Interpolation operators associated with sub-frame sets

Interpolation operators associated with wavelets sets introduced by Dai and Larson play an important role in their operator algebraic approach to wavelet theory. These operators are also related to the von Neumann subalgebras in the ``local commutant' space, which provides the parametrizations of wavelets. It is a particularly interesting question of how to construct operators which are in the local commutant but not in the commutant. Motivated by some questions about interpolation family and C*-algebras in the local commutant, we investigate the interpolation partial isometry operators induced by sub-frame sets. In particular we introduce the -congruence domain of the associated mapping between two sub-frame sets and use it to characterize these partial isometries in the local commutant. As an application, we obtain that if two wavelet sets have the same -congruence domain, then one is a multiresolution analysis (MRA) wavelet set which implies that the other is also an MRA wavelet set.

     

On the role of the shrinkage parameter in local linear smoothing

Summary. It has been shown that local linear smoothing possesses a variety of very attractive properties, not least being its mean square performance. However, such results typically refer only to asymptotic mean squared error, meaning the mean squared error of the asymptotic distribution, and in fact, the actual mean squared error is often infinite. See Seifert and Gasser (1996). This difficulty may be overcome by shrinking the local linear estimator towards another estimator with bounded mean square. However, that approach requires information about the size of the shrinkage parameter. From at least a theoretical viewpoint, very little is known about the effects of shrinkage. In particular, it is not clear how small the shrinkage parameter may be chosen without affecting first-order properties, or whether infinitely supported kernels such as the Gaussian require shrinkage in order to achieve first-order optimal performance. In the present paper we provide concise and definitive answers to such questions, in the context of general ridged and shrunken local linear estimators. We produce necessary and sufficient conditions on the size of the shrinkage parameter that ensure the traditional mean squared error formula. We show that a wide variety of infinitely-supported kernels, with tails even lighter than those of the Gaussian kernel, do not require any shrinkage at all in order to achieve traditional first-order optimal mean square performance. Received: 22 May 1995 / In revised form: 23 January 1997     

小波理论在VaR计算中的应用

本文根据小波理论研究金融市场中的资产组合收益的概率密度函数的估计问题 ,进而讨论金融市场风险的重要度量———VaR的计算问题 ,并给出相应结果 .     

An integral transform associated to the Poisson integral and inversion of Flett potentials

We introduce a new weighted wavelet-like transform, generated by the Poisson integral and a “wavelet measure.” By making use of the relevant Calderón-type reproducing formula, we obtain an explicit inversion formula for the Flett potentials which are interpreted as negative fractional powers of the operator (E+Λ), where Λ=(−Δ)^1/2, Δ is the Laplacian and E is the identity operator.     

Wavelet frames and shift-invariant subspaces of periodic functions

A general approach based on polyphase splines, with analysis in the frequency domain, is developed for studying wavelet frames of periodic functions of one or higher dimensions. Characterizations of frames for shift-invariant subspaces of periodic functions and results on the structure of these subspaces are obtained. Starting from any multiresolution analysis, a constructive proof is provided for the existence of a normalized tight wavelet frame. The construction gives the minimum number of wavelets required. As an illustration of the approach developed, the one-dimensional dyadic case is further discussed in detail, concluding with a concrete example of trigonometric polynomial wavelet frames.     

肝胆胰系统住院病人医疗费用的多因素分析

本文以武汉市某大医院１９９５年肝胆胰系统出院病例为研究样本，采用逐步回归和岭回归方法拟合模型，对医疗费用进行了多病种、多因素研究。研究结果表明，社会学因素、病种因素、病情因素、手术因素、护理因素等对住院费用和住院天数均有不同程度的影响，并且发现ＭＤＣ７疾病与胆囊结石单一疾病的多因素分析效果十分相近。     

Sard-optimal prefilters for the Fast Wavelet Transform

A direct input of function samples into the Fast Wavelet Transform often gives inaccurate results. We use the refinement equation for the construction of prefiltering quadrature formulas which are optimal in Sard's sense, i.e.,in the standard class of functions with ‖ f ^(p)‖₂ < ∞. A detailed analysis of the error and several applications are given. This revised version was published online in August 2006 with corrections to the Cover Date.     

联用色谱数据的多尺度分析

引入基于正交小波基的多尺度分析，并将其用于色谱／光谱二维数据压缩和消除背景影响的研究，结果表明，该法不但成功地消除了复杂的色谱／光谱背景有同时大计压缩数据量，对模拟和实际体系的均获得满意的结果。     

一种自适应的盲水印方法

目前数字水印算法多局限于在图象中嵌入特定的标记,并通过改变空域值或频域系数值来达到目的.提出了一种新颖的自适应盲水印方法.首先基于小波变换的零树结构,找出重要系数,然后根据重要系数所在区域的特性构造出一个序列信息,再利用置乱变换最终得到水印信息,而不修改图象本身的任何特征.因此水印的不可见性从根本上得到了保证.其中,重要系数的选择是自适应于图象的,并且水印的检测是不需要原始图象的盲检测.实验证明该方法的鲁棒性较强,是一种行之有效的方法.     

Estimating function with asymptotic bias and its estimator

We introduce the estimating function with asymptotic bias and investigate the asymptotic behavior of the estimator based on it by using their relationship. The estimator based on the estimating function with asymptotic bias has the asymptotic normality with asymptotic bias. We show that this theory has several interesting applications in practical statistics.