Complete f-moment convergence of moving average process and its application to nonparametric regression models

• Autorzy: Yao Chi , Wang Rui , Chen Ling , Wang Xueyun

Identyfikatory

DOI

10.37190/0208-4147.41.2.10

• Języki publikacji: EN

Abstrakty

EN

In this paper, we establish a general result on complete f-moment convergence of the moving average process based on widely orthant dependent random variables, which generalizes some results in the literature. In addition, an application of complete consistency to nonparametric regression models is provided. Finally, we provide a numerical simulation to verify the validity of our theoretical results.

Słowa kluczowe

EN

complete f-moment convergence; orthant dependent random variables; nonparametric regression models; complete consistency

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2021
• Tom: Vol. 41, Fasc. 2
• Strony: 373--395
• Opis fizyczny: Bibliogr. 30 poz.

Twórcy

autor

Yao Chi

• School of Mathematical Sciences, Anhui University, 230601 Hefei, China

autor

Wang Rui

• School of Mathematical Sciences, Anhui University, 230601 Hefei, China

autor

Chen Ling

• School of Mathematical Sciences, Anhui University, 230601 Hefei, China

autor

Wang Xueyun

• School of Mathematical Sciences, Anhui University, 230601 Hefei, China

Bibliografia

• [1] A. Adler and A. Rosalsky, Some general strong laws for weighted sums of stochastically dominated random variables, Stoch. Anal. Appl. 5 (1987), 1-16.
• [2] A. Adler, A. Rosalsky and R. L. Taylor, Strong laws of large numbers for weighted sums of random elements in normed linear spaces, Int. J. Math. Math. Sci. 12 (1989), 507-529.
• [3] J. I. Baek, T. S. Kim and H. Y. Liang, On the convergence of moving average processes under dependent conditions, Austral. N. Zeal. J. Statist. 45 (2003), 331-342.
• [4] R. M. Burton and H. Dehling, Large deviations for some weakly dependent random processes, Statist. Probab. Lett. 9 (1990), 397-401.
• [5] Y. S. Chow, On the rate of moment convergence of sample sums and extremes, Bull. Inst. Math. Acad. Sinica 16 (1998), 177-201.
• [6] X. Deng and X. J. Wang, An exponential inequality and its application to M estimators in multiple linear models, Statist. Papers 61 (2020), 1607-1627.
• [7] A. A. Georgiev, Local properties of function fitting estimates with applications to system identification, Math. Statist. Appl. B (1983), 141-151.
• [8] J. L. Horowitz and S. Lee, Nonparametric instrumental variables estimation of a quantile regression model, Econometrica 75 (2007), 1191-1208.
• [9] P. L. Hsu and H. Robbins, Complete convergence and the law of large numbers, Proc. Nat. Acad. Sci. U.S.A. 33 (1947), 25-31.
• [10] I. A. Ibragimov, Some limit theorems for stationary processes, Theor. Probab. Appl. 7 (1962), 349-382.
• [11] T. S. Kim, M. H. Ko and Y. K. Choi, Complete moment convergence of moving average processes with dependent innovations, J. Korean Math. Soc. 45 (2008), 355-365.
• [12] D. Li, M. B. Rao and X. Wang, Complete convergence of moving average processes, Statist. Probab. Lett. 14 (1992), 111-114.
• [13] C. Lu, Z. Chen and X. J. Wang, Complete f-moment convergence for widely orthant dependent random variables and its application in nonparametric models, Acta Math. Sci. 35 (2019), 1917-1936.
• [14] D. H. Qiu and P. Y. Chen, Complete and complete moment convergence for weighted sums of widely orthant dependent random variables, Acta Math. Sci. 30 (2014), 1539-1548.
• [15] D. H. Qiu and P. Y. Chen, Convergence for moving average processes under END set-up, Acta Math. Sci. 35 (2015), 756-768.
• [16] D. H. Qiu and J. Xiao, Complete moment convergence for Sung’s type weighted sums under END set-up, Acta Math. Sci. 38 (2018), 1103-1111.
• [17] G. G. Roussas, L. T. Tran and D. A. Ioannides, Fixed design regression for time series: asymptotic normality, J. Multivariate Anal. 40 (1992), 262-291.
• [18] A. T. Shen and C. Q. Wu, Complete q-th moment convergence and its statistical applications, RACSAM 144 (2020), 1-25.
• [19] C. J. Stone, Consistent nonparametric regression regression, Ann. Statist. 5 (1977), 595-620.
• [20] W. F. Stout, Almost Sure Convergence, Probab. Math. Statist. 24, Academic Press, New York, 1974.
• [21] L. Tran, G. Roussas and S. Y. T. Van, Fixed-design regression for linear time series, Ann. Statist. 24 (1996), 975-991.
• [22] K. Y. Wang, Y. B. Wang and Q. W. Gao, Uniform asymptotics for the finite-time ruin probability of a new dependent risk model with a constant interest rate, Methodol. Comput. Appl. 15 (2013), 109-124.
• [23] X. J. Wang, X. Deng, L. L. Zheng and S. H. Hu, Complete convergence for arrays of rowwise negatively superadditive-dependent random variables and its applications, Statistics 48 (2014), 834-850.
• [24] X. J. Wang and S. H. Hu, The consistency of the nearest neighbor estimator of the density function based on WOD samples, J. Math. Anal. Appl. 429 (2015), 497-512.
• [25] X. J. Wang, C. Xu, T. C. Hu, A. Volodin and S. H. Hu, On complete convergence for widely orthant dependent random variables and its applications in nonparametric regression models, Test 23 (2014), 607-629.
• [26] Y. Wu, X. J. Wang, T. C. Hu and A. Volodin, Complete f-moment convergence for extended negatively dependent random variables, RACSAM 113 (2019), 333-351.
• [27] Y. Wu, X. J. Wang and S. H. Hu, Complete moment convergence for weighted sums of weakly dependent random variables and its application in nonparametric regression model, Statist. Probab. Lett. 127 (2017), 56-66.
• [28] Y. Wu, X. J. Wang and A. Rosalsky, Complete moment convergence for arrays of rowwise widely orthant dependent random variables, Acta Math. Sci. 34 (2018), 1531-1548.
• [29] M. M. Xi, R. Wang, Z. Y. Cheng and X. J. Wang, Some convergence properties for partial sums of widely orthant dependent random variables and their statistical applications, Statist. Papers 1 (2018), 1-22.
• [30] W. Z. Yang, H. Y. Xu, L. Chen and S. H. Hu, Complete consistency of estimators for regression models based on extended negatively dependent errors, Statist. Papers 59 (2018), 449-465.