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Keywords:
errors-in-variables regression model; least squares estimator; widely orthant dependent; strong consistency
Summary:
The strong convergence for weighted sums of widely orthant dependent (WOD) random variables is investigated. As an application, we further investigate the strong consistency of the least squares estimator in EV regression model for WOD random variables. A simulation study is carried out to confirm the theoretical results.
References:
[1] Allen, R. G. D.: The assumptions of linear regression. Economica 6 (1939), 191-201. DOI 10.2307/2548931
[2] Carroll, R. J., Ruppert, D., Stefanski, L. A.: Measurement Error in Nonlinear Models. Monographs on Statistics and Applied Probability 63. Chapman & Hall, London (1995). DOI 10.1201/9781420010138 | MR 1630517 | Zbl 0853.62048
[3] Chen, P., Wen, L., Sung, S. H.: Strong and weak consistency of least squares estimators in simple linear EV regression models. J. Stat. Plann. Inference 205 (2020), 64-73. DOI 10.1016/j.jspi.2019.06.004 | MR 4011623 | Zbl 1437.62103
[4] Chen, W., Wang, Y., Cheng, D.: An inequality of widely dependent random variables and its applications. Lith. Math. J. 56 (2016), 16-31. DOI 10.1007/s10986-016-9301-8 | MR 3472103 | Zbl 1385.60040
[5] Choi, B. D., Sung, S. H.: Almost sure convergence theorems of weighted sums of random variables. Stochastic Anal. Appl. 5 (1987), 365-377. DOI 10.1080/07362998708809124 | MR 0912863 | Zbl 0633.60049
[6] Cui, H.: Asymptotic normality of $M$-estimates in the EV model. Syst. Sci. Math. Sci. 10 (1997), 225-236. MR 1469182 | Zbl 0905.62072
[7] Deaton, A.: Panel data from time series of cross-sections. J. Econom. 30 (1985), 109-126. DOI 10.1016/0304-4076(85)90134-4 | Zbl 0584.62193
[8] Deng, X., Tang, X.-F., Wang, S.-J., Wang, X.-J.: On the strong convergence properties for weighted sums of negatively orthant dependent random variables. Appl. Math., Ser. B (Engl. Ed.) 33 (2018), 35-47. DOI 10.1007/s11766-018-3423-1 | MR 3779102 | Zbl 1399.60082
[9] Fazekas, I., Kukush, A. G.: Asymptotic properties of an estimator in nonlinear functional errors-in-variables models with dependent error terms. Comput. Math. Appl. 34 (1997), 23-39. DOI 10.1016/S0898-1221(97)00204-6 | MR 1487730 | Zbl 0911.62054
[10] Fuller, W. A.: Measurement Error Models. Wiley Series in Probability and Mathematical Statistics. John Wiley & Sons, New York (1987). DOI 10.1002/9780470316665 | MR 0898653 | Zbl 0800.62413
[11] Hu, T.: Negatively superadditive dependence of random variables with applications. Chin. J. Appl. Probab. Stat. 16 (2000), 133-144. MR 1812714 | Zbl 1050.60502
[12] Joag-Dev, K., Proschan, F.: Negative association of random variables with applications. Ann. Stat. 11 (1983), 286-295. DOI 10.1214/aos/1176346079 | MR 0684886 | Zbl 0508.62041
[13] Miao, Y., Yang, G., Shen, L.: The central limit theorem for LS estimator in simple linear EV regression models. Commun. Stat., Theory Methods 36 (2007), 2263-2272. DOI 10.1080/03610920701215266 | MR 2396557 | Zbl 1183.62039
[14] Miao, Y., Zhao, F., Wang, K., Chen, Y.: Asymptotic normality and strong consistency of LS estimators in the EV regression model with NA errors. Stat. Pap. 54 (2013), 193-206. DOI 10.1007/s00362-011-0418-x | MR 3016962 | Zbl 1256.62013
[15] Shen, A.: Bernstein-type inequality for widely dependent sequence and its application to nonparametric regression models. Abstr. Appl. Anal. 2013 (2013), Article ID 862602, 9 pages. DOI 10.1155/2013/862602 | MR 3081600 | Zbl 1470.62056
[16] Shen, A., Yao, M., Wang, W., Volodin, A.: Exponential probability inequalities for WNOD random variables and their applications. Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat., RACSAM 110 (2016), 251-268. DOI 10.1007/s13398-015-0233-7 | MR 3462086 | Zbl 1334.60040
[17] Sung, S. H.: Almost sure convergence for weighted sums of i.i.d. random variables. II. Bull. Korean Math. Soc. 33 (1996), 419-425. MR 1419389 | Zbl 0865.60021
[18] Teicher, H.: Almost certain convergence in double arrays. Z. Wahrscheinlichkeitstheor. Verw. Geb. 69 (1985), 331-345. DOI 10.1007/BF00532738 | MR 0787602 | Zbl 0548.60028
[19] Wang, K., Wang, Y., Gao, Q.: Uniform asymptotics for the finite-time ruin probability of a new dependent risk model with a constant interest rate. Methodol. Comput. Appl. Probab. 15 (2013), 109-124. DOI 10.1007/s11009-011-9226-y | MR 3030214 | Zbl 1263.91027
[20] Wang, X., Wu, Y., Hu, S.: Strong and weak consistency of LS estimators in the EV regression model with negatively superadditive-dependent errors. AStA, Adv. Stat. Anal. 102 (2018), 41-65. DOI 10.1007/s10182-016-0286-8 | MR 3749656 | Zbl 1421.62023
[21] Wang, X., Xu, C., Hu, T.-C., Volodin, A., Hu, S.: On complete convergence for widely orthant-dependent random variables and its applications in nonparametric regression models. TEST 23 (2014), 607-629. DOI 10.1007/s11749-014-0365-7 | MR 3252097 | Zbl 1307.60024
[22] Wang, Y., Cheng, D.: Basic renewal theorems for random walks with widely dependent increments. J. Math. Anal. Appl. 384 (2011), 597-606. DOI 10.1016/j.jmaa.2011.06.010 | MR 2825210 | Zbl 1230.60095
[23] Wang, Y., Cui, Z., Wang, K., Ma, X.: Uniform asymptotics of the finite-time ruin probability for all times. J. Math. Anal. Appl. 390 (2012), 208-223. DOI 10.1016/j.jmaa.2012.01.025 | MR 2885767 | Zbl 1237.91139
[24] Wang, Y., Wang, X.: Complete $f$-moment convergence for Sung's type weighted sums and its application to the EV regression models. Stat. Pap. 62 (2021), 769-793. DOI 10.1007/s00362-019-01112-z | MR 4232917 | Zbl 1482.60049
[25] Wu, Q. Y.: Probability Limit Theory for Mixing Sequences. Science Press of China, Beijing (2006).
[26] Xi, M., Wang, R., Cheng, Z., Wang, X.: Some convergence properties for partial sums of widely orthant dependent random variables and their statistical applications. Stat. Pap. 61 (2020), 1663-1684. DOI 10.1007/s00362-018-0996-y | MR 4127491 | Zbl 1453.60081
[27] Xu, S., Miao, Y.: Almost sure convergence of weighted sums for negatively associated random variables. Commun. Stat., Theory Methods 43 (2014), 2581-2594. DOI 10.1080/03610926.2013.841921 | MR 3217835 | Zbl 1316.60043
[28] Yi, Y., Chen, P., Sung, S. H.: Strong laws for weighted sums of random variables satisfying generalized Rosenthal type inequalities. J. Inequal. Appl. 2020 (2020), Article ID 43, 8 pages. DOI 10.1186/s13660-020-02311-1 | MR 4066646 | Zbl 1503.60040
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