共查询到20条相似文献,搜索用时 9 毫秒
1.
将三次样条理论与再生核理论相结合,利用再生核函数巧妙地构造了三次样条函数空间的一组基底.基于三次样条插值的高收敛特点,得到了微分方程边值问题近似解的一种新的求解方法.数值算例展现出算法简单、有效. 相似文献
2.
In this paper, we consider spaces of cubic C^1-spline on a class of triangulations. By using the inductive algorithm, the posed Lagrange interpolation sets are constructed for cubic spline space. It is shown that the class of triangulations considered in this paper are nonsingular for S1/3 spaces. Moreover, the dimensions of those spaces exactly equal to L. L. Schuraaker's low bounds of the dimensions. At the end of this paper, we present an approach to construct triangulations from any scattered planar points, which ensures that the obtained triangulations for S1/3 space are nonsingular. 相似文献
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Let X
1
,...,X
n
be a random sample drawn from distribution function F(x) with density function f(x) and suppose we want to estimate X(x). It is already shown that kernel estimator of F(x) is better than usual empirical distribution function in the sense of mean integrated squared error. In this paper we derive integrated squared error of kernel estimator and compare the error with that of the empirical distribution function. It is shown that the superiority of kernel estimators is not necessarily true in the sense of integrated squared error. 相似文献
6.
立方幂补数除数函数的均值 总被引:7,自引:0,他引:7
王阳 《数学的实践与认识》2004,34(12):144-148
设 n是正整数 ,S(n)是 n的立方幂补数 ,τ(n)表示 n的除数函数 .本文的主要目的是探讨∑n xτ(S(n) )n 和 ∑n xτ(S(n) ) 的渐近性质 ,得到了两个渐近公式 ,进一步解决 F.Smarandache教授提出的第2 8个问题 . 相似文献
7.
介绍了logistic曲线参数估计的一种新方法,它是利用三次样条插值函数求导代替logistic曲线在这一点的导数值,进而利用最小二乘法得出参数的估计值,通过实例分析表明本文提出的方法比一般的三点法估计的参数值k再用线性化方法估计的参数值b,c,拟合精度更高. 相似文献
8.
寇吉垚 《应用数学与计算数学学报》2010,24(2):119-123
本文主要讨论了生存函数的插值问题,使用了非节点端点的三次样条插值和α-power插值两种方法对生存函数进行了插值,并与传统的三种插值假设:死亡均匀分布假设、常数死亡力假设、Balducci假设做了比较.另外,我们对α-power插值中的α进行了拟合,并通过误差分析表明先对α拟合后再进行α-power插值,其插值的误差将会变得非常小,几乎与样条插值相仿. 相似文献
9.
应用三次多项式样条函数解一组四阶单侧、障碍、接触边值问题,取半结点为网格点,并增加了边界方程,应用方法解文献中的数值例子,说明了方法的高效性,数值结果也显示了方法的优越性. 相似文献
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11.
Constance van Eeden 《Annals of the Institute of Statistical Mathematics》1985,37(1):461-472
Summary Asymptotic properties of the mean integrated squared error (MISE) of kernel estimators of a density function, based on a sampleX
1, …,X
n, were obtained by Rosenblatt [4] and Epanechnikov [1] for the case when the densityf and its derivativef′ are continuous. They found, under certain additional regularity conditions, that the optimal choiceh
n0 for the scale factorh
n=Kn−α is given byh
n0=K0n−1/5 withK
0 depending onf and the kernel; they also showed that MISE(h
n0)=O(n−4/5) and Epanechnikov [1] found the optimal kernel.
In this paper we investigate the robustness of these results to departures from the assumptions concerning the smoothness
of the density function. In particular it is shown, under certain regularity conditions, that whenf is continuous but its derivativef′ is not, the optimal value of α in the scale factor becomes 1/4 and MISE(h
n0)=O(n−3/4); for the case whenf is not continuous the optimal value of α becomes 1/2 and MISE(h
n0)=O(n−1/2). For this last case the optimal kernel is shown to be the double exponential density.
Supported by the Natural Sciences and Engineering Research Council of Canada under Grant Nr. A 3114 and by the Gouvernement
du Québec, Programme de formation de chercheurs et d'action concertée. 相似文献
12.
Xiaojing Xiang 《Annals of the Institute of Statistical Mathematics》1995,47(1):105-117
A necessary condition for the asymptotic normality of the sample quantile estimator isf(Q(p))=F(Q(p))>0, whereQ(p) is thep-th quantile of the distribution functionF(x). In this paper, we estimate a quantile by a kernel quantile estimator when this condition is violated. We have shown that the kernel quantile estimator is asymptotically normal in some nonstandard cases. The optimal convergence rate of the mean squared error for the kernel estimator is obtained with respect to the asymptotically optimal bandwidth. A law of the iterated logarithm is also established.This research was partially supported by the new faculty award from the University of Oregon. 相似文献
13.
本文在模糊Lagrange插值的基础上,引进了模糊牛顿插值公式及其适定性定理和求法。并针对“非结点”型边界条件给出了模糊样条函数的具体表示。 相似文献
14.
Alexander A. Georgiev 《Statistics & probability letters》1984,2(1):45-50
The problem of the estimation of functions and their derivatives from noisy observations is considered. The new kernel estimate is shown to be consistent in the mean square sense and an exact bound on the uniform mean squared error is given. An application to the system identification is discussed. 相似文献
15.
??In this paper, semiparametric estimation of a regression function in the third order partially linear autoregressive model with first order autoregressive errors is mainly studied. We suppose that the regression function has a parametric framework, and use the conditional least squares method to obtain the parameter estimators. Then semiparametric estimators of the regression function can be given by combining with the nonparametric kernel function adjustment. Furthermore, under certain conditions, the consistency of the estimators is proved. Finally, simulation research is presented to evaluate the
effectiveness of the proposed method. 相似文献
16.
J. K. Ghorai 《Annals of the Institute of Statistical Mathematics》1991,43(4):747-760
The problem of estimating a smooth quantile function, Q(·), at a fixed point p, 0 < p < 1, is treated under a nonparametric smoothness condition on Q. The asymptotic relative deficiency of the sample quantile based on the maximum likelihood estimate of the survival function under the proportional hazards model with respect to kernel type estimators of the quantile is evaluated. The comparison is based on the mean square errors of the estimators. It is shown that the relative deficiency tends to infinity as the sample size, n, tends to infinity. 相似文献
17.
设(Xi,Yi)1≤i≤n为来自二元总体(X,Y)的平稳,φ-混合样本,记m(x)△E(Y│X=x),m(x)的一种递推型核估计为mn(x)=n∑i=1hi^-1Yik((x-Xi)/hi)/n∑j=1h^-1jk(x-Xj)/hj)。本文在一定的条件下证明了(n/(n∑j=1h^-1j)^1/2)(mn(x1)-m(x1),mn(x2)-m(x2),...mn(xr0)-m(xr0))′依分布收 相似文献
18.
Let (X
t
)
t⩾0 be the n-dimensional hyperbolic Brownian motion, that is the diffusion on the real hyperbolic space having the Laplace–Beltrami operator as its generator. The aim of the paper is to derive the formulas for the Gegenbauer
transform of the Poisson kernel and the Green function of the ball for the process (X
t
)
t⩾0. Under additional hypotheses we prove integral representations for the Poisson kernel. This yields explicit formulas in and spaces for the Poisson kernel and the Green function as well.
相似文献
19.
We give a formula for the heat kernel of a degenerate elliptic partial differential operator L on ℝ2 related to the Heisenberg group. The formula is derived by means of pseudo-differential operators of the Weyl type, {i.e.},
Weyl transforms, and the Fourier–Wigner transforms of Hermite functions, which form an orthonormal basis for L2(ℝ2). Using the heat kernel, we give a formula for the Green function of L. Applications to the global hypoellipticity of L in the sense of tempered distributions, the ultracontractivity and hypercontractivity of the strongly continuous one-parameter
semigroup e−tL, t > 0, are given.
Communicated by B.-W. Schulze (Potsdam)
Mathematics Subject Classifications (2000): 47G30, 47E05. 相似文献
20.
TheBergmanKernelFunctionandFullGroupofHolomorphicAutomorphismonaReinhardtDomainGuanBinxin(管冰辛)WangAn(王安)(Dept.ofMath.,Capital... 相似文献