The weighted two-parameter estimation for linear mixed models with measurement error under stochastic linear mixed restrictions

Document Type : Original Scientific Paper

Authors

1 Department of Mathematics‎, ‎Dezful Branch‎, ‎Islamic Azad University‎, ‎Dezful‎, ‎Iran

2 Department of Mathematics and Statistics‎, ‎Shoushtar Branch‎, ‎Islamic Azad University‎, ‎Shoushtar‎, ‎Iran

Abstract

In this paper‎, ‎the weighted mixed stochastic restricted two-parameter estimator/predictor of fixed/random effects is introduced in linear mixed measurement error models‎, ‎where additional stochastic linear restrictions are assumed to apply to fixed and random effects‎. ‎The asymptotic properties of the proposed estimator are derived‎. ‎Some comparisons are made with other estimators under the criterion of mean squared error matrix‎. ‎Furthermore‎, ‎the proposed methods are used to estimate the biasing parameters‎. ‎Finally‎, ‎a real data analysis and a simulation study are provided to evaluate the theoretical findings of the proposed estimator.

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Eliot, M.N., Ferguson, J., Reilly, M.P. and Foulkes, A.S. (2011). Ridge regression for longitudinal biomarker data. The International Journal of Biostatistics, 7(1):Article 37.
Farebrother, R.W. (1976). Further results on the mean square error of ridge Regression. Journal of the Royal Statistical Society. Series B (Methodological), 38(3):248–250.
Fung, W.K., Zhong, X.P. and Wei, B.C. (2003). On estimation and influence diagnostics in linear mixed measurement error models. American Journal of Mathematical and Management Sciences, 23(1-2):37–59.
Ganjealivand, N., Ghapani, F., Zaherzadeh, A. and Hormozinejad, F. (2021a). Performance of stochastic restricted and unrestricted two-parameter estimators in linear mixed models. Métodos numéricos para cálculo y diseño en ingeniería: Revista internacional, 37(2):1–11.
Ganjealivand, N., Ghapani, F., Zaherzadeh, A. and Hormozinejad, F. (2021b). Stochastic restricted two-parameter estimator in linear mixed measurement error models. Journal of the Iranian Statistical Society, 20(2):79–102.
Ghapani, F. and Babadi, B. (2020). Two parameter weighted mixed estimator in linear measurement error models. Communications in Statistics-Simulation and Computation, 51(12):6936–6946.
Ghapani, F. (2019). Stochastic restricted Liu estimator in linear mixed measurement error models. Communications in Statistics-Simulation and Computation, 51(3):1220–1233.
Harrison, D. and Rubinfeld, D.L. (1978). Hedonic housing prices and the demand for clean air. Journal of Environmental Economics and Management, 5(1):81–102.
Hoerl, A.E. and Kennard, R.W. (1970). Ridge regression: biased estimation for non-orthogonal problems. Technometrics, 12(1):55–67.
Kibria, B.M.G. (2003). Performance of some new ridge regression estimators. Communications in Statistics-Simulation and Computation, 32(2):419–435.
Kuran, O. and Ozkale, M.R. (2016). Gilmour's approach to mixed and stochastic restricted ridge predictions in linear mixed models. Linear Algebra and Its Applications, 508:22–47.
Li, Y. and Yang, H. (2011). A new ridge-type estimator in stochastic restricted linear regression. Statistics, 45(2):123–130.
Liu, X.Q. and Hu, P. (2013). General ridge predictors in a mixed linear model. Statistics, 47(2):363–378.
McDonald, G.C. and Galarneau, D.I. (1975). A Monte Carlo evaluation of some ridge-type estimators. Journal of the American Statistical Association, 70(350):407–416.
Nakamura, T. (1990). Corrected score function for errors-in-variables models: Methodology and application to generalized linear models. Biometrika, 77(1):127–137.
Rao, C.R. and Toutenburg, H. (1995). Linear Models: Least Squares and Alternatives. New York: Springer-Verlag.
Rao, C.R., Toutenburg, H., Shalabh, S.H. and Heumann, C. (2008). Linear Models and Generalizations. Berlin: Springer.
Ozbay, N. and Kaçıranlar, S. (2018). Estimation in a linear regression model with stochastic linear restrictions: a new two-parameter-weighted mixed estimator. Journal of Statistical Computation and Simulation, 88(9):1669–1683.
Ozkale, M.R. and Can, F. (2017). An evaluation of ridge estimator in linear mixed models: an example from kidney failure data. Journal of Applied Statistics, 44(12):2251–2269.
Ozkale, M.R. and Kuran, O. (2018). A further prediction method in linear mixed models: Liu prediction. Communications in Statistics-Simulation and Computation, 49(12):3171–3195.
Yang, H. and Chang, X. (2010). A new two-parameter estimator in linear regression. Communications in Statistics-Theory and Methods, 39:923–934.
Yavarizadeh, B. and Ahmed, S.E. (2021). The weighted ridge estimation for linear mixed models with measurement error under stochastic linear mixed restrictions. Communications in Statistics-Theory and Methods, 51(6):1605–1621.
Yavarizadeh, B., Rasekh, A., Ahmed, S.E. and Babadi, B. (2019b). Ridge estimation in linear mixed measurement error models with stochastic linear mixed restrictions. Communications in Statistics-Simulation and Computation, 51(6):3037–3053.
Yavarizadeh, B., Rasekh, A. and Babadi, B. (2019a). Estimation of parameters in linear mixed measurement error models with stochastic linear restrictions. Communications in Statistics-Theory and Methods, 49(23):5853–5865.
Zare, K., Rasekh, A. and Rasekhi, A.A. (2012). Estimation of variance components in linear mixed measurement error models. Statistical Papers, 53(4):849–863.
Zhong, X.P., Fung, W.K. and Wei, B.C. (2002). Estimation in linear models with random effects and errors-in-variables. Annals of the Institute of Statistical Mathematics, 54(3):595–606.