Linear Measurement Error Models Research Articles

Estimation of Linear Mixed Measurement Error Models in the Presence of Multicollinearity

Estimation of Linear Mixed Measurement Error Models in the Presence of Multicollinearity

Ölçüm Hatalı Kısmi Lineer Karma Modellerde Modified Kernel Ridge Öntahmin Edicilerin Covid-19 Veri Analizi Yoluyla Performans Değerlendirmesi

In this article we describe new predictors under multicollinearity situation in the partially linear mixed measurement error models. In order to achieve this aim, we refer to some preliminary information and use it in order to suggest the modified Kernel ridge predictors in the partially linear mixed measurement error models. In addition, we also attain some mean square error comparisons between our new described modified Kernel ridge predictors and predictors previously described in literature for the partially linear mixed measurement error model. In conclusion, the article showcases real data analysis and a simulation study to illusrate our theoretical findings.

Simple linear functional Errors–In–Variables models with correlated errors

This paper establishes a new estimator for simple linear measurement error models with correlated errors. Under a small-noise asymptotic regime and using perturbation theory, an unbiased estimator has been developed. The consistency and the asymptotic normality of the new estimator have been established and then validated by using synthetic data. Moreover, the confidence intervals of the slope have been revisited. Simulation results show that our estimator is certainly the most stable of existing methods and its performance exceeds that of other existing methods in terms of coverage and interval length.

Kernel mixed and Kernel stochastic restricted ridge predictions in the partially linear mixed measurement error models: an application to COVID-19

In this article, we define mixed predictor and stochastic restricted ridge predictor of partially linear mixed measurement error models by taking advantage of Kernel approximation. Under matrix mean square error criterion, we make the comparison of the superiorities the linear combinations of the new defined predictors. Then we investigate the asymptotic normality characteristics and the situation of the unknown covariance matrix of measurement errors. Finally, the study is ended with a Monte Carlo simulation study and COVID-19 data application.

Testing symmetry of model errors for non linear multiplicative distortion measurement error models

To study the symmetry and asymmetry of the model error under multiplicative distortion measurement errors setting, we propose a correlation coefficient-based measure between the distribution function and the root of density function. The unknown distribution function and density function are estimated from four kinds of residuals: the conditional mean calibration-based residuals, the conditional absolute mean calibration-based residuals, the conditional variance calibration-based residuals, and the conditional absolute logarithmic calibration-based residuals. We study the asymptotic results of the estimators of correlation coefficient-based measure under four calibrations. Next, we consider statistical inference of the correlation coefficient-based measure by using the empirical likelihood method. The empirical likelihood statistics are shown to be an asymptotically standard chi-squared distribution. Simulation studies demonstrate the performance of the proposed estimators and test statistics. A real example is analyzed to illustrate its practical usage.

Diagnostics for partially linear measurement error models

Partially linear models are useful tools to analyze data from economic, genetic, and other fields. Similar to other data analyses, the identification of influential observations that may be potential outliers is an important step beyond estimation in such models. The objective of this article is to develop some diagnostic measures for identifying influential observations in partially linear models when some of the covariates are measured with errors. Deletion measures are developed based on case deletion, mean shift outlier models, and the corrected likelihood of Nakamura (1990). The performance of the methods is illustrated by an artificial example and a real example.

Local influence in linear mixed measurement error models with ridge estimation

This paper deals with the assessment of the effects of minor perturbations of data in the linear mixed measurement error models with Ridge estimation, based on the corrected score function. The local influence approach is used for assessing the influence of small perturbations on the parameter estimates. We examine different types of perturbation schemes including the covariance matrix of the conditional errors, case weight, response, and explanatory perturbation, to identify influential observations. A real data application and a simulation study illustrate the performance of the proposed diagnostics.

Mediation analysis in the presence of continuous exposure measurement error.

The difference method is used in mediation analysis to quantify the extent to which a mediator explains the mechanisms underlying the pathway between an exposure and an outcome. In many health science studies, the exposures are almost never measured without error, which can result in biased effect estimates. This article investigates methods for mediation analysis when a continuous exposure is mismeasured. Under a linear exposure measurement error model, we prove that the bias of indirect effect and mediation proportion can go in either direction but the mediation proportion is usually be less biased when the associations between the exposure and its error-prone counterpart are similar with and without adjustment for the mediator. We further propose methods to adjust for exposure measurement error with continuous and binary outcomes. The proposed approaches require a main study/validation study design where in the validation study, data are available for characterizing the relationship between the true exposure and its error-prone counterpart. The proposed approaches are then applied to the Health Professional Follow-up Study, 1986-2016, to investigate the impact of body mass index (BMI) as a mediator for mediating the effect of physical activity on the risk of cardiovascular diseases. Our results reveal that physical activity is significantly associated with a lower risk of cardiovascular disease incidence, and approximately half of the total effect of physical activity is mediated by BMI after accounting for exposure measurement error. Extensive simulation studies are conducted to demonstrate the validity and efficiency of the proposed approaches in finite samples.

Robust estimation for varying-coefficient partially linear measurement error model with auxiliary instrumental variables

<abstract><p>We study the varying-coefficient partially linear model when some linear covariates are not observed, but their auxiliary instrumental variables are available. Combining the calibrated error-prone covariates and modal regression, we present a two-stage efficient estimation procedure, which is robust against outliers or heavy-tail error distributions. Asymptotic properties of the resulting estimators are established. Performance of our proposed estimation procedure is illustrated through some numerous simulations and a real example. And the results confirm that the proposed methods are satisfactory.</p></abstract>

Kernel Liu prediction approach in partially linear mixed measurement error models

ABSTRACT In this paper, we put forward ‘kernel Liu prediction approach’ instead of ‘kernel prediction approach’ under multicollinearity case in partially linear mixed measurement error model. We obtain the necessary and sufficient condition for the superiority of the linear combinations of the predictors in the sense of the matrix mean square error criterion and give the selection of the Liu biasing parameter via the Conceptual Prediction () criterion. The asymptotic normality condition is examined and the unknown covariance matrix of measurement errors circumstance is derived. We study a numerical example together with a Monte Carlo simulation study to evaluate the performance of the kernel Liu prediction approach at the end of this paper.

Control charts for measurement error models

We consider a linear measurement error model (MEM) with AR(1) process in the state equation which is widely used in applied research. This MEM could be equivalently re-written as ARMA(1,1) process, where the MA(1) parameter is related to the variance of measurement errors. As the MA(1) parameter is of essential importance for these linear MEMs, it is of much relevance to provide instruments for online monitoring in order to detect its possible changes. In this paper we develop control charts for online detection of such changes, i.e., from AR(1) to ARMA(1,1) and vice versa, as soon as they occur. For this purpose, we elaborate on both cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts and investigate their performance in a Monte Carlo simulation study. The empirical illustration of our approach is conducted based on time series of daily realized volatilities.

A two-parameter estimator in linear measurement error model

ABSTRACT This article is concerned with the parameter estimation in linear measurement error model when there is ill-conditioned data. To deal with the multicollinearity problem, a new two-parameter estimator is proposed. The asymptotic properties of the new estimator are considered using the mean squared error matrix. Finally, a Monte Carlo simulation is presented to show the performances of the estimators in terms of simulated mean squared error criteria. According to the results, the new estimator can be suggested as an alternative to the other existing estimators in the presence of ill-conditioned data.

Partial linear additive distortion measurement errors models

We consider partial linear regression models when all the variables are measured with additive distortion measurement errors. To eliminate the effect caused by the distortion, we propose the conditional mean calibration to obtain calibrated variables. A profile least squares estimator for the parameter is obtained, associated with its normal approximation based and empirical likelihood based confidence intervals. For the hypothesis testing on parameters, a restricted estimator under the null hypothesis and a test statistic are proposed. A smoothly clipped absolute deviation penalty is employed to select the relevant variables. The resulting penalized estimators are shown to be asymptotically normal and have the oracle property. Lastly, a score-type test statistic is then proposed for checking the validity of partial linear models. Simulation studies demonstrate the performance of our proposed procedure and a real example is analyzed as illustrate its practical usage.

Kernel ridge prediction method in partially linear mixed measurement error model

In this article, a new kernel prediction method by using ridge regression approach is suggested to combat multicollinearity and the impacts of its existence on various views of partially linear mixed measurement error model. We derive the necessary and sufficient condition for the superiority of the linear combinations of the predictors in the sense of the matrix mean square error criterion and give the selection of the ridge biasing parameter. The asymptotic normality condition is investigated and the unknown covariance matrix of measurement errors circumstance is handled. A real data analysis together with a Monte Carlo simulation study is made to assess endorsement of the kernel ridge prediction method.

Diagnostic measures for the restricted Liu estimator in linear measurement error models

This article concentrated on the diagnostics measures to identify outlier observations using the restricted Liu estimator (RLE) of the vector of parameters in linear measurement error models (LMEMs). To this end, the mean shift outlier model (MSOM) has been determined to detect outliers and the corrected score test statistic. Also, using the RLE, generalized leverage matrices were constructed to identify high-leverage observations. Furthermore, to identify the influential observations, different statistics that are single-case deletion methods are used based on RLE. Finally, a simulation study and a real example are provided to illustrate the performance of the influence measures.

Estimation on functional partially linear single index measurement error model

In this article, we investigate the functional partially linear single index model when measurement error exists in covariates. The main purpose of this article is to correct the biased estimators caused by additive error and construct the asymptotic properties of unknown parameters and function in model. Asymptotic distribution of the parametric component and the convergence rates of the nonparametric part are obtained under some regularity conditions. Compared with existing literatures in this field, such as functional partially linear and semi-functional partial linear regression model with measurement error, good performance in Tecator data analysis illustrates the advantages of the model and the significance of the proposed methodology. In this process, functional slice inverse regression is applied to estimate the functional single index parameter to improve computational efficiency. Furthermore, a simulation study is also carried out for demonstration.

Influence measures and outliers detection in linear mixed measurement error models with Ridge estimation

In this article, we have concentrated on the influence diagnostics based on the mean shift outlier models (MSOM) and case deletion methods in the linear mixed measurement error models with Ridge estimation using the corrected likelihood of Nakamura (1990). We have derived the corrected score test statistic for outliers detection according to MSOM. Then, several case deletion measures are constructed as a tool for influence diagnostics. A parametric bootstrap procedure is used to obtain empirical distributions of the test statistics, and a simulation study has been used to show the performance of the proposed score test statistic and cook distance. Finally, a numerical example is given to illustrate the theoretical results.

Inference in high dimensional linear measurement error models

For a high dimensional linear model with a finite number of covariates measured with errors, we study statistical inference on the parameters associated with the error-prone covariates, and propose a new corrected decorrelated score test and a corresponding score type estimator. This work was motivated by a real data example, where both low dimensional phenotypic variables and high dimensional genotypic variables, single nucleotide polymorphisms (SNPs), are available. One of the phenotypic variables is of clinical interest but measured with error. As is standard in the literature, the high dimensional SNPs are assumed to be measured accurately.We show that the limiting distribution of our corrected decorrelated score test statistic is standard normal under the null hypothesis and retains power under the local alternatives around zero. We also establish the asymptotic normality of the newly proposed estimator, and hence asymptotic confidence intervals can be constructed. The finite-sample performance of the proposed inference procedure is examined through simulation studies. We further illustrate the proposed procedure via an empirical analysis of the real data example mentioned above.

The Mixed Liu Estimator in Stochastic Restricted Linear Measurement Error Model

Ghapani and Babdi [1] proposed a mixed Liu estimator in linear measurement error model with stochastic linear restrictions. In this article, we propose an alternative mixed Liu estimator in the linear measurement error model with stochastic linear restrictions. The performance of the new mixed Liu estimator over the mixed estimator, Liu estimator, and mixed Liu estimator proposed by Ghapani and Babdi [1] are discussed in the sense of mean squared error matrix. Finally, a simulation study is given to show the performance of these estimators.

Assessment of local influence in spatial elliptical linear measurement error models

In this paper, we consider estimation and inference procedures in spatial linear models when some of the covariates are measured with errors. It is assumed that the additive error distributed according to the law belonging to the class of elliptically contoured distributions. The development of the corrected score function with the family of elliptical distributions is the basis for derivation of the estimators. For sensitivity analysis, the local influence approach is used for assessing influence of small perturbations on the parameter estimates. A simulation study is presented illustrating the good performance of the proposed approach, including the robustness property for the heavier tail models. We further illustrate the proposed procedures by an application in a real dataset.