随机变量序列的强极限定理
摘要
引文
[1] Bai, Z. D. and Cheng, P. E. Marcinkiewicz strong laws for linear statistics. Statist. Probab. Lett., 2000, 46, 105—112.
[2] Block, H. W., Savits, T. H. and Shaked, M. Some concepts of negative dependence. Ann. Probab., 1982, 10, 765-772.
[3] Bradley, R. C. Eqnivalent mixing conditions for random fields. Chapel Hill: Technical Roport No.336, Center for Stochastic Processes, Univ of North Carolina, 1990.
[4] Bradkey, R. C. On the spectral density and asymptotic normality of dependence between random variables. J. Theoret. Probab., 1992, 5, 355—373.
[5] Bryc, W. and Smolenski, W. Moment conditions for almost sure convergence of weakly correlated random variables. Proc. Amer. Math. Soc, 1993, 119, 629— 635.
[6] Burton, R. M., Dabrowski, A. R. and Dehling, H. An invariance principle of weakly associated random vectors. Stochastic Process. Appl., 1986, 23, 301—306.
[7] Burton, R. M. and Dehling, H. Large deviations for some weakly dependent random process. Statist. Probab. Lett., 1990, 9, 397—401.
[8] Carroll, R. J. and wand, M. P. Semiparametric estimation inlogistic measure error- in-variables for binary regression models. Biometrika, 1991, 71, 19—26.
[9] Chen, B. On the Chovers law of the iterated logarithm. Applied Mathematics Journal of Chinese Universities, 1993, 8A(2), 197—202.
[10] Chen, P. Y. Limiting behavior of weighted sums with stable distributions. Statist. Probab. Lett., 2002, 60, 367—375.
[11] Chen, P. Y. and Chen, Q. P. LIL for φ— mixing sequence of random variables. Acta Math. Sinica, 2003, 3, 571—580.
[12] Chen, P. Y. and Huang, L. H. The Chover law of the iterated logarithm for random geometric series of stable distribution. Acta Math. Sinica, 2000, 46, 1063—1070.
[13] Choi, B. D. and Sung, S. H. Almost sure convergence theorems of weighted sums of random variables. Stochastic Anal. Appl., 1987, 5, 365—377.
[14] Chover, J. A law of the iterated logarithm for stable summands. Proc. Amer. Math. Soc, 1966, 17(2), 441—443.
[15] Chow, Y. S. and Teicher, H. Probability Theory: Independence, Interchangeability, Martingales. Springer-Verlag, New York, 3rd ed. 1997.
[16] Cox, J. T. and Grimmett, G. Central limit theorems for associated random variables and the percolation model. Ann. Probab., 1984, 12, 514—528.
[17] Cuzick, J. A strong law for weighted sums of i.i.d. random variables. J. Theoret. Probab., 1995, 8, 625—641.
[18] Ebrahimi, N. and Ghosh, M. Multivariate negative dependence. Comm. Statist. Theory and Methods, 1981, 10(4), 307—337.
[19] Esary, J. D., Proschan, F. and Walkup, D. W. Association of random variables with applications. Ann. Math. Statist., 1967, 44, 1466—1474.
[20] Erdos, P. On a theorem of Hsu-Robbins. Ann. Math. Statist., 1949, 20, 286—291.
[21] Gao, J. T., Chen, X. R. and Zhao, L. C. Asymptotic normality of a class of estimator in partial linear models. Acta Math. Sinica, 1994, 37, 256—268.
[22] Ho, H. C. and Hsing, T. Limit theorems for functionals of moving average. Ann. Probab., 1997, 25, 1636—1669.
[23] Hsu, P. L. and Robbins, H. Complete convergence and the law of larege numbers. Proc. Nat. Acad. Sci. (USA), 1947, 33(2), 25—31.
[24] Huang, W. T. and Xu, B. Some Maximal Inequalities and Complete Convergences of Negatively Associated Random Sequences. Statist. Probab. Lett., 2002, 57, 183— 191.
[25] Ibragimov, I. A. Some limit theorems for stationary process. Theory Probab. Appl., 1962, 7, 349—382.
[26] Joag, D. K. Conditional negative dependence in stochastic ordering and interchangeable random variables. In Topics in Statistical Dependence (H. W. Block, A.R. Simpson, and T.H. Savits, Eds.). IMS Lecture Notes. 1990.
[27] Joag, D. K. and Proschan, F. Negative association of random variables with applications. Ann. Statist., 1983, 11, 286—295.
[28] Karlin, S. and Rinott, Y. Classes of orderings of measures and related correlation inequalities. I. Multivariate totally positive distributions. J. Multivariate Anal., 1980a, 10, 467—498.
[29] Karlin, S. and Rinott, Y. Classes of orderings of measures and related correlation inequalities. II. Multivariate reverse rule distributions. J. Multivariate Anal., 1980b, 10, 499—516.
[30] Kim, T. and Baek, J. A central limit theorem for Stationary linear processes under linear positive quadrant dependent process. Stat. Prob. Lett., 2001, 51, 299—305.
[31] Kim, T., Ko, M. and Park, D. Almost sure convergence for linear processes generated by positively dependent processes. Stoch. Anal, and Appl., 2004, 22(1), 143-153.
[32] Ko, M. H., Kim, T. S. and Kim, H. C. Strong laws of large numbers for asymptotically quadrant independent random fields. Comm. Korean Math. Soc, 2004, 19, 765—773.
[33] Lai, T, L., Robbins, H. and Wei, C. Z. Strong consistency of least square estimations in multiple regression. J. Multivariate Anal., 1979, 9, 343—361.
[34] Ledoux, M. and Talagrand, M. Probability in banach spaces. Springer, Berlin, Heidelberg, 1991.
[35] Lehmann, E, L. Some concepts of dependence. Ann. Math. Statist., 1966, 37, 1137—1153.
[36] Li, D. L., Rao, M. B. and Wang, X. C. Complete convergence of moving average processes. Statist. Probab. Lett., 1992, 14, 111—114.
[37] Lehmann, E. L, Some concepts of dependence. Ann. Math. Statist., 1966, 43, 1137—1153.
[38] Liang, H. Y. and Su, C. Complete convergence for weighted sums of NA sequences. Statist. Probab. Lett. 1999, 45, 85—95.
[39] Liang, H. Y. Complete convergence for weighted sums of negatively associated random variables. Statist. Probab. Lett., 2000, 48, 317—325.
[40] Lin, Z. Y. Invariance principle for negatively associated sequence. Chinese Science Bulletin, 1997, 42, 238—242.
[41] Lin, Z. Y. and Lu, C. R. Limit Theory for Mixing Dependent Random Variables. Kluwer Academic Publishers and Science Press, Dordrecht-Beijing, 1997.
[42] Matula, P. A note on the almost sure convergence of sums of negatively dependent random variables. Statist. Probab. Lett., 1992, 15, 209—213.
[43] Miller, C. Three theorems on random fields with ρ*—mixing. J. Theoret. Probab., 1994, 7, 867—882.
[44] Miller, C. A CLT for periodograms of a ρ*-mixing fields. Stoch. Processes Appl., 1995, 60, 313—330.
[45] Newey, W. K. Flexible simulated moment estimation of nonlinear errors-in-variables model. The Review of Economics and Statistcs, 2001, 83(4), 616—627.
[46] Newman, C. M. Normal fluctuations and the FKG inequalities. Comm. Math. Phys., 1980, 75, 119—128.
[47] Newman, C. M. and Wright, A. L. Associated random variables and martingale inequalities. Z. Wahrsch. Verw. Gebiete, 1982, 59, 361—371.
[48] Newman, C. M. Asymptotic independence and limit theorems of probability and negatively dependent random variables. In Inequalities in Statistics and probability. ( Y.L. Tong, Ed.), IMS Lecture Notes-Monograph Series, vol. 5, pp.127-140. Institute of Mathematical Statistics, Hayward, California. 1984.
[49] Peligrad, M. On the asymptotic normality of sequences of weak dependent random variables. J. Theoret. Probab., 1996, 9, 703—715.
[50] Peligrad, M. Maximum of partial sums and an invariance principle for a class weak depend random variables. Proc. Amer. Math. Soc, 1998, 126(4), 1181—1189.
[51] Peligrad, M and Gut, A. Almost sure results for a class of dependent random variables. J. Theoret. Probab., 1999, 12, 87—104.
[52] Peps, M. S. Inference using surrogate outcome data and a validation sample. Biometrika, 1992, 79, 355—365.
[53] Petrov, V. V. Limit theorems of probability theory—sequences of independent random variables. Oxfors, Oxford Science Publications, 1995.
[54] Phillips, P. Time series regression with a unit root. Econometrica, 1987, 55, 277— 302.
[55] Phillips, P. and Solo, V. Asymptotics for linear processes. Ann. Statits., 1992, 20, 971—1001.
[56] Qi, Y. C. and Cheng, P. On the law of the iterated logarithm for the partial sum in the domain of attration of stable distribution. Chinese Ann. Math., 1996, 17A(2), 195—206.
[57] Qin, G. S. Kernel smoothing method in patial linear model under random censorship. Chinese Ann. Math., 1995, 16A, 441—453.
[58] Roussas, G. G. Kernel estimates under association: strong uniform consistency. Statist. Probab. Lett., 1991, 12, 393—403.
[59] Roussas, G. G. Asymptotic Normality of random fields of positively or negatively associated processes. J. Multivariate Anal., 1994, 50, 152—173.
[60] Ruan, H. S., Zhang, L. X. and Wen, J. W. A law of the iterated logarithm for non-stationary weakly negatively associated random variables. Journal of Zhejiang University (Sciences. Edition). 2000, 27(6), 689 -699.
[61] Salvadori, G. Linear combinations of order statistics to estimate the quantiles of gen- eralized pareto and extreme values distributions. Stochastic Environmental Research and Risk Assessment, 2003, 17, 116—140.
[62] Sepanski, J. H. and Carroll, R. J. Semi-parametric quasilikelihood and variance function estimation in measure error models. J. of Economtrics, 1993, 58, 226—253.
[63] Sepanski, J. H., Knickerbocker, R. K. and Carroll, R. J. A semiparametric correction for attenuation. J. Amer. Statist. Assoc, 1994, 89, 1366—1371.
[64] Sepanski, J. H. and Lee, L. F. Semiparametric estimation of nonlinear error-in- variables models with validation study. J. Nonparametric Statistics, 1995, 4, 365— 394.
[65] Shaked, M. A general theory of some positive dependence notions. J. MultivariateAnal., 1982, 12, 199—218.
[66] Shao, Q. M. On complete convergence for a p— mixing sequence. Acta Math. Sinica, 1989, 32, 377—393.
[67] Shao, Q. M. Maximal inequalities for sums of ρ—mixing sequences. Ann. Probab., 1995, 23, 948—965.
[68] Shao, Q. M. A comparison theorem on moment inequalities between Negatively associated and independent random variables. J. Theoreti. Probab., 2000, 13, 343—356.
[69] Shao, Q. M. and Su, C. The law of the iterated logarithm for negatively associated random variables. Stochastic Process Appl., 1999, 83, 139—148.
[70] Stout, W. F. Almost sure convergence, New York Academic Press, 1974.
[71] Su, C, Zhao, L. C and Wang, Y. B. Moment inequalities and weak convergence for NA sequences. Science in China (Ser. A), 1996, 26, 1091—1099.
[72] Su, C. and Qin, Y.S. Limit theorems for negatively associated sequences. Chinese Science Bulletin, 1997, 42, 243—246.
[73] Sung, S. H. Strong laws for weighted sums of i.i.d. random variables. Statist. Probab. Lett., 2001, 52, 413—419.
[74] Taupin, M. L. semi-parametric estimation in the nonlineal structural errors-in-variables model. Ann. Statist, 2001, 29, 66—93.
[75] Utev, S. and Peligrad, M. Maximal inequalities and an invariance principle for a class of weakly dependent random variables. J. Theoret. Probab., 2003, 16, 101—115.
[76] Vasudeva, K. and Divanji, G. LIL for delayed sums under a non-indentically distributed, setup. Theory Prob. Appl., 1992, 37, 534—562.
[77] Wang, Q. H. Estimation of partial linear error-in-variables models with validation data. J. Multivariate Analysis, 1999, 69, 30—64.
[78] Wang, Q. Y., Lin, Y. X. and Gulati, C. M. The invariance principle for linear processes with applications. Econometric Theory, 2002, 18, 119—139.
[79] Wood, T. E. A Berry-Esseen theorem for associated random variables. Ann. Probab. 1983, 11, 1042—1047.
[80] Wu, Q. Y. Convergence properties of pairwise NQD random sequences. Acta Math. Sinica, 2002, 45, 617—624.
[81] Wu, W. B. On the strong convergence of a weighted sums. Statist. Probab. Lett., 1999, 44, 19—22.
[82] Yang, S. C. Moment inequality of random variables partial sums. Science in Chinese (Ser. A), 2000, 30, 218—223.
[83] Yang, Y. Estimation theory in partly linear recession models under range dependence. Advance in Mathematics (in Chinese), 1999, 5, 411—425.
[84] Zhang, L. X. Complete convergence of moving average processes under dependence assumptions. Statist. Probab. Lett., 1996, 30, 165—170.
[85] Zhang, L. X. A functional central limit theorem for asymptotically negative dependence random fields. Acta Math. Hungar., 2000a, 86(3), 237—259.
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[2] Block, H. W., Savits, T. H. and Shaked, M. Some concepts of negative dependence. Ann. Probab., 1982, 10, 765-772.
[3] Bradley, R. C. Eqnivalent mixing conditions for random fields. Chapel Hill: Technical Roport No.336, Center for Stochastic Processes, Univ of North Carolina, 1990.
[4] Bradkey, R. C. On the spectral density and asymptotic normality of dependence between random variables. J. Theoret. Probab., 1992, 5, 355—373.
[5] Bryc, W. and Smolenski, W. Moment conditions for almost sure convergence of weakly correlated random variables. Proc. Amer. Math. Soc, 1993, 119, 629— 635.
[6] Burton, R. M., Dabrowski, A. R. and Dehling, H. An invariance principle of weakly associated random vectors. Stochastic Process. Appl., 1986, 23, 301—306.
[7] Burton, R. M. and Dehling, H. Large deviations for some weakly dependent random process. Statist. Probab. Lett., 1990, 9, 397—401.
[8] Carroll, R. J. and wand, M. P. Semiparametric estimation inlogistic measure error- in-variables for binary regression models. Biometrika, 1991, 71, 19—26.
[9] Chen, B. On the Chovers law of the iterated logarithm. Applied Mathematics Journal of Chinese Universities, 1993, 8A(2), 197—202.
[10] Chen, P. Y. Limiting behavior of weighted sums with stable distributions. Statist. Probab. Lett., 2002, 60, 367—375.
[11] Chen, P. Y. and Chen, Q. P. LIL for φ— mixing sequence of random variables. Acta Math. Sinica, 2003, 3, 571—580.
[12] Chen, P. Y. and Huang, L. H. The Chover law of the iterated logarithm for random geometric series of stable distribution. Acta Math. Sinica, 2000, 46, 1063—1070.
[13] Choi, B. D. and Sung, S. H. Almost sure convergence theorems of weighted sums of random variables. Stochastic Anal. Appl., 1987, 5, 365—377.
[14] Chover, J. A law of the iterated logarithm for stable summands. Proc. Amer. Math. Soc, 1966, 17(2), 441—443.
[15] Chow, Y. S. and Teicher, H. Probability Theory: Independence, Interchangeability, Martingales. Springer-Verlag, New York, 3rd ed. 1997.
[16] Cox, J. T. and Grimmett, G. Central limit theorems for associated random variables and the percolation model. Ann. Probab., 1984, 12, 514—528.
[17] Cuzick, J. A strong law for weighted sums of i.i.d. random variables. J. Theoret. Probab., 1995, 8, 625—641.
[18] Ebrahimi, N. and Ghosh, M. Multivariate negative dependence. Comm. Statist. Theory and Methods, 1981, 10(4), 307—337.
[19] Esary, J. D., Proschan, F. and Walkup, D. W. Association of random variables with applications. Ann. Math. Statist., 1967, 44, 1466—1474.
[20] Erdos, P. On a theorem of Hsu-Robbins. Ann. Math. Statist., 1949, 20, 286—291.
[21] Gao, J. T., Chen, X. R. and Zhao, L. C. Asymptotic normality of a class of estimator in partial linear models. Acta Math. Sinica, 1994, 37, 256—268.
[22] Ho, H. C. and Hsing, T. Limit theorems for functionals of moving average. Ann. Probab., 1997, 25, 1636—1669.
[23] Hsu, P. L. and Robbins, H. Complete convergence and the law of larege numbers. Proc. Nat. Acad. Sci. (USA), 1947, 33(2), 25—31.
[24] Huang, W. T. and Xu, B. Some Maximal Inequalities and Complete Convergences of Negatively Associated Random Sequences. Statist. Probab. Lett., 2002, 57, 183— 191.
[25] Ibragimov, I. A. Some limit theorems for stationary process. Theory Probab. Appl., 1962, 7, 349—382.
[26] Joag, D. K. Conditional negative dependence in stochastic ordering and interchangeable random variables. In Topics in Statistical Dependence (H. W. Block, A.R. Simpson, and T.H. Savits, Eds.). IMS Lecture Notes. 1990.
[27] Joag, D. K. and Proschan, F. Negative association of random variables with applications. Ann. Statist., 1983, 11, 286—295.
[28] Karlin, S. and Rinott, Y. Classes of orderings of measures and related correlation inequalities. I. Multivariate totally positive distributions. J. Multivariate Anal., 1980a, 10, 467—498.
[29] Karlin, S. and Rinott, Y. Classes of orderings of measures and related correlation inequalities. II. Multivariate reverse rule distributions. J. Multivariate Anal., 1980b, 10, 499—516.
[30] Kim, T. and Baek, J. A central limit theorem for Stationary linear processes under linear positive quadrant dependent process. Stat. Prob. Lett., 2001, 51, 299—305.
[31] Kim, T., Ko, M. and Park, D. Almost sure convergence for linear processes generated by positively dependent processes. Stoch. Anal, and Appl., 2004, 22(1), 143-153.
[32] Ko, M. H., Kim, T. S. and Kim, H. C. Strong laws of large numbers for asymptotically quadrant independent random fields. Comm. Korean Math. Soc, 2004, 19, 765—773.
[33] Lai, T, L., Robbins, H. and Wei, C. Z. Strong consistency of least square estimations in multiple regression. J. Multivariate Anal., 1979, 9, 343—361.
[34] Ledoux, M. and Talagrand, M. Probability in banach spaces. Springer, Berlin, Heidelberg, 1991.
[35] Lehmann, E, L. Some concepts of dependence. Ann. Math. Statist., 1966, 37, 1137—1153.
[36] Li, D. L., Rao, M. B. and Wang, X. C. Complete convergence of moving average processes. Statist. Probab. Lett., 1992, 14, 111—114.
[37] Lehmann, E. L, Some concepts of dependence. Ann. Math. Statist., 1966, 43, 1137—1153.
[38] Liang, H. Y. and Su, C. Complete convergence for weighted sums of NA sequences. Statist. Probab. Lett. 1999, 45, 85—95.
[39] Liang, H. Y. Complete convergence for weighted sums of negatively associated random variables. Statist. Probab. Lett., 2000, 48, 317—325.
[40] Lin, Z. Y. Invariance principle for negatively associated sequence. Chinese Science Bulletin, 1997, 42, 238—242.
[41] Lin, Z. Y. and Lu, C. R. Limit Theory for Mixing Dependent Random Variables. Kluwer Academic Publishers and Science Press, Dordrecht-Beijing, 1997.
[42] Matula, P. A note on the almost sure convergence of sums of negatively dependent random variables. Statist. Probab. Lett., 1992, 15, 209—213.
[43] Miller, C. Three theorems on random fields with ρ*—mixing. J. Theoret. Probab., 1994, 7, 867—882.
[44] Miller, C. A CLT for periodograms of a ρ*-mixing fields. Stoch. Processes Appl., 1995, 60, 313—330.
[45] Newey, W. K. Flexible simulated moment estimation of nonlinear errors-in-variables model. The Review of Economics and Statistcs, 2001, 83(4), 616—627.
[46] Newman, C. M. Normal fluctuations and the FKG inequalities. Comm. Math. Phys., 1980, 75, 119—128.
[47] Newman, C. M. and Wright, A. L. Associated random variables and martingale inequalities. Z. Wahrsch. Verw. Gebiete, 1982, 59, 361—371.
[48] Newman, C. M. Asymptotic independence and limit theorems of probability and negatively dependent random variables. In Inequalities in Statistics and probability. ( Y.L. Tong, Ed.), IMS Lecture Notes-Monograph Series, vol. 5, pp.127-140. Institute of Mathematical Statistics, Hayward, California. 1984.
[49] Peligrad, M. On the asymptotic normality of sequences of weak dependent random variables. J. Theoret. Probab., 1996, 9, 703—715.
[50] Peligrad, M. Maximum of partial sums and an invariance principle for a class weak depend random variables. Proc. Amer. Math. Soc, 1998, 126(4), 1181—1189.
[51] Peligrad, M and Gut, A. Almost sure results for a class of dependent random variables. J. Theoret. Probab., 1999, 12, 87—104.
[52] Peps, M. S. Inference using surrogate outcome data and a validation sample. Biometrika, 1992, 79, 355—365.
[53] Petrov, V. V. Limit theorems of probability theory—sequences of independent random variables. Oxfors, Oxford Science Publications, 1995.
[54] Phillips, P. Time series regression with a unit root. Econometrica, 1987, 55, 277— 302.
[55] Phillips, P. and Solo, V. Asymptotics for linear processes. Ann. Statits., 1992, 20, 971—1001.
[56] Qi, Y. C. and Cheng, P. On the law of the iterated logarithm for the partial sum in the domain of attration of stable distribution. Chinese Ann. Math., 1996, 17A(2), 195—206.
[57] Qin, G. S. Kernel smoothing method in patial linear model under random censorship. Chinese Ann. Math., 1995, 16A, 441—453.
[58] Roussas, G. G. Kernel estimates under association: strong uniform consistency. Statist. Probab. Lett., 1991, 12, 393—403.
[59] Roussas, G. G. Asymptotic Normality of random fields of positively or negatively associated processes. J. Multivariate Anal., 1994, 50, 152—173.
[60] Ruan, H. S., Zhang, L. X. and Wen, J. W. A law of the iterated logarithm for non-stationary weakly negatively associated random variables. Journal of Zhejiang University (Sciences. Edition). 2000, 27(6), 689 -699.
[61] Salvadori, G. Linear combinations of order statistics to estimate the quantiles of gen- eralized pareto and extreme values distributions. Stochastic Environmental Research and Risk Assessment, 2003, 17, 116—140.
[62] Sepanski, J. H. and Carroll, R. J. Semi-parametric quasilikelihood and variance function estimation in measure error models. J. of Economtrics, 1993, 58, 226—253.
[63] Sepanski, J. H., Knickerbocker, R. K. and Carroll, R. J. A semiparametric correction for attenuation. J. Amer. Statist. Assoc, 1994, 89, 1366—1371.
[64] Sepanski, J. H. and Lee, L. F. Semiparametric estimation of nonlinear error-in- variables models with validation study. J. Nonparametric Statistics, 1995, 4, 365— 394.
[65] Shaked, M. A general theory of some positive dependence notions. J. MultivariateAnal., 1982, 12, 199—218.
[66] Shao, Q. M. On complete convergence for a p— mixing sequence. Acta Math. Sinica, 1989, 32, 377—393.
[67] Shao, Q. M. Maximal inequalities for sums of ρ—mixing sequences. Ann. Probab., 1995, 23, 948—965.
[68] Shao, Q. M. A comparison theorem on moment inequalities between Negatively associated and independent random variables. J. Theoreti. Probab., 2000, 13, 343—356.
[69] Shao, Q. M. and Su, C. The law of the iterated logarithm for negatively associated random variables. Stochastic Process Appl., 1999, 83, 139—148.
[70] Stout, W. F. Almost sure convergence, New York Academic Press, 1974.
[71] Su, C, Zhao, L. C and Wang, Y. B. Moment inequalities and weak convergence for NA sequences. Science in China (Ser. A), 1996, 26, 1091—1099.
[72] Su, C. and Qin, Y.S. Limit theorems for negatively associated sequences. Chinese Science Bulletin, 1997, 42, 243—246.
[73] Sung, S. H. Strong laws for weighted sums of i.i.d. random variables. Statist. Probab. Lett., 2001, 52, 413—419.
[74] Taupin, M. L. semi-parametric estimation in the nonlineal structural errors-in-variables model. Ann. Statist, 2001, 29, 66—93.
[75] Utev, S. and Peligrad, M. Maximal inequalities and an invariance principle for a class of weakly dependent random variables. J. Theoret. Probab., 2003, 16, 101—115.
[76] Vasudeva, K. and Divanji, G. LIL for delayed sums under a non-indentically distributed, setup. Theory Prob. Appl., 1992, 37, 534—562.
[77] Wang, Q. H. Estimation of partial linear error-in-variables models with validation data. J. Multivariate Analysis, 1999, 69, 30—64.
[78] Wang, Q. Y., Lin, Y. X. and Gulati, C. M. The invariance principle for linear processes with applications. Econometric Theory, 2002, 18, 119—139.
[79] Wood, T. E. A Berry-Esseen theorem for associated random variables. Ann. Probab. 1983, 11, 1042—1047.
[80] Wu, Q. Y. Convergence properties of pairwise NQD random sequences. Acta Math. Sinica, 2002, 45, 617—624.
[81] Wu, W. B. On the strong convergence of a weighted sums. Statist. Probab. Lett., 1999, 44, 19—22.
[82] Yang, S. C. Moment inequality of random variables partial sums. Science in Chinese (Ser. A), 2000, 30, 218—223.
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