Jackknife Ridge Estimation of Parameters in Linear Mixed Measurement Error Models
Keywords:
Jackknife ridge, linear mixed models, measurement errors, score estimateAbstract
The main objective of this paper is to tackle the issue of bias in linear mixed models that utilize ridge estimates, particularly in the presence of measurement error in the fixed-effects variables. To achieve this, we first describe a ridge estimator for linear mixed models and then introduce a new estimator called the jackknife ridge estimator. We compare the jackknife ridge estimator with the ridge estimator, highlighting its bias and mean square error advantages. Furthermore, we derive the asymptotic properties of both estimators. Finally, we conduct a simulation study and provide a numerical example to assess the effectiveness of the jackknife ridge estimator in linear ridge mixed measurement error models.
References
Cook RD. Influential observations in linear regression. J Am Stat Assoc. 1979; 74(365): 169-174.
Davidian M. Nonlinear models for repeated measurement data. Boca Raton: Routledge; 2017.
Demidenko E. Mixed models: theory and applications with R. Hoboken: John Wiley & Sons; 2013.
Diggle PJ, Liang KY, Zeger SL. Analysis of longitudinal data. Oxford: Clarendon Press; 1994.
Emami H. Ridge estimation in semiparametric linear measurement error models. Linear Algebra Appl. 2018; 552: 127-146.
Fuller WA. Measurement error models. Hoboken: John Wiley & Sons; 2009.
Fung WK, Zhong XP, Wei BC. On estimation and influence diagnostics in linear mixed measurement error models. Am J Math Manag Sci. 2003; 23(1-2): 37-59.
Ghapani F. Stochastic restricted Liu estimator in linear mixed measurement error models. Commun Stat Simul Comput. 2019; 51(3): 1220-1233.
Hoerl AE, Kennard RW. Ridge regression: Biased estimation for nonorthogonal problems. Technometrics. 1970; 12(1): 55-67.
Lawless JF, Wang P. A simulation study of ridge and other regression estimators. Commun Stat Theory Methods. 1976; 5(4): 307-323.
Kibria BMG. Performance of some new ridge regression estimators. Commun Stat Simul Comput. 2003; 32(2): 419-435.
Kuran Ö. Mean square error performance of the modified jackknifed ridge predictors in the linear mixed models. Erciyes Univ Fen Bilim Enst Fen Bilim Derg. 2020; 36(3): 400-407.
Lee Y, Nelder JA. Hierarchical generalized linear models. J R Stat Soc Ser B Stat Methodol. 1996; 58(4): 619-656.
Neuhaus JM, McCulloch CE. Covariate decomposition methods for longitudinal missing-at-random data and predictors associated with subject-specific effects. Aust N Z J Stat. 2014; 56(4): 331-345.
Nomura M. On the almost unbiased ridge regression estimator. Commun Stat Simul Comput. 1988;17(3): 729-743.
Nyquist H. Applications of the jackknife procedure in ridge regression. Comput Stat Data Anal. 1988; 6(2): 177-183.
Özkale MR, Can F. An evaluation of ridge estimator in linear mixed models: an example from kidney failure data. J Appl Stat. 2017; 44(12): 2251-2269.
Özkale MR, Kuran Ö. Adaptation of the jackknifed ridge methods to the linear mixed models. J Stat Comput Simul. 2019; 89(18): 3413-3452.
Quenouille MH. Approximate tests of correlation in time series. In: Proceedings of the Cambridge Philosophical Society. Mathematical Proceedings of the Cambridge Philosophical Society; 1949 Jul; Cambridge, UK. Cambridge: Cambridge University Press; 1949. pp. 483-484.
Quenouille MH. Notes on bias in estimation. Biometrika. 1956; 43(3-4): 353-360.
Rao CR, Toutenburg H, Shalabh, Heumann C. Linear models and generalizations: least squares and alternatives. 3rd ed. New York: Springer; 2008.
Seber GAF, Lee AJ. Linear regression analysis. 2nd ed. New York: Springer; 2003.
Singh B, Chaubey YP, Dwivedi TD. An almost unbiased ridge estimator. Sankhya B. 1986; 48: 342-346.
Stefanski LA. The effects of measurement error on parameter estimation. Biometrika. 1985; 72(3): 583-592.
Yavarizadeh B, Rasekh A, Ahmed SE, Babadi B. Ridge estimation in linear mixed measurement error models with stochastic linear mixed restrictions. Commun Stat Simul Comput. 2022; 51(6): 3037-3053.
Zare K, Rasekh A. Diagnostic measures for linear mixed measurement error models. SORT Stat Oper Res Trans. 2011; 35(2): 125-144.
Zare K, Rasekh A, Rasekhi AA. Estimation of variance components in linear mixed measurement error models. Stat Pap. 2012; 53: 849-863.
Zhong XP, Wei BC, Fung WK. Influence analysis for linear measurement error models. Ann Inst Stat Math. 2000; 52: 367-379.
Zhong XP, Fung WK, Wei BC. Estimation in linear models with random effects and errors-in-variables. Ann Inst Stat Math. 2002; 54: 595-606.
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