共查询到20条相似文献,搜索用时 46 毫秒
1.
Consider the nonparametric regression model
, whereg is an unknown function to be estimated on [0, 1],
are the fixed design points in the interval [0, 1] and
is a triangular array of row iid random variables having median zero. The nearest neighbor median estimator
is taken as the estimator of the unknown functiong(x). Median cross validation (mev) criterion is employed to select the smoothing parameterh. Leth
π
*
be the smoothing parameter chosen by mev criterion. Under mild regularity conditions, the upper and lower bounds ofh
π
*
, the rate of convergence and the weak consistency of the median cross-validated estimate
are obtained.
Project supported by the National Natural Science Foundation of China and the Doctoral Foundation of Education of China. 相似文献
2.
Djellout Hacène Guillin Arnaud Wu Liming 《Statistical Inference for Stochastic Processes》1999,2(3):195-225
For a diffusion process dXt = σdB
t + b(t, Xt)dt with (σ
t
) unknown, we study the large and moderate deviations of the estimator
of the quadratic variational process
.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
3.
Yun-xia Li 《应用数学学报(英文版)》2006,22(4):615-626
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
4.
Yu Qing Chen 《Designs, Codes and Cryptography》1998,13(3):247-250
In this paper, we will give a construction of a family of
-difference sets in thegroup
, where q is any power of 2, K is any group with
and G is an abelian 2-group of order
which contains anelementary abelian subgroup of index 2. 相似文献
5.
Precise Asymptotics in the Law of the Iterated Logarithm of Moving-Average Processes 总被引:1,自引:0,他引:1
Yun Xia LI Li Xin ZHANG 《数学学报(英文版)》2006,22(1):143-156
In this paper, we discuss the moving-average process Xk = ∑i=-∞ ^∞ ai+kεi, where {εi;-∞ 〈 i 〈 ∞} is a doubly infinite sequence of identically distributed ψ-mixing or negatively associated random variables with mean zeros and finite variances, {ai;-∞ 〈 i 〈 -∞) is an absolutely solutely summable sequence of real numbers. 相似文献
6.
Some Limit Theorems for a Particle System of Single Point Catalytic Branching Random Walks 总被引:2,自引:0,他引:2
Vladimir VATUTIN Jie XIONG 《数学学报(英文版)》2007,23(6):997-1012
We study the scaling limit for a catalytic branching particle system whose particles perform random walks on Z and can branch at 0 only. Varying the initial (finite) number of particles, we get for this system different limiting distributions. To be more specific, suppose that initially there are n^β particles and consider the scaled process Zt^n(·) = Znt(√n·), where Zt is the measure-valued process 1 and to a representing the original particle system. We prove that Ztn converges to 0 when β 〈1/4 and to a nondegenerate discrete distribution when β=1/4.In addition,if 1/4〈β〈1/2 then n-^(2β-1/2)Zt^n converges to a random limit,while if β 〉21then n^-βZtn converges to a deterministic limit. 相似文献
7.
I. E. Vitrichenko 《Ukrainian Mathematical Journal》1999,51(12):1799-1812
We obtain sufficient conditions for the Perron stability of the trivial solution of a real difference equation of the form
where and. The resuits obtained are valid for the case where.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 12, pp. 1593–1603, December, 1999. 相似文献
8.
P. Koteeswaran K. Nanthi K. Suresh Chandra 《Annals of the Institute of Statistical Mathematics》1985,37(1):409-414
Summary LetX=(X
n; n≧0,X
0=1) be a supercritical Galton-Watson process. The limiting distribution of
) where
is the m.l.e. of the offspring mean, is derived. As an application of this result, some limit theorems leading ultimately
to a parameter free result of statistical interest, are also established. 相似文献
9.
Qi Keng LU Ke WU 《数学学报(英文版)》2007,23(4):577-598
For an integer m ≥ 4, we define a set of 2[m/2] × 2[m/2] matrices γj (m), (j = 0, 1,..., m - 1) which satisfy γj (m)γk (m) +γk (m)γj (m) = 2ηjk (m)I[m/2], where (ηjk (m)) 0≤j,k≤m-1 is a diagonal matrix, the first diagonal element of which is 1 and the others are -1, I[m/2] is a 2[m/1] × 2[m/2] identity matrix with [m/2] being the integer part of m/2. For m = 4 and 5, the representation (m) of the Lorentz Spin group is known. For m≥ 6, we prove that (i) when m = 2n, (n ≥ 3), (m) is the group generated by the set of matrices {T|T=1/√ξ((I+k) 0 + 0 I-K) ( U 0 0 U), (ii) when m = 2n + 1 (n≥ 3), (m) is generated by the set of matrices {T|T=1/√ξ(I -k^- k I)U,U∈ (m-1),ξ=1-m-2 ∑k,j=0 ηkja^k a^j〉0, K=i[m-3 ∑j=0 a^j γj(m-2)+a^(m-2) In],K^-=i[m-3∑j=0 a^j γj(m-2)-a^(m-2) In]} 相似文献
10.
C. C. Y. Dorea 《Semigroup Forum》1983,26(1):287-293
It is well known that the infinitesimal operator
characterizes the Wiener process {W(t), t≥0}. In this paper we show that the family of operators
plays the same role for the q-parameter Wiener process.
Partially supported by CNPq Grant No. 200. 607/82. 相似文献
11.
A. S. Zhuk 《Journal of Mathematical Sciences》2008,150(3):2034-2044
Let M be either the space of 2π-periodic functions Lp, where 1 ≤ p < ∞, or C; let ωr(f, h) be the continuity modulus of order r of the function f, and let
, where
, be the generalized Jackson-Vallée-Poussin integral. Denote
. The paper studies the quantity Km(f − Dn,r,l(f)). The general results obtained are applicable to other approximation methods. Bibliography: 11 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 350, 2007, pp. 52–69. 相似文献
12.
基于左截断右删失数据下的乘积限估计构造了分位数固定宽度序贯置信区间及其估计,研究了序贯置信区间估计的渐近性质。作为副产品,获得了分位数估计近邻点的Bahadur表示定理。这个表示定理是推导分位数固定宽度序贯置信区间估计渐近性质的重要基础。同时,在文中,进行了一些计算机模拟试验,证明了左截断右删失数据下分位数估计的序贯方法是效的和精确的。 相似文献
13.
Milan Jasem 《Mathematica Slovaca》2007,57(2):107-118
In the paper isometries in pseudo MV-algebras are investigated. It is shown that for every isometry f in a pseudo MV-algebra
= (A, ⊕, −, ∼, 0, 1) there exists an internal direct decomposition
of
with
commutative such that
and
for each x ∈ A.
On the other hand, if
is an internal direct decomposition of a pseudo MV-algebra
= (A, ⊕, −, ∼, 0, 1) with
commutative, then the mapping g: A → A defined by
is an isometry in
and
.
相似文献
14.
Zheng Yan LIN Sung Chul LEE 《数学学报(英文版)》2006,22(2):535-544
Let {Xn,n ≥ 0} be an AR(1) process. Let Q(n) be the rescaled range statistic, or the R/S statistic for {Xn} which is given by (max1≤k≤n(∑j=1^k(Xj - ^-Xn)) - min 1≤k≤n(∑j=1^k( Xj - ^Xn ))) /(n ^-1∑j=1^n(Xj -^-Xn)^2)^1/2 where ^-Xn = n^-1 ∑j=1^nXj. In this paper we show a law of iterated logarithm for rescaled range statistics Q(n) for AR(1) model. 相似文献
15.
16.
Chen Debao 《分析论及其应用》1993,9(3):17-28
In this paper we study the degree of approximation by superpositions of a sigmoidal function. We mainly consider the univariate
case. If f is a continuous function, we prove that for any bounded sigmoidal function σ,
. For the Heaviside function H(x), we prove that
. If f is a continuous function of bounded variation, we prove that
and
. For he Heaviside function, the coefficient 1 and the approximation orders are the best possible. We compare these results
with the classical Jackson and Bernstein theorems, and make some conjectures for further study. 相似文献
17.
Jin-hong You Gemai Chen Min Chen Xue-lei JiangUniversity of Regina Regina Saskatchewan SS OA CanadaUniversity of Calgary Calgary Alberta TN N CanadaAcademy of Mathematics System Sciences Chinese Academy of Sciences Beijing China 《应用数学学报(英文版)》2003,19(3):363-370
Consider the partly linear regression model ,where yi's are responses, xi = (xi1, xi2,…,xip)' and ti ∈T are known and nonrandom design points, T is a compact set in the real line is an unknown parameter vector, g(·) is an unknown function and {Ei} isa linear process, i.e., random variables with zeromean and variance o2e. Drawing upon B-spline estimation of g(·) and least squares estimation of 0, we construct estimators of the autocovariances of {Ei}- The uniform strong convergence rate of these estimators to their true values is then established. These results not only are a compensation for those of [23], but also have some application in modeling error structure. When the errors {Ei} are an ARMA process, our result can be used to develop a consistent procedure for determining the order of the ARMA process and identifying the non-zero coefficients of the process. Moreover, our result can be used to construct the asymptotically efficient estimators for parameters in the ARMA error process. 相似文献
18.
F. M. Ragab 《Annali di Matematica Pura ed Applicata》1961,56(1):301-311
Summary The integrals
and
, where n is any positive integer, are evaluated in terms ofMacRobert E-functions and generalized hypergeometric functions. 相似文献
19.
Summary Letm
n, p
denote thep-th quantile based onn observations and let λ
p
denote the population quantile. In this paper consistency of the bootstrap estimate of variance of
is established. 相似文献
20.
Bin Heng SONG Huai Yu JIAN 《数学学报(英文版)》2005,21(5):1183-1190
We establish the existence of fundamental solutions for the anisotropic porous medium equation, ut = ∑n i=1(u^mi)xixi in R^n × (O,∞), where m1,m2,..., and mn, are positive constants satisfying min1≤i≤n{mi}≤ 1, ∑i^n=1 mi 〉 n - 2, and max1≤i≤n{mi} ≤1/n(2 + ∑i^n=1 mi). 相似文献