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关于移动平均过程完全收敛性的研究   总被引:1,自引:0,他引:1  
设{Y~i;-∞<i<∞}是一个独立同分布的 B值随机元的双边无限序列,{ai;-∞<i<∞}是一个绝对可求和的实数序列.定义移动平均过程X_k=sum from i=-∞ ai+kYi,k≥1.本文研究了{X_k;k≥1}部分和序列的完全收敛性,同时针对实值情形,还将随机变量的单纯矩条件过渡到选定的函数类上.得到了实移动平均过程完全收敛性的更一般结果.  相似文献
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This paper studies the model-robust design problem for general models with an unknown bias or contamination and the correlated errors. The true response function is assumed to be from a reproducing kernel Hilbert space and the errors are fitted by the qth order moving average process MA(q), especially the MA(1) errors and the MA(2) errors. In both situations, design criteria are derived in terms of the average expected quadratic loss for the least squares estimation by using a minimax method. A case is studied and the orthogonality of the criteria is proved for this special response. The robustness of the design criteria is discussed through several numerical examples.  相似文献
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张勇  赵世舜  董志山 《东北数学》2007,23(6):549-562
In this paper, we discuss the precise asymptotics of moving-average process Xt =∞∑j=0 ajEt-j under some suitable conditions, where {εt, t∈ Z} is a sequence j=0 of stationary ALNQD random variables with mean zeros and finite variances.  相似文献
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牛司丽  田素霞 《数学杂志》2002,22(3):271-276
设 {ε,εt;t∈ Z}是 iid的 B值随机变量序列 ,{ aj;j∈ Z}是一个实数列 ,满足 ∞j=-∞|aj|<∞ .记 Xt= ∞j=-∞ajεt-j,Sn = nt=1Xt.对 p≥ 1 ,本文研究了n-1 -( p/ 2 ) (2 L2 n) -( p/ 2 ) ni=1 ‖ Si‖p 及 n-1 -( p/ 2 ) (2 L2 n) -( p/ 2 ) ni=0 ‖ Sn- Si‖ p的渐进性质 ,使得 Strassen(1 964)及 Chen(1 994)的一些结果得到推广 .  相似文献
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In this paper we discuss the least-square estimator of the unknown change point in a mean shift for moving-average processes of ALNQD sequence. The consistency and the rate of convergence for the estimated change point are established. The asymptotic distribution for the change point estimator is obtained. The results are also true for ρ-mixing, φ-mixing, α-mixing sequences under suitable conditions. These results extend those of Bai, who studied the mean shift point of a linear process of i.i.d, variables, and the condition ∑j=0^∞j|aj| 〈 ∞ in Bai is weakened to ∑j=0^∞|aj|〈∞.  相似文献
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Let {Y i;∞ < i < ∞} be a doubly infinite sequence of identically distributed-mixing random variables and let {a i;∞ < i < ∞} be an absolutely summable sequence of real numbers.In this paper we study the moments of sup(1 ≤ r < 2,p > 0) under the conditions of some moments.  相似文献
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