from the auxiliary data. Furthermore, we develop optimal sampling strategies which minimize the variance of the mean score estimator for a target exposure under a fixed cost constraint. We consider the setting where an internal pilot is necessary for the optimal design so that the phase two sample is split into a pilot and an adaptive optimal sample. Through simulations and data example, we evaluate efficiency gains of the mean score estimator using the derived optimal validation design compared to balanced and simple random sampling for the phase two sample. We also empirically explore efficiency gains that the proposed discrete optimal design can provide for the Cox proportional hazards model in the setting of a continuous-time survival outcome.

Choosing the frequency of follow-up in longitudinal studies: Is more necessarily better?

Background Follow-up frequency is an important design parameter in longitudinal studies. We quantified the impact of reducing follow-up frequency on the precision of estimated regression parameters, and investigated the impact of incorrectly assuming an exchangeable correlation structure on estimates of the loss of precision resulting from reduced follow-up. Methods We estimated the loss in precision on deleting every second observation from three longitudinal cohorts: patients with Childhood Systemic Lupus Erythematosus (cSLE), the Canadian Haemophilia Prophylaxis Study (CHPS), and patients with Juvenile Dermatomyositis (JDM). We compared these results with those from a theoretical formula assuming an exchangeable correlation structure. Results The increase in sample size needed to compensate for halving follow-up frequency was 9%, 6% and 28% for the cSLE, CHPS and JDM cohorts respectively. Under the assumption of an exchangeable correlation, the estimated increases in sample size were 22%, 11% and 10% respectively. Conclusions Reducing follow-up frequency can result in minimal loss of information, as seen in the CHPS cohort. While using a theoretical formula based on an exchangeable correlation structure is convenient, it can be inaccurate when the true correlation structure is not exchangeable.

A note on: A early warning system for market inefficiency

Abstract Violation of the efficient market hypothesis (EMH) in a specific market may lead to construction of bubbles which is a signal of inefficiencies. Although speculative bubbles soon decay, if they exist for a long time, they will lead to financial crises. Early warning systems (EWSs) are designed to quickly alert the market to crises. Under EMH, the logarithm of price is a martingale process. Thus, it is necessary to use a suitable EWS tool for violation of martingale properties of the logarithm of asset prices. In this paper, using the auto-regressive (ARTA) models, and assuming Markov structure between financial random variables, the conditional means are formulated as a simple regression. Then, using the recursive formula for least square estimates of regression parameters, the hypothesis of variables being martingale is tested. This approach leads to a probability index which serves as an EWS. Then, throughout two real data sets, it is seen that the results of the study are applicable to construct EWS for detecting stock market crashes as well as exchange rate market crises. A discussion section is proposed. Finally, based on these results, conclusions are given.