Jackknife for nonlinear estimating equations
Volume 9, Issue 4 (2022), pp. 377–399
Pub. online: 14 June 2022
Type: Research Article
Open Access
Open Access
Received
23 January 2022
23 January 2022
Revised
26 May 2022
26 May 2022
Accepted
26 May 2022
26 May 2022
Published
14 June 2022
14 June 2022
Abstract
In mixture with varying concentrations model (MVC) one deals with a nonhomogeneous sample which consists of subjects belonging to a fixed number of different populations (mixture components). The population which a subject belongs to is unknown, but the probabilities to belong to a given component are known and vary from observation to observation. The distribution of subjects’ observed features depends on the component which it belongs to.
Generalized estimating equations (GEE) for Euclidean parameters in MVC models are considered. Under suitable assumptions the obtained estimators are asymptotically normal. A jackknife (JK) technique for the estimation of their asymptotic covariance matrices is described. Consistency of JK-estimators is demonstrated. An application to a model of mixture of nonlinear regressions and a real life example are presented.
References
Efron, B., Stein, C.: The jackknife estimate of variance. Ann. Appl. Stat. 9, 586–596 (1981). MR0615434
Grün, B., Leisch, F.: Fitting finite mixtures of linear regression models with varying & fixed effects in R. In: Rizzi, A., Vichi, M. (eds.) Compstat 2006 – Proceedings in Computational Statistics, pp. 853–860. Physica Verlag, Heidelberg, Germany (2006). MR2173118
Maiboroda, R., Sugakova, O.: Statistics of mixtures with varying concentrations with application to DNA microarray data analysis. J. Nonparametr. Stat. 24(1), 201–205 (2012). MR2885834. https://doi.org/10.1080/10485252.2011.630076
Maiboroda, R., Sugakova, O., Doronin, A.: Generalized estimating equations for mixtures with varying concentrations. Can. J. Stat. 41(2), 217–236 (2013). MR3061876. https://doi.org/10.1002/cjs.11170
Maiboroda, R., Sugakova, O.: Jackknife covariance matrix estimation for observations from mixture. Mod. Stoch. Theory Appl. 6(4), 495–513 (2019). MR4047396. https://doi.org/10.15559/19-vmsta145
Masiuk, S., Kukush, A., Shklyar, S., Chepurny, M., Likhtarov, I.: Radiation Risk Estimation: Based on Measurement Error Models. De Gruyter, Berlin, (2017). MR3726857
Miroshnichenko, V., Maiboroda, R.: Asymptotic normality of modified LS estimator for mixture of nonlinear regressions. Mod. Stoch. Theory Appl. 7(4), 435–448 (2020). MR4195645
Shao, J.: Consistency of least-squares estimator and its jackknife variance estimator in nonlinear models. Can. J. Stat. 20(4), 415–428 (1992). MR1208353. https://doi.org/10.2307/3315611
Shao, J., Tu, D.: The Jackknife and Bootstrap. Springer, (2012). MR1351010. https://doi.org/10.1007/978-1-4612-0795-5
Wang, L., Yu, F. Jackknife resample method for precision estimation of weighted total least squares. Commun. Stat., Simul. Comput. (2019). MR4253814. https://doi.org/10.1080/03610918.2019.1580727
Wang, L. Yu, F. Li, Z. Zou, C. Jackknife method for variance components estimation of partial EIV model. J. Surv. Eng. 146(4), (2020). https://doi.org/10.1061/(ASCE)SU.1943-5428.0000327
