Two-step estimation in heteroscedastic linear regression model
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 17 (2017) no. 2, pp. 39-51 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study the problem of estimating a parameter in some linear heteroscedastic regression model in the case where the regressors consist of all order statistics based on the sample of identically distributed not necessarily independent observations with finite second moment. It is assumed that the random errors depend on the parameter and distributions of the corresponding regressors. We propose a two-step procedure for finding explicit asymptotically normal estimates.
Keywords: linear regression, order statistics, heteroscedastic, asymptotic normality, $\varphi$-mixing, two-step estimators.
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Yu. Yu. Linke. Two-step estimation in heteroscedastic linear regression model. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 17 (2017) no. 2, pp. 39-51. http://geodesic.mathdoc.fr/item/VNGU_2017_17_2_a3/

[1] Heyde C. C., Quasi-Likelihood and its Application: A General Approach to Optimal Parameter Estimation, Springer, 1997 | MR | Zbl

[2] Dette H., Holland-Letz T., “A Geometric Characterization of $c$-Optimal Designs for Heteroscedastic Regression”, Ann. Statist., 37 (2009), 4088–4103 | DOI | MR | Zbl

[3] Brown L. D., Levine M., “Variance Estimation in Nonparametric Regression via the Difference Sequence Method”, Ann. Statist., 35:5 (2007), 2219–2232 | DOI | MR | Zbl

[4] Wang L., Brown L. D., Cai T. T., Levine M., “Effect of Mean on Variance Function Estimation in Nonparametric Regression”, Ann. Statist., 36:2 (2008), 646–664 | DOI | MR | Zbl

[5] Seber G., Lee A., Linear Regression Analysis, Wiley, 2003 | MR | Zbl

[6] Carrol R. J., Ruppert D., “A Comparison Between Maximum Likelihood and Generalized Least Squares in Heteroscedastic Linear Model”, J. Amer. Stat. Assoc., 77 (1982), 878–882 | DOI | MR | Zbl

[7] Yu. Yu. Linke, A. I. Sakhanenko, “Asymptotically optimal estimation in the linear regression problem in the case of violation of some classical assumptions”, Sib. Math. J., 2:2 (2009), 302–315 | DOI | MR | Zbl

[8] I. S. Borisov, “Stability of the partial sum process of residuals in a multiple linear regression model”, SEMR, 10 (2013), 727–732 (Russian, English abstract)

[9] Hoeffding W., “On the Distribution of the Expected Values of the Order Statistics”, Ann. Math. Statist., 24:1 (1953), 93–100 | DOI | MR | Zbl

[10] I. S. Borisov, “On the sum of the variances of the order statistics for samples of dependent observations”, SEMR, 11 (2014), 857–862 (Russian, English abstract)

[11] Yu. Yu. Linke, “On the asymptotics of distributions of two-step statistical estimates”, Sib. Math. J., 52:4 (2011), 665–681 | DOI | MR | Zbl

[12] Yu. Yu. Linke, A. I. Sakhanenko, “On asymptotics of the distribution of a two-step statistical estimator of a one-dimensional parameter”, SEMR, 10 (2013), 627–640 (Russian, English abstract) | Zbl

[13] Hajek J., Sidak Z., Theory of Rank Tests, Academic Press, 1967 | MR | Zbl

[14] Petrov V. V., Sums of Independent Random Variables, Springer-Verlag, 1975 | MR | Zbl

[15] S. A. Utev, “Sums of random variables under the $\varphi$-mixing”, Asymptotic Analysis of the Distributions of Stochastic Processes, Nauka, Novosibirsk, 1989 (in Russian)