误差为鞅差序列的回归函数估计的收敛速度

当误差为鞅差序列时,研究固定设计点列情形下非参数回归函数一般权函数的非参数估计,并在一些基本条件下给出了估计的一致最优强收敛速度．     

误差为鞅差序列的回归函数估计的收敛速度

当误差为鞅差序列时,研究了固定设计点列情形下非参数回归函数一般权函数的非参数估计,并在一些基本条件下给出了估计的一致最优强收敛速度.     

半参数回归模型参数估计的收敛速度

没有半参数回归模型Y=X’β g(T) e,其中(X,T)为取值于R~p×[0,1]上的随机向量,β为p维未知参数向量,g是定义在[0,1]上的未知函.e为随机误差,Ee=0,Ee~2=σ~2>0,且(X,T)与σ独立.参数β和σ~2的估计量(?)_n和(?)_n~2通常可利用非参数的权函数估计法与参数的最小二乘方法的结合得到.本文对核函数的情形得到了(?)_n和(?)_n~2的精确的收敛速度——重对数律.所施条件则与证明(?)_n和(?)_n~2的渐近正态性时施加的条件一致.又本文的证明方法对一般的权函数也适用.     

误差为鞅差序列的半参数回归模型估计的相合性

设半参数回归模型Ｙ（ｎ）ｉ＝β·ｘ（ｎ）ｉ＋ｇ（ｔ（ｎ）ｉ）＋Ｅ（ｎ）ｉ,ｉ＝１,２,…,ｎ,本文由最小二乘法和一般加权方法定义的β、ｇ（ｔ）的估计量βｎ,ｇｎ（ｔ）,在误差为鞅差序列下获得了βｎ,ｇｎ（ｔ）的ｒ（≥２）阶平均相合性．     

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。     

鞅差误差序列下半参数EV回归模型的近邻估计

本文研究了误差为鞅差序列的条件下的一维半参数EV回归模型.利用两步估计的方法构造了参数分量和非参数分量的近邻估计,并且分别证明了估计量的L2相合性和强相合性,从而推广了在普通半参数回归模型已有的相关结论.     

半参数回归模型的近邻估计——鞅差误差序列情形

在鞅差误差序列下,给出了半参数回归模型中有关参数β和g(t)的近邻估计,研究了估计量的相合性,在相当一般的条件下,得到了理想的结果。     

固定设计下半参数回归模型参数估计的收敛速度

考虑固定设计下的半参数回归模型：yi=xiβ＋g（ti）＋ei，i=1，…，n．其中{ei}为随机误差，且Ee1=0，Ee12=σ2＞0，对利用通常采用的非参数权函数法结合最小二乘法得到的参数β和σ2的估计量和，本文在适当条件下得到了和的精确的收敛速度-重对数律．     

鞅差时间序列半参数回归模型的小波估计

用小波方法研究了误差为滑动平均鞅差序列的半参数回归模型,得到了小波估计量的矩收敛速度及强收敛性.     

误差为鞅差序列的非参数回归模型的完全相合性

在误差为鞅差序列的条件下,利用截尾方法及鞅差序列的指数不等式,研究了非参数回归模型P-C估计量的完全收敛性,且得到了完全收敛的收敛速度.     

Limit theory for random coefficient first-order autoregressive process under martingale difference error sequence

Phillips and Magdalinos (2007) [1] gave the asymptotic theory for autoregressive time series with a root of the form ρ_n=1+c/k_n, where k_n is a deterministic sequence. In this paper, an extension to the more general case where the coefficients of an AR(1) model is a random variable and the error sequence is a sequence of martingale differences is discussed. A conditional least squares estimator of the autoregressive coefficient is derived and shown to be asymptotically normal. This extends the result of Phillips and Magdalinos (2007) [1] for stationary and near-stationary cases.     

严格伪压缩映象的Ishikawa 迭代序列的收敛率估计

It is shown that any fixed point of each l.ipschitzian, strictly pseudocontractive mapping 7“ on a closed convex subset K of a Banach space X may be norm approximated by Ishikawa iterative procedure. The argument in this paper provides a convergence rate estimate.Moreover the result in this paper improves, generalizes and summarizes some important and elegant recent results.     

Asymptotic distributions of regression and autoregression coefficients with martingale difference disturbances

In this paper a form of the Lindeberg condition appropriate for martingale differences is used to obtain asymptotic normality of statistics for regression and autoregression. The regression model is y_t = Bz_t + v_t. The unobserved error sequence {v_t} is a sequence of martingale differences with conditional covariance matrices {Σ_t} and satisfying sup_{t=1,…, n} {v′_tv_tI(v′_tv_t>a) |z_t, v_t−1, z_t−1, …} 0 as a → ∞. The sample covariance of the independent variables z₁, …, z_n, is assumed to have a probability limit M, constant and nonsingular; max_t=1,…,nz′_tz_t/n 0. If (1/n)Σ_t=1ⁿΣ_t Σ, constant, then √nvec( _n−B) N(0,M⁻¹Σ) and _n Σ. The autoregression model is x_t = Bx_{t − 1} + v_t with the maximum absolute value of the characteristic roots of B less than one, the above conditions on {v_t}, and (1/n)Σ_t=max(r,s)+1(Σ_tv_t−1−rv′_t−1−s) δ_rs(ΣΣ), where δ_rs is the Kronecker delta. Then √nvec( _n−B) N(0,Γ⁻¹Σ), where Γ = Σ_{s = 0}^∞B^sΣ(B′)^s.     

An estimate of the convergence rate in the central limit theorem for two-parameter martingale differences

We present an estimate of the rate of convergence to the normal law of the least squares estimator of the regression coefficient for a random field which is a two-parameter martingale difference sequence.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 8, pp. 1138–1141, August, 1992.     

Weighted least-squares estimators of parametric functions of the regression coefficients under a general linear model

The weighted least-squares estimator of parametric functions K β under a general linear regression model { y, X b, s²S }{\{ {\bf y},\,{\bf X \beta}, \sigma^2{\bf \Sigma} \}} is defined to be K[^(b)]{{\bf K}{\hat{\bf {\beta}}}}, where [^(b)]{\hat{{\bf \beta}}} is a vector that minimizes (y − X β)′V(y − X β) for a given nonnegative definite weight matrix V. In this paper, we study some algebraic and statistical properties of K[^(b)]{{\bf K}\hat{{\bf \beta}}} and the projection matrix associated with the estimator, such as, their ranks, unbiasedness, uniqueness, as well as equalities satisfied by the projection matrices.     

Mean quadratic error of an estimate of splines of first order in a model of linear regression

We study the mean quadratic error of an estimate of splines of the first order, which is obtained by the method of least squares under the assumption that the data represents a superposition of proper values of a spline and a white noise. A quantitative formula for the quadratic mean error is found and its asymptotics is investigated.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 3, pp. 429–432, March, 1991.     

Mean quadratic error of an estimate of splines of first order in a model of linear regression

We study the mean quadratic error of an estimate of splines of the first order, which is obtained by the method of least squares under the assumption that the data represents a superposition of proper values of a spline and a white noise. A quantitative formula for the quadratic mean error is found and its asymptotics is investigated.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 3, pp. 429–432, March, 1991.     

An error estimate for the finite difference scheme for one-phase obstacle problem

In this paper we consider the finite difference scheme approximation for one-phase obstacle problem and obtain an error estimate for this approximation.     

A guaranteed estimate of the parameter reconstruction error in a linear difference system

We consider the problemon reconstructing parameters of a linear autonomous difference discrete-time system from a finite set of approximate observations of the system state. We impose minimal assumptions on the observation error. Namely, we assume that the absolute value of the difference between the state vector and the corresponding observation is componentwise bounded from above by some given constant. Under these assumptions, we propose a theorem on the minimal guaranteed estimate of the parameter reconstruction error and describe the corresponding reconstruction algorithm.