Custom Epoch Estimation for Surveys

The paper provides a method for generating epoch estimates for time series survey data, allowing for different periods of time (or even point estimates) according to user demand. The method uses a modified kriging estimator, which suppresses the contribution of sampling error variability in order to guarantee that custom epoch estimates have an interpolation property. For the veteran population variable of the American Community Survey, we utilize a simple Brownian Motion model of the population process and derive the modified kriging estimator for this case. The tuning parameters of this population model can be calibrated to the data via simple formulas. We illustrate the application of this method to the generation of point estimates of veteran population, an important objective for Veterans Affairs.     

数值解法中的单元形状函数技巧

本文介绍从一组互不相关的函数中推导数值法中单元形状函数的简便而有效的算法,以特定的一维内插方法导出各种二维、三维的内插方法,它们对奇异性的模拟是有益的;为了适用于延伸到无限远的单元,假设形状函数类似于Lagrange多项式,但包含了一个按指数衰减的项。     

具扩充Jacobi结点的Lagrange插值逼近

研究了以扩充Jacobi多项式(1+x)Vn(x)的零点为基点的Lagrange插值多项式Ln(f,x)逼近/k)的一些问题.     

A bayesian estimator for the dependence function of a bivariate extreme‐value distribution

Any continuous bivariate distribution can be expressed in terms of its margins and a unique copula. In the case of extreme‐value distributions, the copula is characterized by a dependence function while each margin depends on three parameters. The authors propose a Bayesian approach for the simultaneous estimation of the dependence function and the parameters defining the margins. They describe a nonparametric model for the dependence function and a reversible jump Markov chain Monte Carlo algorithm for the computation of the Bayesian estimator. They show through simulations that their estimator has a smaller mean integrated squared error than classical nonparametric estimators, especially in small samples. They illustrate their approach on a hydrological data set.     

一种三维复杂介质波前时间的高精度数值算法

基于水平集的波前扩展算法,如FMM(Fast Marching Method)、GMM(Group Marching Method)，作为一类计算复杂介质波前时间的有效方法而被广泛使用。该类算法都是基于程函方程的有限差分格式来计算波传播时间，在介质离散单元尺寸较大的情况下，计算精度较低。为提高波前时间的计算精度，在一个长方体单元内，将任意点的波传播时间用已知节点上波前时间的插值函数表示，然后根据Fermat原理确定未知节点上的波前时间，再结合高效率的GMM算法，形成了一种计算三维复杂介质波前时间的有效算法。数值模拟实验表明，与原GMM算法相比，该算法大大提高了波前时间的计算精度，同时具有很强的稳定性和适应性。     

三向剖分域上的二元二次样条插值与逼近

本文主要用B－网方法研究了平行六边形区域在三向剖分△_6~3下的二元二次样条插值的存在性、唯一性及逼近度问题。在本文末尾我们举例说明本方法是可行的。     

连分式算法插值顺序的有效安排

n节连分式算法是一个实用的一维搜索方法。构造连分式插位函数时,部分分母的计算在该算法中占有较大的比重,本文通过对插值点先后顺序的有效安排,使得部分分母的计算量下降近三分之一。最后,对该算法可能遇到的数值困难提供了一个实施方案。     

Theory & Methods: Krige,Smooth, Both or Neither?

Both kriging and non-parametric regression smoothing can model a non-stationary regression function with spatially correlated errors. However comparisons have mainly been based on ordinary kriging and smoothing with uncorrelated errors. Ordinary kriging attributes smoothness of the response to spatial autocorrelation whereas non-parametric regression attributes trends to a smooth regression function. For spatial processes it is reasonable to suppose that the response is due to both trend and autocorrelation. This paper reviews methodology for non-parametric regression with autocorrelated errors which is a natural compromise between the two methods. Re-analysis of the one-dimensional stationary spatial data of Laslett (1994) and a clearly non-stationary time series demonstrates the rather surprising result that for these data, ordinary kriging outperforms more computationally intensive models including both universal kriging and correlated splines for spatial prediction. For estimating the regression function, non-parametric regression provides adaptive estimation, but the autocorrelation must be accounted for in selecting the smoothing parameter.     

Hermite插值的逐步迭代算法

通过定义插值因子,对Hermite插值问题依次考虑满足插值结点x1;x1,x2;x1,x2,x3;…;x1,x2,…,xs处的插值条件,采用逐步迭代的方法构造插值多项式,得到插值多项式系数的递推公式.给出的数值例子验证了所给算法的有效性.     

非线性回归分析的一种有理逼近

利用有理插值逼近回归函数,把最小二乘法和插值技术结合起来,充分利用已知信息,达到最佳逼近,通过实例,获得了很好的效果。