设{Xn,n≥1}为独立同分布的正平方可积随机变量序列,其共同分布为连续的中尾分布.对于固定的常数a>0,令Sn=∑ from i=1 to n Xi,Mn=max(1≤i≤n)Xi,Sn(a)=∑ from i=1 to n XiI{Mn-a<Xi≤Mn},截断和Tn(a)=Sn-Sn(a).利用弱收敛定...设{Xn,n≥1}为独立同分布的正平方可积随机变量序列,其共同分布为连续的中尾分布.对于固定的常数a>0,令Sn=∑ from i=1 to n Xi,Mn=max(1≤i≤n)Xi,Sn(a)=∑ from i=1 to n XiI{Mn-a<Xi≤Mn},截断和Tn(a)=Sn-Sn(a).利用弱收敛定理和连续映射定理证明了截断和乘积的不变原理.展开更多
对一列独立同分布平方可积的随机变量序列{X_n,n≥1},当随机变量的分布具有中尾分布时,讨论了其截断和T_n(a)的随机乘积的渐近正态性质,其中T_n(a)=S_n-S_n(a),n= 1,2,…,S_n(a)=sum from j=1 to n X_jI{M_n-a<X_j≤M_n},a为某一大...对一列独立同分布平方可积的随机变量序列{X_n,n≥1},当随机变量的分布具有中尾分布时,讨论了其截断和T_n(a)的随机乘积的渐近正态性质,其中T_n(a)=S_n-S_n(a),n= 1,2,…,S_n(a)=sum from j=1 to n X_jI{M_n-a<X_j≤M_n},a为某一大于零的常数,M_n={X_k}.展开更多
设{X_n,n≥1}为i.i.d.r.v.S.,|X_n^(1)|≥|X_n^(2)|≥…≥|X_n^(n)|为{X_i,i≤n}的次序统计量,g为(0,+∞)上正Borel可测函数。我们讨论了截断和^(r)S_n=sum from i=r+t to nX_n^(i)与次序统计量X_n^(r)的比的分布收敛,令(r)T_n=[^(r)S_n...设{X_n,n≥1}为i.i.d.r.v.S.,|X_n^(1)|≥|X_n^(2)|≥…≥|X_n^(n)|为{X_i,i≤n}的次序统计量,g为(0,+∞)上正Borel可测函数。我们讨论了截断和^(r)S_n=sum from i=r+t to nX_n^(i)与次序统计量X_n^(r)的比的分布收敛,令(r)T_n=[^(r)S_n-(n-r)EX_1I{E|X_1|<+∞}]/g(|X_n(r)|),对正的常数列b_n,n≥1,我们得到了对所有的r≥1,^(r)T_n/(?)依分布收敛的充要条件。展开更多
The authors first derive the normal expansion of the joint density function of two orderstatistics from the uniform distribution and then, using the approximation, establish a wayto estimate the normal convergence rat...The authors first derive the normal expansion of the joint density function of two orderstatistics from the uniform distribution and then, using the approximation, establish a wayto estimate the normal convergence rate for trimmed sums. For applications, the convergencerates for the intermediately trimmed sums and heavily trimmed surns are found out.展开更多
This paper deals with the conditional quantile estimation based on left-truncated and right-censored data.Assuming that the observations with multivariate covariates form a stationary α-mixing sequence,the authors de...This paper deals with the conditional quantile estimation based on left-truncated and right-censored data.Assuming that the observations with multivariate covariates form a stationary α-mixing sequence,the authors derive the strong convergence with rate,strong representation as well as asymptotic normality of the conditional quantile estimator.Also,a Berry-Esseen-type bound for the estimator is established.In addition,the finite sample behavior of the estimator is investigated via simulations.展开更多
设{X_n,n≥1}是独立同分布的随机变量列,分布为 F;|X_n^((1))|≥|X_n^((2))|≥…≥|X_n^((n))|是|X_1|,|X_2|,…,|X_n|的次序统计量.对0≤r≤n-1,令^((r))S_n=sum from i=r+1 to n X_n^((i)).当 F 属于 Feller 族时本文研究了截断和(r=r...设{X_n,n≥1}是独立同分布的随机变量列,分布为 F;|X_n^((1))|≥|X_n^((2))|≥…≥|X_n^((n))|是|X_1|,|X_2|,…,|X_n|的次序统计量.对0≤r≤n-1,令^((r))S_n=sum from i=r+1 to n X_n^((i)).当 F 属于 Feller 族时本文研究了截断和(r=r_n 与 n 有关)的渐近分布,在不假定分布连续的条件下改进了 Pruitt 的结果.由此证明了当 F 属于正态吸引场时^((r))S_n 是渐近正态的.Pruitt 猜测适当正则化以后 ^((r))S_n 的极限只能是正态的,对此还构造了一个反例.展开更多
文摘设{Xn,n≥1}为独立同分布的正平方可积随机变量序列,其共同分布为连续的中尾分布.对于固定的常数a>0,令Sn=∑ from i=1 to n Xi,Mn=max(1≤i≤n)Xi,Sn(a)=∑ from i=1 to n XiI{Mn-a<Xi≤Mn},截断和Tn(a)=Sn-Sn(a).利用弱收敛定理和连续映射定理证明了截断和乘积的不变原理.
文摘对一列独立同分布平方可积的随机变量序列{X_n,n≥1},当随机变量的分布具有中尾分布时,讨论了其截断和T_n(a)的随机乘积的渐近正态性质,其中T_n(a)=S_n-S_n(a),n= 1,2,…,S_n(a)=sum from j=1 to n X_jI{M_n-a<X_j≤M_n},a为某一大于零的常数,M_n={X_k}.
文摘设{X_n,n≥1}为i.i.d.r.v.S.,|X_n^(1)|≥|X_n^(2)|≥…≥|X_n^(n)|为{X_i,i≤n}的次序统计量,g为(0,+∞)上正Borel可测函数。我们讨论了截断和^(r)S_n=sum from i=r+t to nX_n^(i)与次序统计量X_n^(r)的比的分布收敛,令(r)T_n=[^(r)S_n-(n-r)EX_1I{E|X_1|<+∞}]/g(|X_n(r)|),对正的常数列b_n,n≥1,我们得到了对所有的r≥1,^(r)T_n/(?)依分布收敛的充要条件。
文摘The authors first derive the normal expansion of the joint density function of two orderstatistics from the uniform distribution and then, using the approximation, establish a wayto estimate the normal convergence rate for trimmed sums. For applications, the convergencerates for the intermediately trimmed sums and heavily trimmed surns are found out.
基金supported by the National Natural Science Foundation of China(No.11271286)the Specialized Research Fund for the Doctor Program of Higher Education of China(No.20120072110007)a grant from the Natural Sciences and Engineering Research Council of Canada
文摘This paper deals with the conditional quantile estimation based on left-truncated and right-censored data.Assuming that the observations with multivariate covariates form a stationary α-mixing sequence,the authors derive the strong convergence with rate,strong representation as well as asymptotic normality of the conditional quantile estimator.Also,a Berry-Esseen-type bound for the estimator is established.In addition,the finite sample behavior of the estimator is investigated via simulations.
文摘设{X_n,n≥1}是独立同分布的随机变量列,分布为 F;|X_n^((1))|≥|X_n^((2))|≥…≥|X_n^((n))|是|X_1|,|X_2|,…,|X_n|的次序统计量.对0≤r≤n-1,令^((r))S_n=sum from i=r+1 to n X_n^((i)).当 F 属于 Feller 族时本文研究了截断和(r=r_n 与 n 有关)的渐近分布,在不假定分布连续的条件下改进了 Pruitt 的结果.由此证明了当 F 属于正态吸引场时^((r))S_n 是渐近正态的.Pruitt 猜测适当正则化以后 ^((r))S_n 的极限只能是正态的,对此还构造了一个反例.
