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在多项式插值理论及样条逼近中,Hermite插值多项式余项的讨论是很重要的。在[1,2]中,给出了一系列Hermite插值多项式余项的表达式,特别是各阶导数余项的表达式。还运用这些表达式讨论了样条函数,给出其余项估计和渐近展开。 随着样条理论的发展,已经用其它函数系代替多项式组成了各种样条函数空间,其中最引人注目的是ECT样条。Pruess讨论的张力样条及C.A.Micchelli讨论的?-样 相似文献
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本文主要研究广义非参数模型B样条Bayes估计 .将回归函数按照B样条基展开 ,我们不具体选择节点的个数 ,而是节点个数取均匀的无信息先验 ,样条函数系数取正态先验 ,用B样条函数的后验均值估计回归函数 .并给出了回归函数B样条Bayes估计的MCMC的模拟计算方法 .通过对Logistic非参数回归的模拟研究 ,表明B样条Bayes估计得到了很好的估计效果 相似文献
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1.前言 关于系数用偶阶导数表示的(2n 1)次样条函数,使用性能较好,但其存在性与唯一性迄今尚未给出证明.这种样条函数与一般的奇次多项式样条函数一样,当n≥2时,方程组的系数矩阵已不具有明显的主对角元素占优,致使J.H.Ahlberg等人说,直接依赖系数矩阵的性质来证明多项式样条函数的存在性是十分困难的,即便是对于 相似文献
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提出了广义变系数模型函数系数的一种新的估计方法.我们用B样条函数逼近函数系数,不具体选择节点的个数,而是节点个数取均匀的无信息先验,样条函数系数取正态先验,用Bayesian模型平均的方法估计各个函数系数.这种估计方法一个主要特点是允许各个函数系数所需节点个数的后验分布不同,因此允许不同函数系数使用不同的光滑参数.另外,本文还给出了Bayesian B样条估计的计算方法,并通过模拟例子,说明广义变系数模型的函数系数可以由Bayesian B样条估计方法得到很好的估计. 相似文献
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中国科学院数学研究所样条函数小组 《数学的实践与认识》1979,(1)
多项式样条函数是样条函数理论中最基本的内容,它的应用也最广.多项式 B 样条函数(以下简称为 B 样条)在多项式样条函数理论中起着极其重要的作用,并且已成为构造曲线、曲面与计算多项式样条的最为有效的工具. 相似文献
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本文考虑变系数测量误差模型的估计问题,得到该模型变系数函数修正的最小二乘B-样条估计,同时得到非参数函数估计的最优收敛速度.模拟结果表明该方法是有效的. 相似文献
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分别以Bemstain多项式以及准均匀B样条为基函数,来逼近线性高振荡常微分方程。通过求解基函数对应的系数方程组,得到方程的近似解。通过数值实验表明用准均匀B样条函数的逼近效果要比Bemstain多项式要好。 相似文献
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The asymptotic normality of polynomial Pitman estimators for the location parameter is proved, the principal term of the formula for the variance of these estimators is obtained, and certain characterization problems are considered that occur in the study of polynomial Pitman estimators.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 43, pp. 30–39, 1974. 相似文献
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An autoregressive-moving average model in which all roots of the autoregressive polynomial are reciprocals of roots of the moving average polynomial and vice versa is called an all-pass time series model. All-pass models generate uncorrelated (white noise) time series, but these series are not independent in the non-Gaussian case. An approximate likelihood for a causal all-pass model is given and used to establish asymptotic normality for maximum likelihood estimators under general conditions. Behavior of the estimators for finite samples is studied via simulation. A two-step procedure using all-pass models to identify and estimate noninvertible autoregressive-moving average models is developed and used in the deconvolution of a simulated water gun seismogram. 相似文献
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本文研究了空间数据变系数部分线性回归中的分位数估计. 模型中的参数估计量通过未知系数函数的分段多项式逼近得到, 而未知系数函数的估计量通过将参数估计量代入模型中并通过局部线性逼近得到. 文中推导了未知参数向量估计量的渐近分布, 并建立了未知系数函数估计量在内点及边界点的渐近分布. 通过Monte Carlo 模拟研究了估计量的有限样本性质. 相似文献
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In this paper, a fixed design regression model where the errors follow a strictly stationary process is considered. In this model the conditional mean function and the conditional variance function are unknown curves. Correlated errors when observations are missing in the response variable are assumed. Four nonparametric estimators of the conditional variance function based on local polynomial fitting are proposed. Expressions of the asymptotic bias and variance of these estimators are obtained. A simulation study illustrates the behavior of the proposed estimators. 相似文献
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Asymptotic Properties of Backfitting Estimators 总被引:2,自引:0,他引:2
Jean D. Opsomer 《Journal of multivariate analysis》2000,73(2):10328
When additive models with more than two covariates are fitted with the backfitting algorithm proposed by Buja et al. [2], the lack of explicit expressions for the estimators makes study of their theoretical properties cumbersome. Recursion provides a convenient way to extend existing theoretical results for bivariate additive models to models of arbitrary dimension. In the case of local polynomial regression smoothers, recursive asymptotic bias and variance expressions for the backfitting estimators are derived. The estimators are shown to achieve the same rate of convergence as those of univariate local polynomial regression. In the case of independence between the covariates, non-recursive bias and variance expressions, as well as the asymptotically optimal values for the bandwidth parameters, are provided. 相似文献
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Zhan-Qian Lu 《Journal of multivariate analysis》1996,59(2):187-205
Nonparametric regression estimator based on locally weighted least squares fitting has been studied by Fan and Ruppert and Wand. The latter paper also studies, in the univariate case, nonparametric derivative estimators given by a locally weighted polynomial fitting. Compared with traditional kernel estimators, these estimators are often of simpler form and possess some better properties. In this paper, we develop current work on locally weighted regression and generalize locally weighted polynomial fitting to the estimation of partial derivatives in a multivariate regression context. Specifically, for both the regression and partial derivative estimators we prove joint asymptotic normality and derive explicit asymptotic expansions for their conditional bias and conditional convariance matrix (given observations of predictor variables) in each of the two important cases of local linear fit and local quadratic fit. 相似文献
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In this paper, we consider the weighted local polynomial calibration estimation and imputation estimation of a non-parametric function when the data are right censored and the censoring indicators are missing at random, and establish the asymptotic normality of these estimators. As their applications, we derive the weighted local linear calibration estimators and imputation estimations of the conditional distribution function, the conditional density function and the conditional quantile function, and investigate the asymptotic normality of these estimators. Finally, the simulation studies are conducted to illustrate the finite sample performance of the estimators. 相似文献
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The problem of asymptotically efficient estimation of the density of invariant measure of a diffusion process is considered.
The efficient estimator is defined with the help of the minimax lower bound on the risk of all estimators. We show that the
local–time and kernel–type estimators are asymptotically efficient for the loss functions with polynomial majorants. The asymptotic
behavior of a wide class of unbiased estimators with the same limit variances is also discussed.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
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Alexandre Leblanc 《Annals of the Institute of Statistical Mathematics》2012,64(5):919-943
It is a known fact that some estimators of smooth distribution functions can outperform the empirical distribution function in terms of asymptotic (integrated) mean-squared error. In this paper, we show that this is also true of Bernstein polynomial estimators of distribution functions associated with densities that are supported on a closed interval. Specifically, we introduce a higher order expansion for the asymptotic (integrated) mean-squared error of Bernstein estimators of distribution functions and examine the relative deficiency of the empirical distribution function with respect to these estimators. Finally, we also establish the (pointwise) asymptotic normality of these estimators and show that they have highly advantageous boundary properties, including the absence of boundary bias. 相似文献
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《Stochastic Processes and their Applications》2002,97(2):307-340
We consider semiparametric fractional exponential (FEXP) estimators of the memory parameter d for a potentially non-stationary linear long-memory time series with additive polynomial trend. We use differencing to annihilate the polynomial trend, followed by tapering to handle the potential non-invertibility of the differenced series. We propose a method of pooling the tapered periodogram which leads to more efficient estimators of d than existing pooled, tapered estimators. We establish asymptotic normality of the tapered FEXP estimator in the Gaussian case with or without pooling. We establish asymptotic normality of the estimator in the linear case if pooling is used. Finally, we consider minimax rate-optimality and feasible nearly rate-optimal estimators in the Gaussian case. 相似文献