实数编码人工免疫算法概率强收敛速度估计研究

取代传统的状态转移矩阵特征值估计方法,运用随机过程相关理论,对实数编码人工免疫算法的收敛速度估计进行了研究,该方法从满足人工免疫算法概率强收敛的必要条件出发,将其作为一般人工免疫算法符合的充分条件,提出了一种实数编码人工免疫算法指数速度概率强收敛的估计新方法.该方法以种群中最佳抗体的最终收敛为判断依据,避免了传统估计方法过于保守的不足,可用于一类人工免疫算法的收敛性和收敛速度的判断,在人工免疫算法实际应用中如何优化其收敛速度具有一定理论参考意义.

函数按二阶Sturm-Liouville算子特征函数展开的收敛速度估计

本文用计算围道积分和使用特征函数渐近式的方法得到函数按二阶Sturm-Liouville 算子特征函数展开前 n 项和与其余弦级数的前项和之差的两个估计,这两个估计分别适用于有界可测函数和有界变差函数的特征展开。这样,我们能从函数的余弦级数的收敛速度估计得到函数的特征函数展开的收敛速度估计。

Hopfield型连续神经网络指数收敛速度的估计

讨论了Hopfield型连续神经网络的指数收敛速度问题 ,从理论上得到了新的局部指数收敛条件 .与以往的结果相比 ,本文导出指数收敛的阶更大 ,指数收敛的速度可更快 .文中还给出了数值举例 .

高维情形下铁磁与反铁磁泛函可正则化极小元的C^(1,α)收敛性

研究一类与铁磁和反铁磁相关的泛函模型,其中p∈(n-1,n),n≥3.利用局部分析技巧,讨论了这类泛函的正则性估计,证明了泛函可正则化极小元的W1l,o cp收敛性,并利用Euler方程解的正则性估计,得到此泛函径向极小元的C1,α收敛性及收敛速度的估计.

Empirical Bayes Estimation for the Parameter of Two-dimen sional One-side Truncated Distribution Families with Linex Loss

In this paper, we construct the EB estim ation for the parameter of the two-dimensional one side truncat ed distribution fam ilies using Linex loss. The convergence rate of EB estimation is given and it is shown that the proposed empirical Bayes estimaiton can be arbitrarily close to 1 under certain conditions.

关于C^k类缺插值样条

关于缺插值样条,近几年来国内外讨论很多,但一般都较为具体。本文的目的是统一处理文献[1]～[22],系统讨论C^h类缺插值样条。我们不仅得到样条的精确收敛速度估计,而且对各种情形均给出逐项渐近展开。

Empirical Bayes Absolute Error Loss Estimation for Parameter of One-Side Truncation Distribution Families

In this paper we propose an absolute error loss EB estimator for parameter of one-side truncation distribution families. Under some conditions we have proved that the convergence rates of its Bayes risk is o, where 0<λ,r≤1,Mn≤lnln n (for large n),Mn→∞ as n→∞.

Strong Convergence Rates of Double Kernel Estimates of Conditional Desity Under Stationary Sequences

In the paper,we study the strong convergence rates of double kernel estimates of conditional density under stationary sequences.

On the L_p Convergence Rate of Kernel Estimates for the Nonparametric Regression Function

Let (X,Y) be an R^d×R^1 valued random vector (X_1,Y_1),…, (X_n,Y_n) be a random sample drawn from (X,Y), and let E|Y|<∞. The regression function m(x)=E(Y|X=x) for x∈R^d is estimated by where, and h_n is a positive number depending upon n only, nad K is a given nonnegative function on R^d. In the paper, we study the L_p convergence rate of kernel estimate m_n(x) of m(x) in suitable condition, and improve and extend the results of Wei Lansheng.

A Generalization of (0, M) Interpolation

In this paper we introduce a new kind of interpolation of function with period 2π and establish the rate of convergence.The usual Birkhoff interpolation is a special case of our new interpolation as a linnit case.

Convergence Rates of Wavelet Estimators in Semiparametric Regression Models Under NA Samples

Consider the following heteroscedastic semiparametric regression model：where {Xi, 1 〈 i 〈 n} are random design points, errors {ei, 1 〈 i 〈 n} are negatively associated （NA） random variables, （r2 = h（ui）, and {ui} and {ti} are two nonrandom sequences on [0, 1]. Some wavelet estimators of the parametric component β, the non- parametric component g（t） and the variance function h（u） are given. Under some general conditions, the strong convergence rate of these wavelet estimators is O（n- 1 log n）. Hence our results are extensions of those re, sults on independent random error settings.

Convergence error estimates of the Crank-Nicolson scheme for solving decoupled FBSDEs

In this work, we theoretically analyze the convergence error estimates of the Crank-Nicolson （C-N） scheme for solving decoupled FBSDEs. Based on the Taylor and ItS-Taylor expansions, the Malliavin calculus theory （e.g., the multiple Malliavin integration-by-parts formula）, and our new truncation error cancelation techniques, we rigorously prove that the strong convergence rate of the C-N scheme is of second order for solving decoupled FBSDEs, which fills the gap between the second-order numerical and theoretical analysis of the C-N scheme.

Partial functional linear quantile regression

This paper studies estimation in partial functional linear quantile regression in which the dependent variable is related to both a vector of finite length and a function-valued random variable as predictor variables. The slope function is estimated by the functional principal component basis. The asymptotic distribution of the estimator of the vector of slope parameters is derived and the global convergence rate of the quantile estimator of unknown slope function is established under suitable norm. It is showed that this rate is optirnal in a minimax sense under some smoothness assumptions on the covariance kernel of the covariate and the slope function. The convergence rate of the mean squared prediction error for the proposed estimators is also established. Finite sample properties of our procedures are studied through Monte Carlo simulations. A real data example about Berkeley growth data is used to illustrate our proposed methodology.

ESTIMATION ON SEMIVARYING COEFFICIENT MODELS WITH DIFFERENT DEGREES OF SMOOTHNESS

Semivarying coefficient models are frequently used in statistical models.In this paper,under the condition that the coefficient functions possess different degrees of smoothness,a two-stepmethod is proposed.In the case,one-step method for the smoother coefficient functions cannot beoptimal.This drawback can be repaired by using the two-step estimation procedure.The asymptoticmean-squared error for the two-step procedure is obtained and is shown to achieve the optimal rate ofconvergence.A few simulation studies are conducted to evaluate the proposed estimation methods.

Weighted estimation of single index models with right censored responses

In this paper, the unknown link function, the direction parameter, and the heteroscedastic variance in single index models are estimated by the random weight method under the random censorship, respectively. The central limit theory and the convergence rate of the law of the iterated logarithm for the estimator of the direction parameter are derived, respectively. The optimal convergence rates for the estimators of the link function and the heteroscedastic variance are obtained. Simulation results support the theoretical results of the paper.

ASYMPTOTICS FOR THE DISTRIBUTION FUNCTION ESTIMATORS OF THE ERRORS IN SEMI-PARAMETRIC REGRESSION MODELS

This paper considers the convergence rates for nonparametric estimators of the error distribution in semi-parametric regression models. By establishing some general laws of the iterated logarithm, it shows that the rates of convergence of either the empirical distribution or a smoothed version of the empirical distribution function matches exactly the rates obtained for an independent sample from the error distribution.