Chebyshev半迭代的预处理法

在Chebyshev半迭代的基础上建立一种预处理迭代法,经过预处理的迭代算法,其渐近收敛速度有几何级的增长。对任一给定的整数q≥2,在一定条件下,可以通过选择适当的预处理矩阵。

关于参数矩阵的线性经验Bayes估计

设X为p×q随机矩阵,θ为p×q参数矩阵,且θ有先验分布G(Vec(θ)),给定θ,X有条件密度f(Vec(X)｜Vec(θ)).选取矩阵损失L(D(X),θ)=(D(X)-θ)′(D(X)-θ),并在风险矩阵的迹的大小比较标准下讨论θ的线性经验tr Bayes估计及其渐近性质.获得经验tr Bayes估计D tr(X)= X+U(X- X),及具有o(N-1δ-2N)的渐近收敛速度.

基于亏量方程的多重网格解法(英文)

基于亏量方程提出了一种生成多重网格插值公式的新方法 ,新插值公式充分利用了粗网格的信息 ,因而具有更高的精度 .对Poisson方程 ,各向异性方程 ,双调和方程 ,甚至三维问题的数值试验表明 ,新插值公式改进了多重网格法的渐近收敛速度 ,节省了存储空间及计算时间 .

Parallel EOI algorithm with different insertion schemes

A parallel embedding overlapped iterative (EOI) algorithm about classicimplicit equations with asymmetric Saul'yev schemes (CIS-EOI) to solve one-dimensional diffusionequations is discussed to improve the properties of the segment classic implicit iterative (SCII)algorithm. The structure of CIS-EOI method is given and the stability of scheme and convergence ofiteration are proved by matrix method. The property of gradual-approach convergence is alsodiscussed. It has been shown that the convergent rate is faster and the property of gradual-approachconvergence also becomes better with the increasing of the net point in subsystems than with theSCII algorithm. The simulation examples show that the parallel iterative algorithm with a differentinsertion scheme CIS-EOI is more effective.

Estimator of a change point in single index models

This paper considers the problem of change point in single index models.In order to obtain asymptotically valid confidence intervals for the estimation of the change point,the convergence rate and asymptotic distribution of the change point estimate is studied.Some simulation results are presented which show that the numerical performance of our estimator is satisfactory.

Convergence and optimality of BS-type discrete hedging strategy under stochastic interest rate

We focus on the asymptotic convergence behavior of the hedging errors of European stock option due to discrete hedging under stochastic interest rates. There are two kinds of BS-type discrete hedging differ in hedging instruments: one is the portfolio of underlying stock, zero coupon bond, and the money market account (Strategy BSI); the other is the underlying stock, zero coupon bond (Strategy BSII). Similar to the results of the deterministic interest rate case, we show that convergence speed of the discounted hedging errors is 1/2-order of trading frequency for both strategies. Then, we prove each of the BS-type strategy is not only locally optimal, but also globally optimal under the corresponding measure. Finally, we give some numerical examples to illustrate the results. All the discussion is based on non-arbitrage condition and zero transaction cost.

Sieve M-estimator for a semi-functional linear model

We propose sieve M-estimator for a semi-functional linear model in which the scalar response is explained by a linear operator of functional predictor and smooth functions of some real-valued random variables.Spline estimators of the functional coefficient and the smooth functions are considered,and by selecting appropriate knot numbers the optimal convergence rate and the asymptotic normality can be obtained under some mild conditions.Some simulation results and a real data example are presented to illustrate the performance of our estimation method.

Conditional Quantile Estimation with Truncated,Censored and Dependent Data

This paper deals with the conditional quantile estimation based on left-truncated and right-censored data.Assuming that the observations with multivariate covariates form a stationary α-mixing sequence,the authors derive the strong convergence with rate,strong representation as well as asymptotic normality of the conditional quantile estimator.Also,a Berry-Esseen-type bound for the estimator is established.In addition,the finite sample behavior of the estimator is investigated via simulations.

Consistency of Chi-Squared Test with Varying Number of Classes

The classical chi-squared goodness of fit test assumes the number of classes is fixed,meanwhile the test statistic has a limiting chi-square distribution under the null hypothesis.It is well known that the number of classes varying with sample size in the test has attached more and more attention.However,in this situation,there is not theoretical results for the asymptotic property of such chi-squared test statistic.This paper proves the consistency of chi-squared test with varying number of classes under some conditions.Meanwhile,the authors also give a convergence rate of KolmogorovSimirnov distance between the test statistic and corresponding chi-square distributed random variable.In addition,a real example and simulation results validate the reasonability of theoretical result and the superiority of chi-squared test with varying number of classes.