Random Symmetrical Sampling

We eall following sampling a random symmetrieal sampling:Let the 512亡5 of a population疡二哎Yl,Y:,…,Y二},N二ZK(K 15 a pasitive whole namber),We divide the疡into two grups:‘,~{Y:,Y:,…,Y.}、e:={Y.+;,Y,+:,…,Y,}too draw a radom sample whieh sizes”一2泛(and庵15a pasitive whole number,andl(k簇K),First we draw a simple random sampley:,y:,…,y,from the‘,,Sinee the sample Correspondly to get a sampley;,y妥,一,y几from the。:and to satisfythat when苏from the 02 and to satisfy that when少‘15…     

Sampling and Π-sampling expansions

Using the hyperfinite representation of functions and generalized functions this paper develops a rigorous version of the so-called ‘delta method’ approach to sampling theory. This yields a slightly more general version of the classical WKS sampling theorem for band-limited functions.     

Slice Sampling σ-Stable Poisson-Kingman Mixture Models

The article is concerned with the use of Markov chain Monte Carlo methods for posterior sampling in Bayesian nonparametric mixture models.In particular, we consider the problem of slice sampling mixture models for a large class of mixing measures generalizing the celebrated Dirichlet process. Such a class of measures, known in the literature as σ-stable Poisson-Kingman models, includes as special cases most of the discrete priors currently known in Bayesian nonparametrics, for example, the two-parameter Poisson-Dirichlet process and the normalized generalized Gamma process. The proposed approach is illustrated on some simulated data examples. This article has online supplementary material.     

Double Moving Extremes Ranked Set Sampling Design

The traditional simple random sampling(SRS) design method is inefficient in many cases. Statisticians proposed some new designs to increase efficiency. In this paper, as a variation of moving extremes ranked set sampling(MERSS), double MERSS(DMERSS) is proposed and its properties for estimating the population mean are considered. It turns out that, when the underlying distribution is symmetric, DMERSS gives unbiased estimators of the population mean. Also, it is found that DMERSS is more efficie...     

Sampling theorems and difference sturm—liouville problems

In this work we drive sampling theorems associated with infinite Sturm-Linuville difference problems. Among them, we obtain the analogze, for difference problems, of the result obtained by Zayed for the continuous case on the half-line [O, +∞). Also, we obtain a sampling theorem when the operator associated with the problem has a Hilbert-Schmidt resolvent operator. In particular, sampling theorems associated with Green's functions are included.     

Kramer’s Sampling Theorem With Discontinuous Kernels

Kramer’s sampling theorem provides an algorithm for reconstructing a function ?, in the form $$ f(t)=\int_{a}^{b}\ F(x)K(x,t)dx,\qquad {\rm for\ some}\ F\ \in\ L^{2}(a,b), $$ from its values at a discrete set of points. In all the known examples, the kernel of the transform, K(x,t) is continuous in x and entire in t, even though the proof of the theorem shows that the continuity in x is not essential. This raises the question of whether it is possible to find an example of Kramer’s theorem with a discontinuous kernel. The aim of the paper is to answer this question in the affirmative. We show how one can construct a family of discontinuous kernels for which Kramer’s theorem holds and, in addition, each member of this family arises from a Sturm-Liouville problem, but with discontinuous initial conditions.     

Mantel-Haenszel Estimator for Common Odds Ratio under Inverse Sampling

We consider K independent 2×2 tables arising from the inverse sampling, and propose Mantel-Haenszel (M-H) estimator for the common odds ratio and the variance estimate of the estimator. The conditions for the asymptotic efficiency of this estimator are also discussed in this article.     

Behavior of Shannon’s Sampling Series for Hardy Spaces

In this paper the convergence behavior of the Shannon sampling series is analyzed for Hardy spaces. It is well known that the Shannon sampling series is locally uniformly convergent. However, for practical applications the global uniform convergence is important. It is shown that there are functions in the Hardy space such that the Shannon sampling series is not uniformly convergent on the whole real axis. In fact, there exists a function in this space such that the peak value of the Shannon sampling series diverges unboundedly. The proof uses Fefferman’s theorem, which states that the dual space of the Hardy space is the space of functions of bounded mean oscillation. This work was partly supported by the German Research Foundation (DFG) under grant BO 1734/9-1.     

Sampling, Filtering and Sparse Approximations on Combinatorial Graphs

In this paper we address sampling and approximation of functions on combinatorial graphs. We develop filtering on graphs by using Schrödinger’s group of operators generated by combinatorial Laplace operator. Then we construct a sampling theory by proving Poincare and Plancherel-Polya-type inequalities for functions on graphs. These results lead to a theory of sparse approximations on graphs and have potential applications to filtering, denoising, data dimension reduction, image processing, image compression, computer graphics, visualization and learning theory.     

基于Linear Sampling方法的二维可穿透区域反演

提出用时间调和声散射远场信息来反演二维可穿透目标的一种Linear Sampling方法,通过提取包含可穿透目标的一个样本区域的支集的点列来实现反演的,因为其在区域内与区域外有显著的不同取值,由此而获得区域的逼近.这个算法特别吸引人之处是不需关于障碍物的任何先验信息.并且只需散射场在某个有限孔径中的部分远场信息,即可获得穿透区域的一个逼近.一些数值算例保证了这个反演算法是有效的和实用的.     

Analysis of a Linear Sampling Method for Identification of Obstacles

Some difficulties are pointed out in the methods for identification of obstacles based on the numerical verification of tile inclusion of a function in the range of an operator. Numerical examples are given to illustrate theoretical conclusions. Alternative methods of identification of obstacles are mentioned： the Support Function Method （SFM） and the Modified Rayleigh Conjecture （MRC） method.     

Multidimensional Lagrange–Yen-Type Interpolation Via Kotel'nikov–Shannon Sampling Formulas

Direct finite interpolation formulas are developed for the Paley–Wiener function spaces and , where contains all bivariate entire functions whose Fourier spectrum is supported by the set = Cl{(u, v) |u| + |v| < ], while in the Fourier spectrum support set of its d-variate entire elements is [–, ] ^d . The multidimensional Kotel'nikov–Shannon sampling formula remains valid when only finitely many sampling knots are deviated from the uniform spacing. By using this interpolation procedure, we truncate a sampling sum to its irregularly sampled part. Upper bounds of the truncation error are obtained in both cases.According to the Sun–Zhou extension of the Kadets -theorem, the magnitudes of deviations are limited coordinatewise to . To avoid this inconvenience, we introduce weighted Kotel'nikov–Shannon sampling sums. For , Lagrange-type direct finite interpolation formulas are given. Finally, convergence-rate questions are discussed.     

A Kind of the ASN' Extreme Value forMeasuring Double Sampling Plan

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Periodic Nonuniform Dynamical Sampling in ℓ2(ℤ) and Shift-Invariant Spaces

In this article, we mainly study the periodic nonuniform dynamical sampling in ?²(?) and shift-invariant spaces. We first provide a su?cient and necessary condition for c∈?²(?) which can be reconstructed by its spatial and temporal samples. Then we give a concrete example to show that the su?cient and necessary condition is feasible. Finally, we discuss the periodic nonuniform dynamic sampling problem in shift-invariant spaces.     

Sampling Theorem and Discrete Fourier Transform on?the?Hyperboloid

Using Coherent-State (CS) techniques, we prove a sampling theorem for holomorphic functions on the hyperboloid (or its stereographic projection onto the open unit disk $\mathbb{D}_{1}$ ), seen as a homogeneous space of the pseudo-unitary group SU(1,1). We provide a reconstruction formula for bandlimited functions, through a sinc-type kernel, and a discrete Fourier transform from N samples properly chosen. We also study the case of undersampling of band-unlimited functions and the conditions under which a partial reconstruction from N samples is still possible and the accuracy of the approximation, which tends to be exact in the limit N????.     

A Survey of the Whittaker-Shannon Sampling Theorem and Some of its Extensions

The aim of this paper is to present a survey of results concerning the WhittakerKotel′nikov-Raabe-Shannon-Someya sampling theorem and its various extensions obtained at Aachen since 1977. This theorem, basic in communication engineering, is often called the cardinal interpolation series theorem in mathematical circles. The interconnections of the sampling theorem (in the setting of Paley-Wiener space) with the theory of Fourier series and integrals are examined. Emphasis is placed upon error analysis, including the aliasing, round-off (or quantization), and time jitter errors. Some new error estimates are given, others are improved: many of the proofs are reduced to a common structure. Both deterministic and probabilistic methods are employed, whereas these results are worked out in detail, the paper also contains a brief discussion of some of the various generalizations.     

Empirical Likelihood Inference Under Stratified Random Sampling in the Presence of Measurement Error

Suppose that several different imperfect instruments and one perfect instrument are used independently to measure some characteristic of a population. In order to make full use of the sample information, in this paper the empirical likelihood method is put forward for making inferences on parameters of interest under stratified random sampling in the presence of measurement error, Our results show that it can lead to estimators which are asymptotically normal and utilize all the available sample information. We also obtain the asymptotic distribution of empirical likelihood testing statistics. In particular, we apply the method to obtain estimator and confidence interval of population mean.     

A Sampling Method for Solving Inverse Scattering Problems with a Locally Perturbed Half Plane

In this paper,we will consider the scattering of time—harmonic electromagnetic waves by aninfinitely long cylinder with a perfectly conducting boundary.The problem is modelled by aDirichlet problem for the Helmholtz equation.Adopting Cartesion coordinates(Xl,X2,X3)in础we assume that the boundary is the XlX3一plane with the perturbation independent of z3and local with respect to X1.Furthermore,we assume that the elect:tic and magnetic fieldsare invariant with respect to X3 and we restrict …     

A “Density-Based” Algorithm for Cluster Analysis Using Species Sampling Gaussian Mixture Models

We propose a new model for cluster analysis in a Bayesian nonparametric framework. Our model combines two ingredients, species sampling mixture models of Gaussian distributions on one hand, and a deterministic clustering procedure (DBSCAN) on the other. Here, two observations from the underlying species sampling mixture model share the same cluster if the distance between the densities corresponding to their latent parameters is smaller than a threshold; this yields a random partition which is coarser than the one induced by the species sampling mixture. Since this procedure depends on the value of the threshold, we suggest a strategy to fix it. In addition, we discuss implementation and applications of the model; comparison with more standard clustering algorithms will be given as well. Supplementary materials for the article are available online.     

Sampling Consensus of 2nd-Order Multi-Agent Systems Based on Time-Varying Topology北大核心CSCD

基于速度一致位移差保持不变的一致性概念,研究了二阶多智能体系统在时变拓扑下的采样一致性问题。首先,引入虚拟领导者,将具有时变拓扑结构的多智能体系统的采样一致性问题转换为误差系统的采样控制稳定性问题。其次,通过预估采样误差,研究采样误差对系统达到一致性的影响。最后,应用Lyapunov稳定性理论,分析所构造的误差系统的稳定性,并给出该误差系统最终稳定的充分条件。数值仿真结果验证了理论分析的有效性和正确性。