1. Home
  2. Issues
  3. Volume 6, Issue 4 (2019)
  4. Jackknife covariance matrix estimation f ...

Modern Stochastics: Theory and Applications


Jackknife covariance matrix estimation for observations from mixture
Volume 6, Issue 4 (2019), pp. 495–513
Pub. online: 7 November 2019      Type: Research Article      Open accessOpen Access
Received
20 May 2019
Revised
7 September 2019
Accepted
14 October 2019
Published
7 November 2019

Abstract

A general jackknife estimator for the asymptotic covariance of moment estimators is considered in the case when the sample is taken from a mixture with varying concentrations of components. Consistency of the estimator is demonstrated. A fast algorithm for its calculation is described. The estimator is applied to construction of confidence sets for regression parameters in the linear regression with errors in variables. An application to sociological data analysis is considered.

References

[1] 
Borovkov, A.A.: Mathematical Statistics. Gordon and Breach Science Publishers, Amsterdam (1998). MR1712750
[2] 
Branham, R.: Total Least Squares in Astronomy. In: Total Least Squares and Errors-in-Variables Modeling, pp. 375–384. Springer, Dordrecht (2002). MR1952962. https://doi.org/10.1007/978-94-017-3552-0_33
[3] 
Cheng, C.-L., Van Ness, J.: Statistical Regression with Measurement Error, Kendall’s Library of Statistics 6. Arnold, London (1999). MR1719513
[4] 
Maiboroda, R.: Statistical analysis of mixtures. Kyiv University Publishers, Kyiv (in Ukrainian) (2003)
[5] 
Maiboroda, R., Sugakova, O.: Statistics of mixtures with varying concentrations with application to DNA microarray data analysis. J. Nonparametr. Stat. 24(1), 201–215 (2012). MR2885834. https://doi.org/10.1080/10485252.2011.630076
[6] 
Maiboroda, R., Navara, H., Sugakova, O.: Orthogonal regression for observations from mixtures. Teor. Imovir. Mat. Stat. 99, 152–167 (2018)
[7] 
Miroshnichenko V, M.R.: Confidence ellipsoids for regression coefficients by observations from a mixture. Mod. Stoch. Theory Appl. 5(2), 225–245 (2018). MR3813093. https://doi.org/10.15559/18-vmsta105
[8] 
Masiuk, S., Kukush, A., Shklyar, S., Chepurny, M., Likhtarov, I. (eds.): Radiation Risk Estimation: Based on Measurement Error Models, 2nd edn. de Gruyter series in Mathematics and Life Sciences, vol. 5. de Gruyter (2017). MR3726857
[9] 
McLachlan, G.J., Lee, S.X., Rathnayake, S.I.: Finite Mixture Models. Ann. Rev. Stat. Appl. 6, 355–378 (2019). MR3939525. https://doi.org/10.1146/annurev-statistics-031017-100325
[10] 
Petrov, V.: Limit theorems of probability theory: sequences of independent random variables. Clarendon Press
[11] 
Shao, J.: Mathematical statistics. Springer, New York (2007). MR2002723. https://doi.org/10.1007/b97553
[12] 
Shao, J., Tu, D.: The Jackknife and Bootstrap. Springer (2012). MR1351010. https://doi.org/10.1007/978-1-4612-0795-5
[13] 
Seber, G., Lee, A.: Linear regression analysis. Wiley (2003). MR1958247. https://doi.org/10.1002/9780471722199
[14] 
Therneau Terry, M., Grambsch Patricia, M.: Modeling Survival Data Extending the Cox Model. Springer (2000). MR1774977. https://doi.org/10.1007/978-1-4757-3294-8
[15] 
Wolter, K.: Introduction To Variance Estimation. Springer (2007). MR2288542

Full article Related articles Cited by PDF XML
Full article Related articles Cited by PDF XML

Copyright
© 2019 The Author(s). Published by VTeX
Open access article under the CC BY license.

Keywords
Finite mixture model orthogonal regression mixture with varying concentrations nonparametric estimation asymptotic covariance matrix estimation confidence ellipsoid jackknife errors-in-variables model

MSC2010
62J05 62G20

Metrics
since March 2018
754

Article info
views

640

Full article
views

418

PDF
downloads

173

XML
downloads


Share


RSS