References
- Cuzick J. A strong law for weighted sums of i.i.d. random variables. J Theor Probab. 1995;8(3):625–641.
- Bai ZD, Cheng PE. Marcinkiewicz strong laws for linear statistics. Stat Probab Lett. 2000;46:105–112.
- Wu QY. A strong limit theorem for weighted sums of sequences of negatively dependent random variables. J Inequal Appl. 2010;2010:Article ID 383805.
- Huang HW, Wang DC, Peng JY. On the strong law of large numbers for weighted sums of φ-mixing random variables. J Math Inequal. 2014;8:465–473.
- Hu D, Chen PY, Sung SH. Strong laws for weighted sums of ψ-mixing random variables and applications in errors-in-variables regression models. TEST. 2017;26:600–617.
- Wu Y, Wang XJ, Hu SH, et al. Weighted version of strong law of large numbers for a class of random variables and its applications. TEST. 2018;27:379–406.
- Yi YC, Chen PY, Sung SH. Strong laws for weighted sums of random variables satisfying generalized Rosenthal type inequalities. J Inequal Appl. 2020;2020:Article ID 43.
- Chen PY, Sung SH. A Marcinkiewicz–Zygmund type strong law for weighted sums of φ-mixing random variables and its application. J Math Anal Appl. 2022;505(1):Article ID 125572.
- Fama EF. The behaviour of stock market prices. J Bus. 1965;38(1):34–105.
- Stuck BW, Kleine B. A statistical analysis of telephone noise. Bell Syst Tech J. 1974;53:1263–1320.
- Stuck BW. Minimum error dispersion linear filtering of scalar symmetric stable processes. IEEE Trans Autom Control. 1978;23(3):507–509.
- Safiullin NZ, Chabdarov SM. Transformation of non-Gaussian random processes by radio devices. Telecommun Radio Eng. 1978;32:114–116.
- DuMouchel WH. Estimating the stable index a in order to measure tail thickness. Ann Stat. 1983;11:1019–1031.
- Davis RA, Knight K, Liu J. M-estimation for auto-regressions with infinite variance. Stoch Process Their Appl. 1992;40:145–180.
- Mikosch T, Gadrich T, Klüppelberg C, et al. Parameter estimation for ARMA models with infinite variance innovations. Ann Stat. 1995;23:305–326.
- Kokoszka PS, Taqqu MS. Parameter estimation for infinite variance fractional ARIMA. Ann Stat. 1996;24:1880–1913.
- Szewczak ZS. Marcinkiewicz laws with infinite moments. Acta Math Hungar. 2010;127(1–2):64–84.
- Chen Z, Li RZ, Wu YH. Weighted quantile regression for AR model with infinite variance errors. J Nonparametr Stat. 2012;24(3):715–731.
- Nakata T. Weak laws of large numbers for weighted independent random variables with infinite mean. Stat Probab Lett. 2016;109:124–129.
- Dung LV, Son TC, Hai Yen NT. Weak laws of large numbers for sequences of random variables with infinite rth moments. Acta Math Hungar. 2018;156:408–423.
- Wang KY, Wang YB, Gao QW. Uniform asymptotics for the finite-time ruin probability of a new dependent risk model with a constant interest rate. Methodol Comput Appl Probab. 2013;15:109–124.
- Liu L. Precise large deviations for dependent random variables with heavy tails. Stat Probab Lett. 2009;79:1290–1298.
- Lehmann E. Some concepts of dependence. Ann Math Stat. 1966;37:1137–1153.
- Joag-Dev K, Proschan F. Negative association of random variables with applications. Ann Stat. 1983;11:286–295.
- Hu TZ. Negatively superadditive dependence of random variables with applications. Chin J Appl Probab Stat. 2000;16:133–144.
- Jiang T, Xu H. Max–Sum local equivalence of random variables with Farlie–Gumbel–Morgenstern joint distribution. Sci Sin Math. 2016;46(1):67–80.
- Tang QH, Vernic R. The impact on ruin probabilities of the association structure among financial risks. Stat Probab Lett. 2007;77(14):1522–1525.
- Cossette H. On the compound Poisson risk model with dependence based on a generalized Farlie–Gumbel–Morgenstern copula. Insurance Math Econ. 2008;43(3):444–455.
- Wang YB, Cheng DY. Basic renewal theorems for random walks with widely dependent increments. J Math Anal Appl. 2011;384:597–606.
- Chen Y, Wang L, Wang YB. Uniform asymptotics for the finite-time ruin probabilities of two kinds of nonstandard bidimensional risk models. J Math Anal Appl. 2013;401:114–129.
- Wang XJ, Xu C, Hu T-C, et al. On complete convergence for widely orthant-dependent random variables and its applications in nonparametric regression models. TEST. 2014;23:607–629.
- Yang WZ, Liu TT, Wang XH, et al. On the Bahadur representation of sample quantiles for widely orthant dependent sequences. Filomat. 2014;28:1333–1343.
- Wang XJ, Hu SH. The consistency of the nearest neighbor estimator of the density function based on WOD samples. J Math Anal Appl. 2015;429(1):497–512.
- Naderi H, Matuła P, Amini M, et al. On stochastic dominance and the strong law of large numbers for dependent random variables. RACSAM. 2016;110:771–782.
- Chen PY, Sung SH. A Spitzer-type law of large numbers for widely orthant dependent random variables. Stat Probab Lett. 2019;154:Article ID 108544.
- Shen AT, Wu CQ. Complete q-th moment convergence and its statistical applications. RACSAM. 2020;114:Article ID 35.
- Bingham N, Goldie C, Teugels J. Regular variation. Cambridge: Cambridge University Press; 1989.
- Lorentz GG. Borel and Banach properties of methods of summation. Duke Math J. 1955;22:129–141.
- Chow YS, Lai TL. Limiting behavior of weighted sums independent random variables. Ann Probab. 1973;1:810–824.
- Déniel Y, Derriennic Y. Sur la convergence presque sure, au sens de Cesàro d'ordre α, 0<α<1, de variables aléatoires et indépendantes et identiquement distribuées. Probab Theory Related Fields. 1988;79:629–636.
- Heinkel B. An infinite-dimensional law of large numbers in Cesàro's sense. J Theor Probab. 1990;3:533–546.
- Li DL, Rao MB, Jiang TF, et al. Complete convergence and almost sure convergence of weighted sums of random variables. J Theor Probab. 1995;8(1):49–76.
- Lai TL, Robbins H, Wei CZ. Strong consistency of least squares estimates in multiple regression. J Multivar Anal. 1979;9:343–361.
- Chen GJ, Lai TL, Wei CZ. Convergence systems and strong consistency of least squares estimates in regression models. J Multivar Anal. 1981;11(3):319–333.
- Baltagi BH, Krämer W. Consistency, asymptotic unbiasedness and bounds on the bias of s2 in the linear regression model with error component disturbances. Stat Pap. 1994;35(1):323–328.
- Song SH. Consistency and asymptotic unbiasedness of s2 in the serially correlated error components regression model for panel data. Stat Pap. 1996;37(3):267–275.
- Hu SH, Zhu CH, Chen YB. Fixed-design regression for linear time series. Acta Math Sci Ser B. 2002;22(1):9–18.
- Hu SH, Pan GM, Gao QB. Estimate problem of regression models with linear process errors. Appl Math A J Chin Univ. 2003;18A(1):81–90.
- Yang WZ, Xu HY, Chen L, et al. Complete consistency of estimators for regression models based on extended negatively dependent errors. Stat Pap. 2018;59(2):449–465.
- Wu Y, Wang XJ. Strong laws for weighted sums of m-extended negatively dependent random variables and its applications. J Math Anal Appl. 2021;494:Article ID 124566.
- Priestley MB, Chao MT. Nonparametric function fitting. J R Stat Soc Ser B (Methodology). 1972;34(3):385–392.
- Georgiev AA, Greblicki W. Nonparametric function recovering from noisy observations. J Stat Plan Inference. 1986;13:1–14.
- Georgiev AA. Consistent nonparametric multiple regression: the fixed design case. J Multivar Anal. 1988;25(1):100–110.
- Fan Y. Consistent nonparametric multiple regression for dependent heterogeneous processes. J Multivar Anal. 1990;33(1):72–88.
- Roussas GG, Tran LT, Ioannides DA. Fixed design regression for time series: asymptotic normality. J Multivar Anal. 1992;40:262–291.
- Tran LT, Roussas GG, Yakowitz S, et al. Fixed-design regression for linear time series. Ann Stat. 1996;24:975–991.
- Liang HY, Jing BY. Asymptotic properties for estimates of nonparametric regression models based on negatively associated sequences. J Multivar Anal. 2005;95:227–245.
- Thanh LV, Yin G. Weighted sums of strongly mixing random variables with an application to nonparametric regression. Stat Probab Lett. 2015;105:195–202.
- Antoniadis A, Gregoire G, Mckeague IW. Wavelet methods for curve estimation. J Am Stat Assoc. 1994;89:1340–1353.
- Chai GX, Liu YJ. Wavelet estimation of regression function based on mixing sequence under fixed design. J Math Res Exposition. 2001;21(4):554–560.
- Xue LG. Uniform convergence rates of the wavelet estimator of regression function under mixing error. Acta Math Sci Ser A. 2002;22(4):528–535.
- Li YM, Yang SC, Zhou Y. Consistency and uniformly asymptotic normality of wavelet estimator in regression model with associated samples. Stat Probab Lett. 2008;78:2947–2956.
- Li YM, Guo JH. Asymptotic normality of wavelet estimator for strong mixing errors. J Korean Stat Soc. 2009;38(4):383–390.
- Zhou XC, Lin JG, Yin CM. Asymptotic properties of wavelet-based estimator in nonparametric regression model with weakly dependent processes. J Inequal Appl. 2013;2013:Article ID 261.
- Ding LW, Chen P, Li YM. Consistency for wevelet estimator in nonparametric regression model with extended negatively dependent samples. Stat Pap. 2018;61(6):2331–2349.
- Wang XJ, Wu Y, Wang R, et al. On consistency of wavelet estimator in nonparametric regression models. Stat Pap. 2021;62(2):935–962.
- Wu Y, Yu W, Wang XJ. Strong representations of the Kaplan–Meier estimator and hazard estimator with censored widely orthant dependent data. Comput Stat. 2021;DOI: 10.1007/s00180-021-01125-z, in press.
- Zhou XC. Complete moment convergence of moving average processes under φ-mixing assumption. Stat Probab Lett. 2010;80:285–292.