部分线性模型中估计的渐近正态性

考虑回归模型其中是未知函数，（ｘ＿ｉ，ｔ＿ｉ，ｕ＿ｉ）是固定非随机设计点列，β是待估参数，ｅ＿ｉ是随机误差。基于ｇ（·）及ｆ（·）的一类非参数估计（包括常见的核估计和近邻估计），我们构造了β的加权最小二乘估计，并证得了最小二乘估计和加权最小二乘估计的渐近正态性。     

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。     

纵向数据下部分线性EV模型的渐近性质

研究了纵向数据下部分线性EV函数关系模型.应用一般非参数权函数法和广义最小二乘法给出了未知参数β,误差方差σ2以及未知函数g(·)的估计.在一般的条件下,证明了β,σ2估计的渐近正态性,同时也给出了未知函数g(·)估计的收敛速度,其结果是独立数据情形下相应结果的推广.     

误差为鞅差序列的部分线性模型中估计的渐近正态性

考虑回归模型yi=xiβ g(ti) ei,i=1,2,…,n,其中(xi,ti)是固定非随机设计点列,g(.)是未知函数,β是待估参数,ei是随机误差且关于非降σ-代数列{Fi,i≥1}为鞅差序列,且满足E(e2n|Fn-1)-σ2=op(1),n→∞,其中0<2σ<∞为未知常数,本文基于g(.)的一类非参数估计的β的最小二乘估计■和2σ的估计量■,在适当条件下证明了其具有渐近正态性,从而推广了[1]在ei为iid情形下的结果.     

线性模型中最小一乘估计的渐近正态性

考虑线性回归模型(1.1),其中β。为未知的回归系数向量,e₁,e₂,…独立且各有中位数零,定义β。的最小一乘估计为极值问题(1.2)的解,本文首先论述了文献中关于渐近正态性的工作,并指出其中错误所在,然后在最一般的条件下证明了的渐近正态性(定理1).特别,对{经X_i}施加的条件与最小二乘估计的渐近正态性条件相同(见(1.6)式),说明这一条件是无可改进的。     

一个半参数回归模型的渐近正态性

考虑半多数回归模型yi＝xiβ＋g（xi）＋εi，lin，这里xi是具有已知方差σ的独立同分布随机样本，εi是具有零均值和有限方基σ2的独立同分布随机误差．β，g和εi的分布密度是未知的．本文作者构造了一个具有更小渐近方差的β的一个渐近正态估计．     

部分线性变系数模型Backfitting估计的渐近性质

作为部分线性模型与变系数模型的推广,部分线性变系数模型是一类应用广泛的数据分析模型.利用Backfitting方法拟合这类特殊的可加模型,可得到模型中常值系数估计量的精确解析表达式,该估计量被证明是n~(1/2)相合的.最后通过数值模拟考察了所提估计方法的有效性.     

随机删失场合部分线性模型中的核光滑方法

考虑模型Ｙ＝Ｘβ＋ｇ（Ｔ）＋ｅ。其中ｇ为［０，１］上的未知光滑函数，β为一维待估参数，为不可观察误差．当观察受到随机删失时，本文基于核光滑和综合数据方法导出了β和ｇ的估计βｎ＊和ｇｎ＊证明了βｎ＊的渐近正态性，并获得了ｇｎ＊的非参数收敛速度Ｏ（ｎ－１／３）     

广义线性模型中极大拟似然估计的渐近正态性与强相合性

在广义线性模型中,当λn→∞,supi≥1 E||ei||2+α<∞(对某个α>0), 且其他一些正则条件满足时,证明了极大拟似然估计(MQLE)是渐近正态的;进 一步假定 ,证明了MQLE是强相合的,其中λn(λn) 是∑i=1 nZiZiT的最小(最大)特征根,Zi是有界的p×q回归系数,ei=yi-Eyi,yi 是q×1响应变量．也讨论了设计阵Zi是自适应的情形．     

Consistency and normality of Huber-Dutter estimators for partial linear model

For partial linear model Y = Xτβ0 g0(T) with unknown β0 ∈ Rd and an unknown smooth function g0, this paper considers the Huber-Dutter estimators of β0, scale σ for the errors and the function g0 approximated by the smoothing B-spline functions, respectively. Under some regularity conditions, the Huber-Dutter estimators of β0 and σ are shown to be asymptotically normal with the rate of convergence n-1/2 and the B-spline Huber-Dutter estimator of g0 achieves the optimal rate of convergence in nonparametric regression. A simulation study and two examples demonstrate that the Huber-Dutter estimator of β0 is competitive with its M-estimator without scale parameter and the ordinary least square estimator.     

Asymptotic normality of double-indexed linear permutation statistics

The paper provides sufficient conditions for the asymptotic normality of statistics of the form a _ijb_RiRj, wherea _ijandb _ijare real numbers andR _iis a random permutation.     

Asymptotic normality of the extreme quantile estimator based on the POT method

The POT (Peaks-Over-Threshold) approach consists in using the generalized Pareto distribution (GPD) to approximate the distribution of excesses over thresholds. In this Note, we propose extreme quantile estimators based on this method. We establish their asymptotic normality under suitable general assumptions. To cite this article: J. Diebolt et al., C. R. Acad. Sci. Paris, Ser. I 341 (2005).     

Asymptotic normality of H-L estimators based on dependent data

LetX ₁,X ₂, ... be a strictly stationary φ-mixing sequence of r.v.'s with a common continuous cdfF. Let θ be a location parameter ofF. We prove the asymptotic normality of a class of Hodges-Lehmann estimators of θ under various regularity conditions on the mixing number φ and the underlyingF. We also establish the asymptotic linearity of signed rank statistics in the parameter θ. Our results also enable us to study the effect of φ-dependence on the asymptotic power of signed rank tests for testingH ₀: θ=0 againstH _n :θ=θ ₀ n ^?1/2,θ ₀≠0. Finally these results are shown to remain valid for strongly mixing processes {X _i } also.     

The Dantzig selector for a linear model of diffusion processes

In this paper, a linear model of diffusion processes with unknown drift and diagonal diffusion matrices is discussed. We will consider the estimation problems for unknown parameters based on the discrete time observation in high-dimensional and sparse settings. To estimate drift matrices, the Dantzig selector which was proposed by Candés and Tao in 2007 will be applied. We will prove two types of consistency of the Dantzig selector for the drift matrix; one is the consistency in the sense of \(l_q\) norm for every \(q \in [1,\infty ]\) and another is the variable selection consistency. Moreover, we will construct an asymptotically normal estimator for the drift matrix by using the variable selection consistency of the Dantzig selector.

     

Asymptotic normality of wavelet estimator in heteroscedastic regression model

The following heteroscedastic regression model Y_i=g(x_i) σ_ie_i(1≤i≤n)is considered,where it is assumed thatσ_i~2=f(u_i),the design points(x_i,u_i)are known and nonrandom,g and f are unknown functions.Under the unobservable disturbance e_i form martingale differences,the asymptotic normality of wavelet estimators of g with f being known or unknown function is studied.     

Asymptotic normality of spectral estimates

The asymptotic normality of some spectral estimates, including a functional central limit theorem for an estimate of the spectral distribution function, is proved for fourth-order stationary processes. In contrast to known results it is not assumed that all moments exist or that the process is linear. The data are allowed to be tapered. Using some recent results on the central limit theorem for stationary processes, corollaries are obtained for strong and φ-mixing sequences and linear transformations of martingale differences.     

Asymptotic normality and strong consistency of maximum quasi-likelihood estimates in generalized linear models

In a generalized linear model with q x 1 responses, the bounded and fixed (or adaptive) p × q regressors Zi and the general link function, under the most general assumption on the minimum eigenvalue of ZiZ'i,the moment condition on responses as weak as possible and the other mild regular conditions, we prove that the maximum quasi-likelihood estimates for the regression parameter vector are asymptotically normal and strongly consistent.