一个新的含参量Hilbert型不等式

应用权系数方法给出Hilbert型无穷级数的一个带有最佳常数的新的不等式，同时给出一些应用．     

Hilbert核奇异积分方程反演公式的推导

利用非齐次PR问题给出了Hilbert核奇异积分方程反演公式的推导。     

Estimating a covariance function having an un unknown scale kakameter

The structure of a family ρ of measures corresponding to a zero-mean Gaussian process with covariance αR(s,t) is discussed. When R itself is known (R and T completely arbitrary), it is shown that ρ is either homogeneous or composed of singular measures, depending on whether the reproducing kernel Hilbert space H(R,T) is finite- or infinite-dimensional. For the case dim H < ∞ the MLE α is given; when dim H = ∞ an almost sure discriminator is constructed. More generally, it is shown that when R itself depends upon a parameter θ (not necessarily a scalar) and certain broad assumptions are met, one may describe the orthogonal decomposition of P and estimate both a and θ.     

Predictive information and distance between past and future of a time series

A characterization for the nullity of the cosine angle between two subspaces of a Hilbert space is established. Given a time series x, we use this characterization in order to investigate the relationship between the notions of predictor space and distance between the information contained in the past and in the future of x. In particular, we prove that the predictor space of x coincides with the zero vector space {0} if and only if this distance achieves its maximum value.     

Location and scale parameter estimation from randomly censored data

The problem of location and scale parameter estimation from randomly censored data is analyzed through use of a regression model for the Kaplan-Meier quantlle process. Continuous time regression techniques are employed to construct estimators that are both asymptotically normal and efficient. Estimators with a particularly simple form are obtained for the Koziol-Green model for random censorship. In the event of no censoring the regression model, and resulting estimators, reduce to those proposed by Parzen (1979 a, b).     

非简谐振子湮没算符高次幂的广义本征态

构造了非简谐振子湮没算符高次幂的广义本征态，发现它们构成完备Ｈｉｌｂｅｒｔ空间．     

Testing for additivity and joint effects in multivariate nonparametric regression using Fourier and wavelet methods

We consider the problem of testing for additivity and joint effects in multivariate nonparametric regression when the data are modelled as observations of an unknown response function observed on a d-dimensional (d 2) lattice and contaminated with additive Gaussian noise. We propose tests for additivity and joint effects, appropriate for both homogeneous and inhomogeneous response functions, using the particular structure of the data expanded in tensor product Fourier or wavelet bases studied recently by Amato and Antoniadis (2001) and Amato, Antoniadis and De Feis (2002). The corresponding tests are constructed by applying the adaptive Neyman truncation and wavelet thresholding procedures of Fan (1996), for testing a high-dimensional Gaussian mean, to the resulting empirical Fourier and wavelet coefficients. As a consequence, asymptotic normality of the proposed test statistics under the null hypothesis and lower bounds of the corresponding powers under a specific alternative are derived. We use several simulated examples to illustrate the performance of the proposed tests, and we make comparisons with other tests available in the literature.     

Strong convergence properties for partial sums of asymptotically negatively associated random vectors in Hilbert spaces

Abstract

In this paper, we investigate the almost sure convergence for partial sums of asymptotically negatively associated (ANA, for short) random vectors in Hilbert spaces. The Khintchine-Kolmogorov type convergence theorem, three series theorem and the Kolmogorov type strong law of large numbers for partial sums of ANA random vectors in Hilbert spaces are obtained. The results obtained in the paper generalize some corresponding ones for independent random vectors and negatively associated random vectors in Hilbert spaces.     

EMD算法和循环平稳理论在机械故障诊断中的应用

针对非平稳非线性的循环平稳信号提出了基于Hilbert变换的EMD分解重构消噪法;用带有强噪音和高斯噪声的典型循环平稳信号进行了仿真,并结合二阶循环平稳分析法对信号进行了信息提取.在实验部分,该文试用基于Hilbert变换的EMD分解重构和循环平稳理论结合的方法对运转中的故障轴承信号进行了分析,实验结果表明,这种应用能有效提取出信号中的有用信息,成功提取旋转机械运转产生的信号中的故障信息.     

二阶分布参数系统反射反馈的极点配置

讨论了二阶分布参数系统反射反馈的极点配置问题,即在二阶发展方程描述的控制系统中,考虑反射控制律反馈的闭环控制系统的反本征值问题;在复可分的Hilbert空间中,将算子的非零单重的二次本征值问题转化为算子扰动的一次本征值问题,获得了本征值是内积方程的根的重要结果,在构造的单重极点的半纯函数得到了问题的解和解的构造性表达式。