Complete f-moment convergence for arrays of random variables and its applications in semiparametric and EV regression models

• Autorzy: He Yongping , Shen Yan , Wang Rui , Wang Xuejun

Identyfikatory

DOI

10.37190/0208-4147.00174

• Języki publikacji: EN

Abstrakty

EN

We study the complete f-moment convergence for arrays of rowwise random variables satisfying a Rosenthal type moment inequality, and then establish general results on the complete moment convergence and complete convergence for partial sums and weighted sums of arrays of rowwise random variables. As applications, we further describe the statistical properties of complete f-moment convergence in both semiparametric regression models and simple linear errors-in-variables models. The asymptotic properties for estimators are established. We also provide some simulations to verify the validity of the theoretical results.

Słowa kluczowe

EN

complete convergence; complete f-moment convergence; strong consistency; emiparametric regression models; simple linear errors-in-variables models

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2024
• Tom: Vol. 44, Fasc. 1
• Strony: 87--118
• Opis fizyczny: Bibliogr. 45 poz., wykr.

Twórcy

autor

He Yongping

• School of Automation Beijing Institute of Technology Beijing 100081, P.R. China
• School of Big Data and Statistics Anhui University Hefei 230601, P.R. China

autor

Shen Yan

• School of Big Data and Statistics Anhui University Hefei 230601, P.R. China

autor

Wang Rui

• School of Big Data and Statistics Anhui University Hefei 230601, P.R. China

autor

Wang Xuejun

• School of Big Data and Statistics Anhui University Hefei 230601, P.R. China

Bibliografia

• 1.A. Adler and A. Rosalsky (1987), Some general strong laws for weighted sums of stochasticall dominated random variables, Stochastic Anal. Appl. 5, 1-16.
• 2. A. Adler, A. Rosalsky and R. L. Taylor (1989), Strong laws of large numbers for weighted sums of random elements in normed linear spaces, Int. J. Math. Math. Sci. 12, 507-529.
• 3.J. I. Baek and H. Y. Liang (2006), Asymptotics of estimators in semi-parametric model under NA samples, J. Statist. Planning Inference 136, 3362-3382.
• 4. L. E. Baum and M. Katz (1965), Convergence rate in the law of large numbers, Trans. Amer. Math. Soc. 120, 108-123.
• 5.M. Chang and Y. Miao (2023), Weak law of large numbers and complete convergence for general dependent sequences, Acta Math. Hungar. 169, 469-388.
• 6.P. Y. Chen, L. Wen and S. H. Sung (2020), Strong and weak consistency of least squares estimators in simple linear EV regression models, J. Statist. Planning Inference 205, 64-73.
• 7.Y. S. Chow (1988), On the rate of moment convergence of sample sums and extremes, Bull. Inst. Math. Acad. Sinica 16, 177-201.
• 8.A. Deaton (1985), Panel data from time series of cross-sections, J. Econometrics 30, 109-126.
• 9.X. Deng and X. J. Wang (2017), Equivalent conditions of complete moment convergence and complete integral convergence for NOD sequences, Bull. Korean Math. Soc. 54, 917-933.
• 10.X. Deng, X. J. Wang, S. H. Hu and M. Hu (2019), A general result on complete convergence for weighted sums of linear processes and its statistical applications, Statistics 53, 903-920.
• 11.E. A. Duran, W. K. H¨ardle and M. Osipenko (2012), Difference based ridge and Liu type estimators in semiparametric regression models, J. Multivariate Anal. 105, 164-175.
• 12.R. F. Engle, C. W. J. Granger and R. A. Weiss (1986), Semiparametric estimates of the relations between weather and electricity sales, J. Amer. Statist. Assoc. 81, 310-320.
• 13.P. Erd˝os (1949), On a theorem of Hsu and Robbins, Ann. Math. Statist. 20, 286-291.
• 14.G. L. Fan, H. Y. Liang, J. F. Wang and H. X. Xu (2010), Asymptotic properties for LS estimators in EV regression model with dependent errors, Adv. Statist. Anal. 94, 89-103.
• 15.P. L. Hsu and H. Robbins (1947), Complete convergence and the law of large numbers, Proc. Nat. Acad. Sci. USA 33, 25-31.
• 16.S. H. Hu (2006), Fixed-design semiparametric regression for linear time series, Acta Math. Sci. Ser. B 26, 74-82.
• 17.D. Hu, P. Y. Chen and S. H. Sung (2017), Strong laws for weighted sums of ψ-mixing random variables and applications in errors-in-variables regression models, TEST 26, 600-617.
• 18.K. Joag-Dev and F. Proschan (1983), Negative association of random variables with applications, Ann. Statist. 11, 286-295.
• 19.B. A. Johnson, D. Y. Lin and D. Zeng (2008), Penalized estimating functions and variable selection in semiparametric regression models, J. Amer. Statist. Assoc. 103, 672-680.
• 20.M. H. Ko (2017), The complete moment convergence for CNA random vectors in Hilbert spaces, J. Inequalities Appl. 2017, art. 290, 11 pp.
• 21.J. J. Lang, J. B. Qi, F. Zhang and X. J Wang (2023), Complete f -moment convergence for weighted sums of asymptotically almost negatively associated random variables and its application in semiparametric regression models, Stochastics 95, 1510-1535.
• 22.L. X. Li, X. J. Wang and C. Yi (2024), Complete f -moment convergence for a class of random variables with related statistical applications, Stochastic Models 40, 375-398.
• 23.Y. X. Li and L. X. Zhang (2004), Complete moment convergence of moving average processes under dependence assumptions, Statist. Probab. Lett. 70, 191-197.
• 24.J. X. Liu and X. R. Chen (2005), Consistency of LS estimator in simple linear EV regression models, Acta Math. Sci. Ser. B 25, 50-58.
• 25.Y. Miao, J. Shi and Z. Yu (2022), On the complete convergence and strong law for dependent random variables with general moment conditions, Acta Math. Hungar. 168, 425-442.
• 26.Y. Miao, K. Wang and F. F. Zhao (2011), Some limit behaviors for the LS estimator in simple linear EV regression models, Statist. Probab. Lett. 81, 92-102.
• 27.G. M. Pan, S. H. Hu, L. B. Fang and Z. D. Cheng (2003), Mean consistency for a semiparametric regression model, Acta Math. Sci. Ser. A 23, 598-606.
• 28.V. V. Petrov (1995), Limit Theorems of Probability Theory: Sequences of Independent Random Variables, Oxford Univ. Press, New York.
• 29.D. H. Qiu and P. Y. Chen (2014), Complete and complete moment convergence for weighted sums of widely orthant dependent random variables, Acta Math. Sinica English Ser. 30, 1539-1548.
• 30.D. H. Qiu, P. Y. Chen and J. Xiao (2017), Complete moment convergence for sequences of END random variables, Acta Math. Appl. Sinica Chinese Ser. 40, 436-448.
• 31.D. H. Qiu, H. Urmeneta and A. Volodin (2014), Complete moment convergence for weighted sums of sequences of independent random elements in Banach spaces, Collect. Math. 65, 155-167.
• 32.J. L. D. Silva (2020), On the convergence of series of moments for row sums of random variables, Filomat 34, 1875-1888.
• 33.S. H. Sung (2009), Moment inequdities and complete moment convergence, J. Inequalities Appl. 2009, art. 271265, 14 pp.
• 34.S. H. Sung (2010), Complete convergence for weighted sums of ρ∗−mixing random variables, Discrete Dynamics Nature Soc. 2010, art 630608, 13 pp.
• 35.X. F. Tang, M. M. Xi, W. Y. Chen, Y. Wu and X. J. Wang (2017), Complete moment convergence for arrays of rowwise NA random variables, Appl. Math. Ser. A 32, 66-78.
• 36.M. M. Wang, M. Wang, X. J. Wang and F. Zhang (2023a), Complete f -moment convergence for arrays of rowwise m-negatively associated random variables and its statistical applications, Stochastic Models 39, 632-661.
• 37.X. J. Wang, X. Chen, T. C. Hu and A. Volodin (2023b), Complete f -moment convergence for masymptotic negatively associated random variables and related statistical applications, J. Non-parametric Statist. (online), 29 pp.
• 38.X. J. Wang, X. Deng, L. L. Zheng and S. H. Hu (2014), Complete convergence for arrays of rowwise negatively superadditive dependent random variables and its applications, Statistics 48, 834-850.
• 39.X. J. Wang and S. H. Hu (2014), Complete convergence and complete moment convergence for martingale difference sequence, Acta Math. Sinica English Ser. 30, 119-132.
• 40.Y. Wu, X. J. Wang, T. C. Hu and A. Volodin (2019), Complete f -moment convergence for extended negatively dependent random variables, RACSAM 113, 333-351.
• 41.Y. F. Wu, M. O. Cabrea and A. Volodin (2014), Complete convergence and complete moment convergence for arrays of rowwise END random variables, Glasnik Mat. 49, 449-468.
• 42.W. Z. Yang, Y. W. Wang, X. H. Wang and S. H. Hu (2013), Complete moment convergence for randomly weighted sums of martingale differences, J. Inequalities Appl. 2013, art. 396, 13 pp.
• 43.S. P. Zheng, F. Zhang, C. H. Wang and X. J. Wang (2024), A general result on complete f -moment convergence with its application to nonparametric regression models, Stochastic Models 40, 123-151.
• 44.H. L. Zhou, C. Lu and X. J. Wang (2023a), Complete f -moment convergence for sums of asymptotically almost negatively associated random variables with statistical applications, Stochastics (online), 25 pp.118 Y. He et al.
• 45.J. Y. Zhou, J. G. Yan and F. Du (2023b), Complete and complete f -moment convergence for arrays of rowwise END random variables and some applications, Sankhya 85, 1307-1330.