Confidence ellipsoids for regression coefficients by observations from a mixture
Volume 5, Issue 2 (2018), pp. 225–245
Pub. online: 4 June 2018
Type: Research Article
Open Access
Open Access
Received
29 January 2018
29 January 2018
Revised
16 May 2018
16 May 2018
Accepted
19 May 2018
19 May 2018
Published
4 June 2018
4 June 2018
Abstract
Confidence ellipsoids for linear regression coefficients are constructed by observations from a mixture with varying concentrations. Two approaches are discussed. The first one is the nonparametric approach based on the weighted least squares technique. The second one is an approximate maximum likelihood estimation with application of the EM-algorithm for the estimates calculation.
References
Autin, F., Pouet, Ch.: Test on the components of mixture densities. Statistics & Risk Modeling 28(4), 389–410 (2011). MR2877572. https://doi.org/10.1524/strm.2011.1065
Benaglia, T., Chauveau, D., Hunter, D.R., mixtools, Y.D.S.: An R Package for Analyzing Finite Mixture Models. Journal of Statistical Software 32(6), 1–29 (2009). https://doi.org/10.18637/jss.v032.i06
Borovkov, A.A.: Mathematical statistics. Gordon and Breach Science Publishers, Amsterdam (1998). MR1712750
Faria, S.: Soromenhob Gilda Fitting mixtures of linear regressions. Journal of Statistical Computation and Simulation 80(2), 201–225 (2010). MR2757044. https://doi.org/10.1080/00949650802590261
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
Liubashenko, D., Maiboroda, R.: Linear regression by observations from mixture with varying concentrations. Modern Stochastics: Theory and Applications 2(4), 343–353 (2015). MR3456142. https://doi.org/10.15559/15-VMSTA41
Maiboroda, R., Kubaichuk, O.: Asymptotic normality of improved weighted empirical distribution functions. Theor. Probab. Math. Stat. 69, 95–102 (2004). MR2110908. https://doi.org/10.1090/S0094-9000-05-00617-4
Maiboroda, R., Sugakova, O.: Statistics of mixtures with varying concentrations with application to DNA microarray data analysis. Journal of nonparametric statistics. 24(1), 201–205 (2012). MR2885834. https://doi.org/10.1080/10485252.2011.630076
Maiboroda, R.E., Sugakova, O.V., Doronin, A.V.: Generalized estimating equations for mixtures with varying concentrations. The Canadian Journal of Statistics 41(2), 217–236 (2013). MR3061876. https://doi.org/10.1002/cjs.11170
Maiboroda, R., Sugakova, O.: Sampling bias correction in the model of mixtures with varying concentrations. Methodology and Computing in Applied Probability. 17(1) (2015). MR3306681. https://doi.org/10.1007/s11009-013-9349-4
McLachlan, G.: Krishnan Thriyambakam The EM Algorithm and Extensions, 2nd edn. Wiley, (2008). MR2392878. https://doi.org/10.1002/9780470191613
Seber, G.A.F., Lee, A.J.: Linear Regression Analysys. Wiley, (2003). MR1958247. https://doi.org/10.1002/9780471722199
Shao, J.: Mathematical statistics. Springer, New York (1998). MR1670883
Titterington, D.M., Smith, A.F., Makov, U.E.: Analysis of Finite Mixture Distributions. Wiley, New York (1985). MR0838090
