EXACT EVALUATIONS OF FINITE TRIGONOMETRIC SUMS BY SAMPLING THEOREMS

We use the sampling representations associated with Sturm-Liouville difference operators to derive generalized integral-valued trigonometric sums. This extends the known results where zeros of Chebyshev polynomials of the first kind are involved to the use of the eigenvalues of difference operators, which leads to new identities. In these identities Bernoulli’s numbers play a role similar to that of Euler’s in the old ones. Our technique differs from that of Byrne-Smith (1997) and Berndt-Yeap (2002).     

Superconvergence of Legendre projection methods for the eigenvalue problem of a compact integral operator

In this paper, we consider the Galerkin and collocation methods for the eigenvalue problem of a compact integral operator with a smooth kernel using the Legendre polynomials of degree ≤n. We prove that the error bounds for eigenvalues are of the order O(n^−2r) and the gap between the spectral subspaces are of the orders O(n^−r) in L₂-norm and O(n^1/2−r) in the infinity norm, where r denotes the smoothness of the kernel. By iterating the eigenvectors we show that the iterated eigenvectors converge with the orders of convergence O(n^−2r) in both L₂-norm and infinity norm. We illustrate our results with numerical examples.     

可变抽样区间的非正态EWMA图的经济设计

本文主要讨论非正态总体下,可变抽样区间的EWMA图的经济设计问题。首先利用Burr分布近似各种非正态分布,建立可变抽样区间的非正态EWMA图的经济模型,使总期望费用最型小来确定参数的最优值;其次用遗传算法来寻找该经济模型的最优解,并给出工业中的一个例子;最后对可变抽样区间的非正态EWMA图的经济模型进行灵敏度分析。     

动态测量数据的合理性检验方法研究

采样数据合理性检验,是数据处理中重要的一环,它的主要功能是鉴别采样数据中可能含有的异常值,并进行相应的机理分析与修复工作.本文从飞行器外测系统工程应用的角度出发,给出了两种简单易行的判断方法.     

Nonsynchronous covariation process and limit theorems

An asymptotic distribution theory of the nonsynchronous covariation process for continuous semimartingales is presented. Two continuous semimartingales are sampled at stopping times in a nonsynchronous manner. Those sampling times possibly depend on the history of the stochastic processes and themselves. The nonsynchronous covariation process converges to the usual quadratic covariation of the semimartingales as the maximum size of the sampling intervals tends to zero. We deal with the case where the limiting variation process of the normalized approximation error is random and prove the convergence to mixed normality, or convergence to a conditional Gaussian martingale. A class of consistent estimators for the asymptotic variation process based on kernels is proposed, which will be useful for statistical applications to high-frequency data analysis in finance. As an illustrative example, a Poisson sampling scheme with random change point is discussed.     

A pseudo-empirical log-likelihood estimator using scrambled responses

In this paper, we propose an empirical log-likelihood estimator for estimating the population mean of a sensitive variable in the presence of an auxiliary variable. A new concept of conditional mean squared error of the empirical likelihood estimator is introduced. The proposed method is valid for simple random and without replacement sampling (SRSWOR) and could easily be extended for complex survey designs. The relative efficiency of the proposed pseudo-empirical log-likelihood estimator with respect to the usual, and to a recent estimator due to Diana and Perri (2009b), has been investigated through a simulation study.     

基于DCSBM模型的受访者驱动抽样调查估计量改进

大数据背景下,将受访者驱动抽样(RDS)用于网络抽样调查,解决了传统抽样调查难以获得可用抽样框、难以接触被调查者以及难以获得回答等问题,也使得网络调查可以实现概率抽样,得到一定误差范围内的总体参数估计.然而,在实际抽样过程中,同质性问题(即样本单元在推荐同伴时倾向于推荐那些与自己有相同属性的同伴)会导致RDS估计量的方...     

排序集抽样下Inverse Rayleigh分布的Fisher信息量及其在参数估计中的应用

文章分别在简单随机抽样和排序集抽样下研究了Inverse Rayleigh分布中对应样本所含刻度参数θ的Fisher信息量.数值结果表示,同等样本容量的排序集样本比简单随机样本提供更多关于θ的信息.接着分别基于简单随机样本和排序集样本构造了θ的一些优良估计,并对估计结果进行了数值比较.     

Normal approximation and fourth moment theorems for monochromatic triangles

Given a graph sequence denote by T₃(G_n) the number of monochromatic triangles in a uniformly random coloring of the vertices of G_n with colors. In this paper we prove a central limit theorem (CLT) for T₃(G_n) with explicit error rates, using a quantitative version of the martingale CLT. We then relate this error term to the well-known fourth-moment phenomenon, which, interestingly, holds only when the number of colors satisfies . We also show that the convergence of the fourth moment is necessary to obtain a Gaussian limit for any , which, together with the above result, implies that the fourth-moment condition characterizes the limiting normal distribution of T₃(G_n), whenever . Finally, to illustrate the promise of our approach, we include an alternative proof of the CLT for the number of monochromatic edges, which provides quantitative rates for the results obtained in [7].