برآورد مدل‌های خطی آمیخته با خطا در اندازه‌گیری در حضور هم‌خطی

در این مقاله، برآوردگر ریج،  برآوردگر محدود شده موزون  و برآوردگر ریج محدود شده موزون در مدل‌های خطی آمیخته با خطا در اندازه‌گیری در حضور هم‌خطی در نظر گرفته می‌شود. سپس ویژگی‌های مجانبی برآوردگرهای به‌دست آمده بررسی می‌شود. شرایط لازم و کافی برای برتری برآوردگر ریج محدود شده موزون نسبت به برآوردگر محدود شده موزون به منظور تعیین پارامتر ریج با استفاده از ماتریس میانگین توان‌های دوم خطا تعیین می‌شود و سرانجام با استفاده از مطالعه شبیه‌سازی و ارائه یک مثال از داده‌های واقعی عملکرد برآوردگرهای به‌دست آمده مورد ارزیابی قرار می‌گیرد.

estimation of linear mixed measurement error models in the presence of multicollinearity

linear mixed effects models are the most common statistical tools towards inference about repeated measurement data and in particular, longitudinal data in biomedical, agricultural, environmental and also in economics and social sciences. these models are an extension of simple linear models withvarious combinations of fixed and random effects. in these models, regressors are often measured with negligible errors. hence it is of great interest to study the estimation for the measurement error models. also, the presence ofcollinearity in such models complicates the problem of parameter estimation.to conquer the collinearity problem, many alternative biased estimators havebeen proposed. a popular technique to overcome the collinearity problem isto consider parameter estimation in addition to the sample information suchas some exact or stochastic linear restrictions on the unknown parameters.our primary aim in this paper is to obtain the weighted ridge estimator offixed and random effects in stochastic restricted linear mixed measurementerror models when collinearity is present.material and methods:the asymptotic properties of the resulting estimates are examined. the necessaryand sufficient conditions, for the superiority of the different estimatorsbased on the mean squared error matrix of estimators are investigated. furthermore,the selection of the ridge biasing parameter is discussed. a real data analysis is provided to illustrate the theoretical results and a simulationstudy is conducted to characterize the performance of estimators in thelinear mixed measurementresults and discussion:with the increase of the levels of collinearity, measurement error and variancethe estimated mean square error values of the estimators increase ingeneral. also, the weighted mixed ridge estimator has a smaller estimatedmean square error value than the other estimators. in addition, we can getmore exact estimators of the parameters when we get more dependent priorinformation. therefore, we conclude that the proposed estimator can performbetter than the other estimators.conclusion:in this paper, we obtain the ridge estimator, weighted mixed estimator andweighted mixed ridge estimator for the vector of parameters in linear mixedmeasurement error models when additional stochastic linear restrictions onthe parameter vector are assumed to hold. in order to investigate the performanceof the estimators, mean square error matrix comparisons were doneand the selection of the ridge biasing parameter was given. both the numericalexample results and simulation study indicate that always the restrictedestimator is better than the unrestricted estimator. also, there exists a ridgebiasing parameter such that the ridge and mixed ridge estimators dominatesthe corrected estimator and restricted estimator, respectively in the senseof having a smaller mean square error value. in addition, results show thatthe biasing parameter affects the performance of the ridge estimators. furthermore,this study confirms the use of stochastic linear restrictions in thepresence of collinearity.