关于误差方差估计渐近正态收敛速度的上,下界

考虑线性回归模型 Y_■=x_4~′β+e_■ i=1,2,…设误差序列■,i≥1满足条件:e_■ i≥1 i.i.d.,Ee_1=0,Ee_1~2=σ~2>0,∞>Var e_1~2=τ~2>0。记■_n~2=1/(n-r){sum from j=1 to n e■-sum from k=1 to r (sum from j=1 to n a_(akj)■_j)~2} δ(n)=τ~(-2)E(■_1~2-σ~2)~2I_((|■-σ~2|≥■τ)+τ~(-3)n~(1/2)|E(■_1~2-σ~2)~3I_((|■_1~2-σ~2|<(nτ)~(1/2))+τ~(-4)n~(-1)E■_1~2-σ~2)~4I_((|■-σ~2|0使得■|P(■_n~2-σ~2)/(Var■_n~2)~(1/2))≤x)-Φ(x)|≤C(δ(n)+n~(-1/2)) ■|P(■_n~2-σ~2)/(Var■_n~2)~(1/2))≤x)-Φ(x)|+n~(-1/2)≥C_1δ(n)。     

广义线性回归拟似然估计的强相合性

本文研究了广义线性模型y=μ(x'β0)+e中形如∑xi(yi-μ(xiβ))=0的拟似然方程,在一定的条件下证明了当n充分大时此方程以概率1有解βn,得到了βn的强相合性和收敛速度.     

自适应设计广义线性回归多维拟似然估计的渐近正态性

本文研究了自适应设计下广义线性回归的拟似然方程∑ni=1xi(yi-μ(xi′β))=0,其中yi是q维向量,xi是p×q阶随机矩阵,在一定条件下证明了方程的解^βn具有渐进正态的性质.     

部分线性模型中参数估计的Bootstrap逼近

考虑回归模型 :yi=xiβ+g(ti) +σiei,1≤ i≤ n.其中 σ2i=f(ui) ,(xi,ti,ui)是固定非随机设计点列 ,f (· )和 g(· )是未知函数 ,β是待估参数 ,ei 是随机误差 .对文 [1 ]给出的基于 g(· )及 f(· )的一类非参数估计的β的最小二乘估计β^ n和加权最小二乘估计βn,本文通过重抽样的方法构造了 β^n 和 βn 的 Bootstrap统计量 β^ *n 和 β*n .证明了在给定原样本的条件下 ,n (β^ *n -β^ n)和 n (β*n -β^ n)分别与 n (β^ n-β)和 n (βn-β)有相同的渐近分布 .     

广义线性回归拟似然估计的强相合性

本文研究了广义线性模型g=μ(x'β0)+e中形如的拟似然方程,在一定的条件下证明了当n充分大时此方程以概率1有解βn,得到了βn的强相合性和收敛速度.     

广义线性回归拟似然估计的渐近正态性

研究了形如n∑i=1xi(yi-μ(xi′β))=0拟似然方程,在一定的条件下证明了拟似然估计βn的渐近正态性;并进一步证明了可用于β0大样本统计推断的渐近正态性结果．     

变换数据对线性模型拟合值的影响

一、引言考虑线性回归模型其中Y是n维观测向量,X是n×p阶段设计矩阵,且其秩为R(X)=p,β为p维未知参数向量,e为n维随机误差向量、对于模型(1.1),β的最小二乘估计(The Least Squares Estimate,以下简记为LS估计)     

一个有趣数列的单调性

利用不等式(π4(n-1)/2n 4(n+))^(1/2)1<∫_0^(π/2)sin^nxdx<(π(4n+5)/2 (n+1)(4n+3))^(1/2),对有趣数列{(n+c)^(1/2)∫_0^(π/2)sin^nxdx}的单调性再次进行了分析论证,并对已有结论进行了改进.     

随机截断下部分线性模型中参数估计的渐近性质

考虑部分线性回归模型Yi＝xiβ g(ti) σiej,i＝1，2，…，n其中σi^2＝／f(ui)．当Yi因受某种随机干扰而被右截断时，就截断分布巳知的情形，利用所获得的截断观察数据构造了β，g，f的估计量β^～n，g^～n，f^～n，并在一定条件下，证明了β^～n的渐近正态性，同时得到了g^～n，f^～n的最优收敛速度。     

误差为鞅差序列的半参数回归模型估计的相合性

设半参数回归摸型Y^(n)=β·χi(1) g(l1^(n)) 1 ^(n),i=1,2,…．n,本由最小二乘法和一般加权方法定义的β、g(t)的怙计量βn,gn(t)．在误差为鞅差序列下获得了βn gn(f)的r(≥2)阶平均相合性。     

Projektive Skalen,Tschebyscheff-Polynome und Fibonacci-Zahlen

Summary. Let $\widehat{\widehat T}_n$ and $\overline U_n$ denote the modified Chebyshev polynomials defined by $\widehat{\widehat T}_n (x) = {T_{2n + 1} \left(\sqrt{x + 3 \over 4} \right) \over \sqrt{x + 3 \over 4}}, \quad \overline U_{n}(x) = U_{n} \left({x + 1 \over 2}\right) \qquad (n \in \mathbb{N}_{0},\ x \in \mathbb{R}).$ For all $n \in \mathbb{N}_{0}$ define $\widehat{\widehat T}_{-(n + 1)} = \widehat{\widehat T}_n$ and $\overline U_{-(n + 2)} = - \overline U_n$, furthermore $\overline U_{-1} = 0$. In this paper, summation formulae for sums of type $\sum\limits^{+\infty}_{k = -\infty} \mathbf a_{\mathbf k}(\nu; x)$ are given, where $\bigl(\mathbf a_{\mathbf k}(\nu; x)\bigr)^{-1} = (-1)^k \cdot \Bigl( x \cdot \widehat{\widehat T}_{\left[k + 1 \over 2\right] - 1} (\nu) +\widehat{\widehat T}_{\left[k + 1 \over 2\right]}(\nu)\Bigr) \cdot \Bigl(x \cdot \overline U_{\left[k \over 2\right] - 1} (\nu) + \overline U_{\left[k \over 2\right]} (\nu)\Bigr)$ with real constants $ x, \nu $. The above sums will turn out to be telescope sums. They appear in connection with projective geometry. The directed euclidean measures of the line segments of a projective scale form a sequence of type $(\mathbf a_{\mathbf k} (\nu;x))_{k \in \mathbb{Z}}$ where $ \nu $ is the cross-ratio of the scale, and x is the ratio of two consecutive line segments once chosen. In case of hyperbolic $(\nu \in \mathbb{R} \setminus] - 3,1[)$ and parabolic $\nu = -3$ scales, the formula $\sum\limits^{+\infty}_{k = -\infty} \mathbf a_{\mathbf k} (\nu; x) = {\frac{1}{x - q_{{+}\atop(-)}}} - {\frac{1}{x - q_{{-}\atop(+)}}} \eqno (1)$ holds for $\nu > 1$ (resp. $\nu \leq - 3$), unless the scale is geometric, that is unless $x = q_+$ or $x = q_-$. By $q_{\pm} = {-(\nu + 1) \pm \sqrt{(\nu - 1)(\nu + 3)} \over 2}$ we denote the quotient of the associated geometric sequence.

     

基于RBF和PSO的双喉道气动矢量喷管优化设计

本文探索了一种能多变量综合优化的方法,即对喷管进行参数化设计后,用均匀试验设计(UED)将试验样本均匀散布在设计区间内,求出各性能参数后,利用径向基神经网络(RBF)对试验样本进行拟合,再用粒子群算法(PSO)对训练好的神经网络进行寻优,找出了更好的双喉道气动矢量喷管设计参数组合。数值模拟结果显示,优化后的双喉道气动矢量喷管的矢量角有了明显提高。试验表明这种优化方法具有很好的优化能力,可以用来对喷管几何外形进行参数优化。      

$\mathbb{C}^n$中一类星形映射子族的增长定理及推广的Roper-Suffridge算子

在有界星形圆形域上定义了一个新的星形映射子族, 它包含了$\alpha$阶星形映射族和$\alpha$阶强星形映射族作为两个特殊子类. 给出了此类星形映射子族的增长定理和掩盖定理. 另外, 还证明了Reinhardt域$\Omega_{n,p_{2},\cdots,p_{n}}$上此星形映射子族在Roper-Suffridge算子 \begin{align*} F(z)=\Big(f(z_{1}),\Big(\frac{f(z_{1})}{z_{1}}\Big)^{\beta_{2}}(f'(z_{1}))^{\gamma_{2}}z_{2},\cdots, \Big(\frac{f(z_{1})}{z_{1}}\Big)^{\beta_{n}}(f'(z_{1}))^{\gamma_{n}}z_{n}\Big)' \end{align*} 作用下保持不变, 其中 $\Omega_{n,p_{2},\cdots,p_{n}}=\{z\in {\mathbb{C}}^{n}:|z_1|^2+|z_2|^{p_2}+\cdots + |z_n|^{p_n}<1\}$, $p_{j}\geq1$, $\beta_{j}\in$ $[0, 1]$, $\gamma_{j}\in[0, \frac{1}{p_{j}}]$满足$\beta_{j}+\gamma_{j}\leq1$, 所取的单值解析分支使得 $\big({\frac{f(z_{1})}{z_{1}}}\big)^{\beta_{j}}\big|_{z_{1}=0}=1$, $(f'(z_{1}))^{\gamma_{j}}\mid_{{z_{1}=0}}=1$, $j=2,\cdots,n$. 这些结果不仅包含了许多已有的结果, 而且得到了新的结论.     

广义KdV--BO方程的Cauchy问题的局部适定性的改进结果

In this paper we prove that the Cauchy problem associated with the generalized KdV-BO equation ut ＋ uxxx ＋ λH（uxx） ＋ u^2ux = 0, x ∈ R, t ≥ 0 is locally wellposed in Hr^s（R） for 4/3 〈r≤2, b〉1/r and s≥s（r）= 1/2- 1/2r. In particular, for r = 2, we reobtain the result in [3].     

On the pullback of an arithmetic theta function

In this paper, we describe a relationship between the simplest examples of arithmetic theta series. The first of these are the weight 1 theta series ${\widehat{\phi}_{\mathcal C}(\tau)}$ defined using arithmetic 0-cycles on the moduli space ${\mathcal C}$ of elliptic curves with CM by the ring of integers ${O_{\kappa}}$ of an imaginary quadratic field. The second such series ${\widehat{\phi}_{\mathcal M}(\tau)}$ has weight 3/2 and takes values in the arithmetic Chow group ${\widehat{{\rm CH}}^1(\mathcal{M})}$ of the arithmetic surface associated to an indefinite quaternion algebra ${B/\mathbb{Q}}$ . For an embedding ${O_\kappa \rightarrow O_B}$ , a maximal order in B, and a two sided O _B -ideal Λ, there is a morphism ${j_\Lambda:{\mathcal C} \rightarrow {\mathcal M}}$ and a pullback ${j_\Lambda^*: \widehat{{\rm CH}}^1(\mathcal{M}) \rightarrow \widehat{{\rm CH}}^1(\mathcal C)}$ . Our main result is an expression for the pullback ${j^*_\Lambda \widehat{\phi}_{\mathcal M}(\tau)}$ as a linear combination of products of ${\widehat{\phi}_{\mathcal C}(\tau)}$ ’s and classical weight ${\frac{1}{2}}$ theta series.     

On the existence of full dimensional KAM torus for fractional nonlinear Schrodinger equation

In this paper,\ we study fractional nonlinear Schrodinger equation (FNLS) with periodic boundary condition $$ \textbf{i}u_{t}=-(-\Delta)^{s_{0}} u-V*u-\epsilon f(x)|u|^4u,\ ~~x\in \mathbb{T}, ~~t\in \mathbb{R}, ~~s_{0}\in (\frac12,1),~~~~~~~~~~~~~~~~~~~~~~~~~~~~(0.1) $$ where $(-\Delta)^{s_{0}}$ is the Riesz fractional differentiation defined in [21] and $V*$ is the Fourier multiplier defined by $\widehat{V*u}(n)=V_n\widehat{u}(n),\ V_n\in\left[-1,1\right],$ and $f(x)$ is Gevrey smooth. We prove that for $0\leq|\epsilon|\ll1$ and appropriate $V$,\ the equation (0.1) admits a full dimensional KAM torus in the Gevrey space satisfying $ \frac12e^{-rn^{\theta}}\leq \left|q_n\right|\leq 2e^{-rn^{\theta}}, \theta\in (0,1),$ which generalizes the results given by [8-10] to fractional nonlinear Schrodinger equation.     

由$q$-积分算子定义的某些亚纯函数类的Fekete-Szeg\"{o}问题

本文首先引入满足如下条件$$-\frac{qzD_{q}f(z)}{f(z)}\prec \varphi (z)$$和$$\frac{-(1-\frac{\alpha }{q})qzD_{q}f(z)+\alpha qzD_{q}[zD_{q}f(z)]}{(1-\frac{\alpha}{q})f(z)-\alpha zD_{q}f(z)}\prec \varphi (z)~(\alpha \in\mathbb{C}\backslash (0,1],\ 0相似文献   

带粗糙初始值向列型液晶流的适定性

考虑了R~n上n(n≥2)维向列型液晶流(u,d)当初值属于Q_α~(-1)(R~n,R~n)×Q_α(R~n,S~2)(其中α∈(0,1))时Cauchy问题的适定性,这里的Q_α(R~n)最早由Essen,Janson,Peng和Xiao(见[Essen M,Janson S,Peng L,Xiao J.Q space of several real variables,Indiana Univ Math J,2000,49:575-615])引入,是指由R~n中满足的所有可测函数f全体所组成的空间.上式左端在取遍Rn中所有以l(I)为边长且边平行于坐标轴的立方体I的全体中取上确界,而Q_α~(-1)(R~n):=▽·Q_α(R~n).最后证明了解(u,d)在类C([0,T);Q_(α,T)~(-1)(R~n,R~n))∩L_(loc)~∞((0,T);L~∞(R~n,R~n))×C([0,T);Q_α,T(R~n,S~2))∩L_(loc)~∞((0,T);W~(1,∞)(R~n,S~2))(其中0T≤∞)中是唯一的.     

Weighted Compact Commutator of Bilinear Fourier Multiplier Operator

Let T_σ be the bilinear Fourier multiplier operator with associated multiplier σ satisfying the Sobolev regularity that sup κ∈Z∥σ_κ∥W~s(R~(2n)) ∞ for some s ∈ (n, 2n]. In this paper, it is proved that the commutator generated by T_σ and CMO(R~n) functions is a compact operator from L~(p1)(R~n, w_1) × L~(p2)(R~n, w_2) to L~p(R~n, ν_w) for appropriate indices p_1, p_2, p ∈ (1, ∞) with1 p=1/ p_1 +1/ p_2 and weights w_1, w_2 such that w = (w_1, w_2) ∈ A_(p/t)(R~(2n)).