Hill估计的重对数律

设{x_n,n≥1}是i.i.d.序列,分布函数具有形式F(x)=1-(L(x))/(x~(1/O)),x>0,其中L(x)是缓慢变化函数,0相似文献   

解色散方程u_t=au_(xxx)的一族绝对稳定的高精度差分格式

1.引言 建立KdV方程u_t+uu_x+u_(xxx)=0的差分格式,在某种程度上可看作是方程u_t+uu_x=0和u_t+u_(xxx)=0的叠加.方程u_t+uu_x=0的差分格式已为人们所熟悉,而色散方程u_t=au_(xxx)的差分格式,仅在[1—3]中讨论过.     

Hill估计的重对数律

设{X_n,n≥1}是 i.i.d.序列,分布函数具有形式 F(x)=1-,x>0,其中 L(x)是缓慢变化函数,0相似文献   

重尾扰动下近非平稳自回归模型的Bootstrap推断

考虑近非平稳一阶自回归模型,Xt=θXt-1+ut,其中θn=1-γ/n,γ为一固定常数,{ut}为一重尾随机扰动项.对θn及其最小二乘估计(θ)n,采用bootstrap再抽样方法逼近(θ)n-θn的分布,并证明了该再抽样方法的渐近有效性.     

带有对流项Sobolev方程的基于两个变换的Crank-Nicolson分裂正定混合有限元方法(英文)

本文研究和讨论了含对流项二阶Sobolev方程的一个新的分裂正定混合有限元方法.引入两个变换:q=u_t和σ=α(x)▽u+b(x)▽u_t,解关于▽u的常微分方程σ=α(x)▽u+b(x)▽u_t,将Sobolev方程转换成含有三个变量的一阶积分微分系统.在这个积分微分系统中,关于实际压力σ的方程是独立对称正定的,并可以独立于变量u和q=u_t求解,然后可以求解出变量u和q.推导了半离散和Crank-Nicolson全离散先验误差估计和稳定性.最后,通过一些数值结果验证了新的分裂正定混合有限元方法的可行性.     

紧带边曲面上的Abel定理

设F是格为g的紧带边曲面,它的边界围道为б_1,…,б_n.б_i方向被取定为相对于Riemann曲面F是正的。定理设δ是F上的一个零维链,它的系数和为m;k_1…,k_n为n个整数,满足k_1+…k_n=m.那末,存在一个在б_i上绝对值为1,幅角改变量为2k_(iπ)(i=1,…,n),并以δ为除子的F上的半纯函数的充要条件是:在F上存在一个一维链c,它的边界可以表示为     

一类高阶非线性波动型方程整体解的存在性和指数衰减性

研究了一类带有阻尼和源项的高阶非线性波动方程u_(tt)+A+u_t+aAu_t=b|u|~(q-1)u的初边值问题,这里A=(-△)m,m≥1是一个自然数,a≥0,b 0和q1是实数通过构造稳定集证明了这个问题整体解的存在,并应用乘子方法建立了整体解的指数衰减估计同时,在初始能量非负和a=0的条件下,得到了解在有限时间内发生爆破.     

含奇异项的Schrodinger-Poisson系统正解的多重性

本文研究如下含奇异项的Schr?dinger-Poisson系统{u=φ=0,/-ΔФ=u^2,-Δu=φu=|u|^(p-2)u+λu^(=γ),x∈ЭΩ,x∈Ω,x∈Ω,正解的存在性,其中ΩСR^(3)是光滑有界域,λ是正参数,γ∈(0,1),p∈(2,6).首先将"扰动"技巧用以解决带奇异项问题所对应泛函在零点处不可微的难点,其次应用Ekeland变分原理和山路引理得到该问题对应的扰动泛函存在局部极小和山路型的临界点,最后通过估计序列有一致的下界并对扰动取极限后得到两个正解的存在性.     

KdVKS方程的局部适定性（英文）

本文研究了KdVKS方程u_t+δ?_x~3u+μ(?_x~4u+?_x~2u)+α(?_xu)~2=0的Cauchy问题.利用Tao的[k;Z]乘子范数估计的方法,在Sobolev空间Hs(R),s-1中证明了初值问题的局部适定性,结论改进了现有的Biagioni等的结果.     

等差数列的两个判定方法

本文给出等差数列的两个判定方法,并举例说明其应用。 1.通项公式判定法:数列{a_n}为等差数列的充要条件是a_n=k_n+b.(k,b为常数) 证:若{a_n}是公差为d的等差数列,则a_n=a_1+(n-1)d=dn+(a_1-d),记d=k,a_1-d=b,∴a_n=kn+。若a_n=kn+b,(k,b为常数),则a_(n+1)-a_n=k(n+1)+b-(kn+l)=k, (n=1,2,…) 故{a_n}是等差数列。 2.前几项和判定法:数列{a_n}为等差数列的充要条件是S_n=an~2+bn,(a,b为常数) 证:若{a_n}是等差数列,则S_n=na_1+n(n-1)/2 d=(d/2)n~2+(2n_1-d)n/2     

SIMEX Estimation for Composite Quantile Regression Model with Measurement Error

Composite quantile regression model with measurement error is considered. The SIMEX estimators of the unknown regression coefficients are proposed based on the composite quantile regression. The proposed estimators not only eliminate the bias caused by measurement error, but also retain the advantages of the composite quantile regression estimation. The asymptotic properties of the SIMEX estimation are proved under some regular conditions. The finite sample properties of the proposed method are studied by a simulation study, and a real example is analyzed.     

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??Composite quantile regression model with measurement error is considered. The SIMEX estimators of the unknown regression coefficients are proposed based on the composite quantile regression. The proposed estimators not only eliminate the bias caused by measurement error, but also retain the advantages of the composite quantile regression estimation. The asymptotic properties of the SIMEX estimation are proved under some regular conditions. The finite sample properties of the proposed method are studied by a simulation study, and a real example is analyzed.     

Composite hierachical linear quantile regression

Multilevel （hierarchical） modeling is a generalization of linear and generalized linear modeling in which regression coefficients are modeled through a model, whose parameters are also estimated from data. Multilevel model fails to fit well typically by the use of the EM algorithm once one of level error variance （like Cauchy distribution） tends to infinity. This paper proposes a composite multilevel to combine the nested structure of multilevel data and the robustness of the composite quantile regression, which greatly improves the efficiency and precision of the estimation. The new approach, which is based on the Gauss-Seidel iteration and takes a full advantage of the composite quantile regression and multilevel models, still works well when the error variance tends to infinity, We show that even the error distribution is normal, the MSE of the estimation of composite multilevel quantile regression models nearly equals to mean regression. When the error distribution is not normal, our method still enjoys great advantages in terms of estimation efficiency.     

Efficient estimation and variable selection for infinite variance autoregressive models

In this paper, a self-weighted composite quantile regression estimation procedure is developed to estimate unknown parameter in an infinite variance autoregressive (IVAR) model. The proposed estimator is asymptotically normal and more efficient than a single quantile regression estimator. At the same time, the adaptive least absolute shrinkage and selection operator (LASSO) for variable selection are also suggested. We show that the adaptive LASSO based on the self-weighted composite quantile regression enjoys the oracle properties. Simulation studies and a real data example are conducted to examine the performance of the proposed approaches.     

Estimation and test procedures for composite quantile regression with covariates missing at random

In this paper, we study the weighted composite quantile regression (WCQR) for general linear model with missing covariates. We propose the WCQR estimation and bootstrap test procedures for unknown parameters. Simulation studies and a real data analysis are conducted to examine the finite performance of our proposed methods.     

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Most regression modeling is based on traditional mean regression which results in non-robust estimation results for non-normal errors. Compared to conventional mean regression, composite quantile regression (CQR) may produce more robust parameters estimation. Based on a composite asymmetric Laplace distribution (CALD), we build a Bayesian hierarchical model for the weighted CQR (WCQR). The Gibbs sampler algorithm of Bayesian WCQR is developed to implement posterior inference. Finally, the proposed method are illustrated by some simulation studies and a real data analysis.     

部分线性单指标模型的复合分位数回归及变量选择

本文提出复合最小化平均分位数损失估计方法 (composite minimizing average check loss estimation,CMACLE)用于实现部分线性单指标模型(partial linear single-index models,PLSIM)的复合分位数回归(composite quantile regression,CQR).首先基于高维核函数构造参数部分的复合分位数回归意义下的相合估计,在此相合估计的基础上,通过采用指标核函数进一步得到参数和非参数函数的可达最优收敛速度的估计,并建立所得估计的渐近正态性,比较PLSIM的CQR估计和最小平均方差估计(MAVE)的相对渐近效率.进一步地,本文提出CQR框架下PLSIM的变量选择方法,证明所提变量选择方法的oracle性质.随机模拟和实例分析验证了所提方法在有限样本时的表现,证实了所提方法的优良性.     

Composite quantile regression for single-index models with asymmetric errors

For the single-index model, a composite quantile regression technique is proposed in this paper to construct robust and efficient estimation. Theoretical analysis reveals that the proposed estimate of the single-index vector is highly efficient relative to its corresponding least squares estimate. For the single-index vector, the proposed method is always valid across a wide spectrum of error distributions; even in the worst case scenario, the asymptotic relative efficiency has a lower bound 86.4 %. Meanwhile, we employ weighted local composite quantile regression to obtain a consistent and robust estimate for the nonparametric component in the single-index model, which is adapted to both symmetric and asymmetric distributions. Numerical study and a real data analysis can further illustrate our theoretical findings.     

An effective method to reduce the computational complexity of composite quantile regression

In this article, we aim to reduce the computational complexity of the recently proposed composite quantile regression (CQR). We propose a new regression method called infinitely composite quantile regression (ICQR) to avoid the determination of the number of uniform quantile positions. Unlike the composite quantile regression, our proposed ICQR method allows combining continuous and infinite quantile positions. We show that the proposed ICQR criterion can be readily transformed into a linear programming problem. Furthermore, the computing time of the ICQR estimate is far less than that of the CQR, though it is slightly larger than that of the quantile regression. The oracle properties of the penalized ICQR are also provided. The simulations are conducted to compare different estimators. A real data analysis is used to illustrate the performance.     

Modal Regression Based on Nonparametric Quantile Estimator

Modal regression based on nonparametric quantile estimator is given. Unlike the traditional mean and median regression, modal regression uses mode but not mean or median to represent the center of a conditional distribution, which helps the model to be more robust for outliers, asymmetric or heavy-taileddistribution. Most of solutions for modal regression are based on kernel estimation of density. This paper studies a new solution for modal regression by means of nonparametric quantile estimator. This method builds on the fact that the distribution function is the inverse of the quantile function, then the flexibility of nonparametric quantile estimator is utilized to improve the estimation of modal function. The simulations and application show that the new model outperforms the modal regression model via linear quantile function estimation.