Wavelet Density Estimation of Censoring Data and Evaluate of Mean Integral Square Error with Convergence Ratio and Empirical Distribution of Given Estimator

Wavelet has rapid development in the current mathematics new areas. It also has a double meaning of theory and application. In signal and image compression, signal analysis, engineering technology has a wide range of applications. In this paper, we use wavelet method, for estimating the density function for censoring data. We evaluate the mean integrated squared error, convergence ratio of given estimator. Also, we obtain empirical distribution of given estimator and verify the conclusion by two simulation examples.

CONVERGENCE OF LOGARITHMIC MEANS OF MULTIPLE WALSH-FOURIER SERIES

Norlund logarithmic means of multiple Walsh-Fourier series acting from space L In^d-1 L （[0, 1）d）, d≥1 into space weak - LI（[0,1）^d） are studied. The maximal Orlicz space such that the Norlund logarithmic means of multiple Walsh-Fourier series for the functions from this space converge in d-dimensional measure is found.

CONVERGENCE OF A CLASS OF MEANS OF H^p FUNCTIONS(0

In this paper we study the convergence nf a class of means on H^p(G)(0<p<1),the means take the Bochner-Riesz means in[1],the generalized Bochner-Riesz means in[2],and the operators T^(Φ_r)in[3]as special cases.We obtain weak-type estimates for the associated maximal operators and the maximal mean boundedness for the means.

MEAN CONVERGENCE OF SOME POSITIVE OPERATORS

L'convergence with 0<p<infinity of the positive operators F.(da,f) and G.(da,f), introduced by Nevai P. [3], and Qn,8(da,f), introduced by Hermann T. and Vertesi P. [1] to f is an element of C[-1,1] is proved to hold for very general measures.

MEAN CONVERGENCE OF HERMITE-FEJER TYPE INTERPOLATION ON AN ARBITRARY SYSTEM OF NODES

In this paper sufficient conditions for mean convergence and rate of convergence of Hermite-Fejer type interpolation in the Lp norm on an arbitrary system of nodes are presented.

WEIGHTED MEAN CONVERGENCE OF HAKOPIAN INTERPOLATION ON THE DISK

In this paper, we study weighted mean integral convergence of Hakopian interpolation on the unit disk D. We show that the inner product between Hakopian interpolation polynomial Hn（f;x,y） and a smooth function g（x,y） on D converges to that of f（x,y） and g（x,y） on D when n →∞ , provided f（x,y） belongs to C（D） and all first partial derivatives of g（x,y） belong to the space LipM^α（0 〈 α ≤1）. We further show that provided all second partial derivatives of g（x,y） also belong to the space LipM^α and f（x,y） belongs to C^1 （D）, the inner product between the partial derivative of Hakopian interpolation polynomial δ/δx Hn（f;z,y） and g（x,y） on D converges to that between δ/δxf（x,y） and g（x,y） on D when n →∞. oo.

The Mean Convergence Order of Extended Hermite-Fejér Interpolation Operators

Weighted Lp mean convergence of Extended Hermite-Fejer operators based on the zeros of orthogonal polynomials with respct to the general weight and Jacobi weight is investigated. Suf ficient conditions for such convergence for all continuous functions are given.

MEAN CONVERGENCE OF HERMITE-FEJER TYPE INTERPOLATION

L' convergence of Hermite-Fejer interpolation and quasi-Hermite-Fejer interpolation based upon ze- ros of general orthogonal polynomials is investigated. This paper 'almost' characterizes such convergence for all continuous functions.

L^p CONVERGENCE OF CESRO MEANS ON SPHERE

Let R be r-dimensional Euclidean space with . Denote by the unit sphere in For we denote by (f) its Cesàro means of order for spherical harmonic expansions. The special value of is known as the critical one. For , we set This paper proves that N^co u holds for a,ty f e L,0 (log+ L)2~po (log+ log+ L)'(,0~', forth I > 1.

ON THE LOCALIZATION AND CONVERGENCE OF MULTIPLE FOURIER INTEGRAL BY BOCHNER-RIESZ MEANS

In this paper we consider lim _(R-) B_R^(f,x_0), in one case that f_x_0 (t) is a ABMV function on [0, ∞], and in another case that f∈L_(m-1)~1(R~) and x^k/~kf∈BV(R) when |k| = m-1 and f(x) = 0 when |x -x_0|<δ for some δ>0. Our theormes improve the results of Pan Wenjie ([1]).

Some Mean Convergence Theorems for the Maximum of Normed Double Sums of Banach Space Valued Random Elements

In this correspondence,we establish mean convergence theorems for the maximum of normed double sums of Banach space valued random elements.Most of the results pertain to random elements which are M-dependent.We expand and improve a number of particular cases in the literature on mean convergence of random elements in Banach spaces.One of the main contributions of the paper is to simplify and improve a recent result of Li,Presnell,and Rosalsky[Journal of Mathematical Inequalities,16,117–126(2022)].A new maximal inequality for double sums of M-dependent random elements is proved which may be of independent interest.The sharpness of the results is illustrated by four examples.

Some Improvement on Convergence Rates of Kernel Density Estimator

In this paper two kernel density estimators are introduced and investigated. In order to reduce bias, we intuitively subtract an estimated bias term from ordinary kernel density estimator. The second proposed density estimator is a geometric extrapolation of the first bias reduced estimator. Theoretical properties such as bias, variance and mean squared error are investigated for both estimators. To observe their finite sample performance, a Monte Carlo simulation study based on small to moderately large samples is presented.

On complete convergence in Marcinkiewicz-Zygmund type SLLN for random variables

We consider a generalization of Baum-Katz theorem for random variables satisfying some cover conditions.Consequently,we get the results for many dependent structures,such as END,ϱ^(*)mixing,ϱ^(-)mixing andφ-mixing,etc.

Theoretical convergence analysis of complex Gaussian kernel LMS algorithm

With the vigorous expansion of nonlinear adaptive filtering with real-valued kernel functions,its counterpart complex kernel adaptive filtering algorithms were also sequentially proposed to solve the complex-valued nonlinear problems arising in almost all real-world applications.This paper firstly presents two schemes of the complex Gaussian kernel-based adaptive filtering algorithms to illustrate their respective characteristics.Then the theoretical convergence behavior of the complex Gaussian kernel least mean square（LMS） algorithm is studied by using the fixed dictionary strategy.The simulation results demonstrate that the theoretical curves predicted by the derived analytical models consistently coincide with the Monte Carlo simulation results in both transient and steady-state stages for two introduced complex Gaussian kernel LMS algonthms using non-circular complex data.The analytical models are able to be regard as a theoretical tool evaluating ability and allow to compare with mean square error（MSE） performance among of complex kernel LMS（KLMS） methods according to the specified kernel bandwidth and the length of dictionary.

Convergence Rate of Estimator forNonparametric Regression Model under ρ-mixing Errors

In this paper, we investigate the nonparametric regression model based on ρ-mixing errors, which are stochastically dominated by a nonnegative random variable. Weobtain the convergence rate for the weighted estimator of unknown function g（x） in pth-mean, which yields the convergence rate in probability. Moreover, an example of the nearestneighbor estimator is also illustrated and the convergence rates of estimator are presented.

Convergence Properties of Piecewise Power Approximations

We address the problem of convergence of approximations obtained from two versions of the piecewise power-law representations arisen in Systems Biology. The most important cases of mean-square and uniform convergence are studied in detail. Advantages and drawbacks of the representations as well as properties of both kinds of convergence are discussed. Numerical approximation algorithms related to piecewise power-law representations are described in Appendix.

基于平均密度优化初始聚类中心的k-means算法

现有的基于密度优化初始聚类中心的k-means算法存在聚类中心的搜索范围大、消耗时间久以及聚类结果对孤立点敏感等问题,针对这些问题,提出了一种基于平均密度优化初始聚类中心的k-means算法adk-means。该算法将数据集中的孤立点划分出来,计算出剩余数据集样本的平均密度,孤立点不参与聚类过程中各类所含样本均值的计算;在大于平均密度的密度参数集合中选择聚类中心,根据最小距离原则将孤立点分配给离它最近的聚类中心,直至将数据集完整分类。实验结果表明,这种基于平均密度优化初始聚类中心的k-means算法比现有的基于密度的k-means算法有更快的收敛速度,更强的稳定性及更高的聚类精度,消除了聚类结果对孤立点的敏感性。

Mean Shift算法的收敛性分析

作为迭代算法,Mean Shift的收敛性研究是应用的基础,而Comaniciu和李乡儒分别证明了Mean Shift的收敛性,但证明过程存在错误.首先指出了Comaniciu和李乡儒的证明过程存在错误;然后,从数学上重新证明了Mean Shift算法的局部收敛性,并指出其收敛到局部极大值的条件;最后,从几何上举反例分析了Mean Shift的收敛性,并进行了深入比较和讨论.这为Mean Shift算法的深入研究及应用奠定了基础.

Mean Shift算法的收敛性讨论

作为一种有效的迭代算法,Mean Shift具有的良好的特性,在聚类分析、视觉跟踪、图像平滑和图像分割等领域得到广泛应用.李乡儒指出了Comuniciu关于算法收敛性证明中的错误,并给出了一个算法收敛的间接条件.但是用什么样的核函数、在什么条件下算法收敛仍然没有直接的结果.本文首先指出最近发表的一篇文献中关于MeanShift算法收敛条件及证明过程理解上的错误.然后对常用的核函数用于算法时的收敛性进行分析,得到了几个对算法扩展和应用有意义的结论.

基于共轭梯度法的快速Mean Shift图像分割

针对均值漂移算法收敛速度较慢的问题,本文提出了基于共轭梯度的快速均值漂移算法,并将其用于图像分割。该算法利用共轭梯度法简便,存储需求小,收敛速度介于最速下降法和牛顿法之间,具有较好的全局收敛性和较快的收敛速度的特点,通过交替执行均值漂移算法和共轭梯度算法提高经典均值漂移算法的收敛速度。对合成图像和真实图像的实验结果表明了新算法不但提高了经典均值漂移算法的速度,而且在进行图像分割时保持了良好的分割结果。