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Maximal Moment Inequality for Partial Sums of Strong Mixing Sequences and Application 被引量：13

Maximal Moment Inequality for Partial Sums of Strong Mixing Sequences and Application
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摘要 Some maximal moment inequalities for partial sums of the strong mixing random variable sequence are established. These inequalities use moment sums as up-boundary and improve the corre- sponding ones obtained by Shao （1996）. To show the application of the inequalities, we apply them to discuss the asymptotic normality of the weight function estimate for the fixed design regression model. Some maximal moment inequalities for partial sums of the strong mixing random variable sequence are established. These inequalities use moment sums as up-boundary and improve the corre- sponding ones obtained by Shao （1996）. To show the application of the inequalities, we apply them to discuss the asymptotic normality of the weight function estimate for the fixed design regression model.
作者 Shah Chao YANG
机构地区 Department of Mathematics
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2007年第6期1013-1024,共12页 数学学报（英文版）
基金 the Natural Science Foundation of China(10161004) the Natural Science Foundation of Guangxi(04047033)
关键词 strong mixing maximal moment inequality fixed design regression model weight functionestimate asymptotic normality strong mixing, maximal moment inequality, fixed design regression model, weight functionestimate, asymptotic normality
分类号 O17 [理学—基础数学]
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参考文献31

  • 1Billingsley, P.: Convergence of Probability Measures, Wiley, New York, 1968.
  • 2Peligrad, M.: Invariance principles for mixing sequencs of random variales. Ann. Probab., 10, 968-981 (1982).
  • 3Peligrad, M.: Convergence rates of the strong law for stationary mixing sequences. Z. Wahrsch. Verw. Gebirte, 70, 307-314 (1985).
  • 4Peligrad, M.: On the central limit theorem for p-mixing sequences of random variables. Ann. Probab., 15, 1387-1394 (1987).
  • 5Roussas, G. G., Ioannides, D. A.: Moment inequalities for mixing sequences of random variables. Stochastic Anal. Appl., 5, 61-120 (1987).
  • 6Shao, Q. M.: A moment inequality and its applications. Acta Mathematica Sinica, Chinese Series,, 31, 736-747 (1988).
  • 7Shao, Q. M.: Complete convergence for p-mixing sequences. Acta Mathematica Sinica, Chinese Series, 32, 377-393 (1989).
  • 8Shao, Q. M.: Maximal inequalities for partial sums of p-mixing sequences. Ann. Probab., 23, 948-965 (1995).
  • 9Yang, S. C.: Moment inequality for mixing sequences and nonparametric estimation. Acta Mathematica Sinica, Chinese Series, 40, 271-279 (1997).
  • 10Zhang, L. X.: Rosenthal type inequalities for B-valued shrong mixing random fields and their applications. Science in China (Series A), 41(7), 736-745 (1998).

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Acta Mathematica Sinica,English Series
2007年 第6期

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