1. Home
  2. Issues
  3. Volume 7, Issue 4 (2020)
  4. Asymptotic normality of modified LS esti ...

Modern Stochastics: Theory and Applications


Asymptotic normality of modified LS estimator for mixture of nonlinear regressions
Volume 7, Issue 4 (2020), pp. 435–448
Pub. online: 8 December 2020      Type: Research Article      Open accessOpen Access
Received
21 August 2020
Revised
8 November 2020
Accepted
16 November 2020
Published
8 December 2020

Abstract

We consider a mixture with varying concentrations in which each component is described by a nonlinear regression model. A modified least squares estimator is used to estimate the regressions parameters. Asymptotic normality of the derived estimators is demonstrated. This result is applied to confidence sets construction. Performance of the confidence sets is assessed by simulations.

References

[1] 
Autin, F., Pouet, Ch.: Test on the components of mixture densities. Stat. Risk. Model. 28(4), 389–410 (2011). MR2877572. https://doi.org/10.1524/strm.2011.1065
[2] 
Benaglia, T., Chauveau, D., Hunter, D.R., Young, D.S.: mixtools: An R Package for Analyzing Finite Mixture Models. J. Stat. Softw. 32(6), 1–29 (2009)
[3] 
Borovkov, A.A.: Mathematical statistics. Gordon and Breach Science Publishers, Amsterdam (1998). MR1712750
[4] 
Faria, S., Soromenho, G.: Fitting mixtures of linear regressions. J. Stat. Comput. Simul. 80(2), 201–225 (2010). https://doi.org/10.1080/00949650802590261
[5] 
Grün, B., Friedrich, L.: 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
[6] 
Liubashenko, D., Maiboroda, R.: Linear regression by observations from mixture with varying concentrations. Mod. Stoch. Theory Appl. 2(4), 343–353 (2015). MR3456142. https://doi.org/10.15559/15-VMSTA41
[7] 
Maiboroda, R.: Statistical analysis of mixtures. Kyiv University Publishers, Kyiv (2003). (in Ukrainian)
[8] 
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
[9] 
Miroshnichenko, V.O.: Generalized least squares estimates for mixture of nonlinear regressions. Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics & Mathematics 219(5).
[10] 
Maiboroda, R., Kubaichuk, O.: Asymptotic normality of improved weighted empirical distribution functions. Theory Probab. Math. Stat. 69, 95–102 (2004). MR2110908. https://doi.org/10.1090/S0094-9000-05-00617-4
[11] 
Maiboroda, R.E., Sugakova, O.V.: Estimation and classification by observations from mixture. Kuiv University Publishers, Kyiv (2008). (in Ukrainian)
[12] 
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
[13] 
Maiboroda, R.E., Sugakova, O.V., Doronin, A.V.: Generalized estimating equations for mixtures with varying concentrations. Can. J. Stat. 41(2), 217–236 (2013). MR3061876. https://doi.org/10.1002/cjs.11170
[14] 
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 (2017). MR3726857
[15] 
McLachlan, G., Krishnan, T.: The EM Algorithm and Extensions, 2nd edn. Wiley (2008). MR2392878. https://doi.org/10.1002/9780470191613
[16] 
Seber, G.A.F., Wild, C.J.: Nonlinear Regression. Wiley (2003). MR0986070. https://doi.org/10.1002/0471725315
[17] 
Shao, J.: Mathematical statistics. Springer, New York (1998). MR1670883
[18] 
Shao, J., Tu, D.: The Jackknife and Bootstrap. Springer, NY (1995). MR1351010. https://doi.org/10.1007/978-1-4612-0795-5
[19] 
Titterington, D.M., Smith, A.F., Makov, U.E.: Analysis of Finite Mixture Distributions. Wiley, New York (1985). MR0838090

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

Copyright
© 2020 The Author(s). Published by VTeX
Open access article under the CC BY license.

Keywords
Finite mixture model nonlinear regression mixture with varying concentrations semiparametric estimation confidence ellipsoid

MSC2010
62J05 62G20

Metrics
since March 2018
387

Article info
views

 493

Full article
views
379

PDF
downloads

 130

XML
downloads


Share


RSS