Linear regression by observations from mixture with varying concentrations

Liubashenko, Daryna; Maiboroda, Rostyslav

doi:10.15559/15-VMSTA41

Modern Stochastics: Theory and Applications

Linear regression by observations from mixture with varying concentrations

Volume 2, Issue 4 (2015), pp. 343–353

Daryna Liubashenko Rostyslav Maiboroda

https://doi.org/10.15559/15-VMSTA41

Pub. online: 4 December 2015 Type: Research Article

Open Access

Received
20 October 2015

Revised
22 November 2015

Accepted
26 November 2015

Published
4 December 2015

Abstract

We consider a finite mixture model with varying mixing probabilities. Linear regression models are assumed for observed variables with coefficients depending on the mixture component the observed subject belongs to. A modification of the least-squares estimator is proposed for estimation of the regression coefficients. Consistency and asymptotic normality of the estimates is demonstrated.

References

[1]

Autin, F., Pouet, Ch.: Test on the components of mixture densities. Stat. Risk. Model. 28(4), 389–410 (2011). MR2877572. doi:10.1524/strm.2011.1065

[2]

Billingsley, P.: Probability and Measure, 3rd edn. Wiley, New York (1995). MR1324786

[3]

Borovkov, A.A.: Mathematical Statistics. Gordon and Breach Science Publishers, Amsterdam (1998). MR1712750

[4]

Doronin, O.V.: Lower bound for a dispersion matrix for the semiparametric estimation in a model of mixtures. Theory Probab. Math. Stat. 90, 71–85 (2015). MR3241861. doi:10.1090/tpms/950

[5]

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)

[6]

Maiboroda, R.: Statistical Analysis of Mixtures. Kyiv University Publishers, Kyiv (2003) (in Ukrainian)

[7]

Maiboroda, R.E., Sugakova, O.V.: Estimation and classification by observations from mixture. Kyiv University Publishers, Kyiv (2008) (in Ukrainian)

[8]

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. doi:10.1080/10485252.2011.630076

[9]

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. doi:10.1002/cjs.11170

[10]

McLachlan, G.J., Peel, D.: Finite Mixture Models. Wiley–Interscience, New York (2000). MR1789474. doi:10.1002/0471721182

[11]

Seber, G.A.F., Lee, A.J.: Linear Regression Analysis. Wiley, New York (2003). MR1958247. doi:10.1002/9780471722199

[12]

Shcherbina, A.: Estimation of the mean value in the model of mixtures with varying concentrations. Theory Probab. Math. Stat. 84, 151–164 (2012). MR2857425. doi:10.1090/S0094-9000-2012-00866-1

[13]

Titterington, D.M., Smith, A.F., Makov, U.E.: Analysis of Finite Mixture Distributions. Wiley, New York (1985)

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Keywords

Finite mixture model linear regression mixture with varying concentrations nonparametric estimation asymptotic normality consistency

MSC2010

62J05 62G20

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