Comparing confidence limits for short-run process incapability index Cpp

Process incapability index C_pp has been proposed in the manufacturing industry to assess process incapability. In industries it is sometimes unable to get large samples, and, hence, the CAN (consistent and asymptotically normal) property of the unbiased estimator for C_pp is missing. In this paper, six bootstrap methods are applied to construct upper confidence bounds (UCBs) of C_pp for short-urn production processes where sample size is small; standard bootstrap (SB), Bayesian bootstrap (BB), bootstrap pivotal (BP), percentile bootstrap (PB), bias-corrected percentile bootstrap (BCPB), and bias-corrected and accelerated bootstrap (BCa). A numerical simulation study is conducted in order to demonstrate the performance of the six various estimation methods. We further investigate the accuracy of the six methods by calculating the relative coverage (defined as the ratio of coverage percentage to average length of UCB). Detailed discussions of simulation results for seven short-run processes are presented. Finally, one real example from Ford Company’s Windsor Casting Plant is used to illustrate the six interval estimation methods.     

多面转镜激光器扫频光学相干层析成像系统的全光谱重采样方法

在多面转镜激光器扫频光学相干层析成像系统中,激光器存在着输出光谱错位与扫频范围波动的问题.目前的重采样方法中,普遍利用互相关运算校正光谱错位,并进行大范围的截取,保证扫频范围的一致性,但这会导致成像信噪比与分辨率的降低.本文用马赫-曾德尔干涉仪(MZI)采集到的干涉信号对扫频范围波动的问题进行了详细的测量与分析,其中干涉信号的解缠相位曲线的非随机性和平行性,表明该类激光器输出光谱的波长分布具备一致性.在此基础上,提出了一种用最长扫频范围的MZI干涉信号,对样品干涉信号进行时域光谱对齐、然后进行一对多插值的重采样方法.实验与分析表明,该方法利用了所有的光谱信号,保证了样品干涉信号的能量利用率,能有效提高图像的信噪比与分辨率.     

基于压缩感知/重采样的NMR噪声抑制新方法

发展高灵敏检测方法是分析化学的永恒主题之一,提高信号强度和降低噪声水平是增强灵敏度的根本途径.在核磁共振波谱(NMR)分析中,通常采用高磁场强度的谱仪或复杂的脉冲实验方法来提高信号强度,或通过使用超低温探头来降低噪声水平,但这无疑会提高实验成本或增加实验难度.相较而言,利用数据后处理方法辨识和抑制噪声,是更为经济的提高信噪比(SNR)的途径.因此,该文在前期研究中发展的基于统计学中重采样原理的数据后处理方法(NASR)的基础上,通过引入压缩感知(CS)技术,对重采样方法进行了优化改进,所发展的NMR数据处理新方法(CS_NASR)可有效排除主观因素影响,提高处理结果的鲁棒性.     

Order Determination for Multivariate Autoregressive Processes Using Resampling Methods

LetX₁, …, X_nbe observations from a multivariate AR(p) model with unknown orderp. A resampling procedure is proposed for estimating the orderp. The classical criteria, such as AIC and BIC, estimate the orderpas the minimizer of the function[formula]wherenis the sample size,kis the order of the fitted model, Σ²_kis an estimate of the white noise covariance matrix, andC_nis a sequence of specified constants (for AIC,C_n=2m²/n, for Hannan and Quinn's modification of BIC,C_n=2m²(ln ln n)/n, wheremis the dimension of the data vector). A resampling scheme is proposed to estimate an improved penalty factorC_n. Conditional on the data, this procedure produces a consistent estimate ofp. Simulation results support the effectiveness of this procedure when compared with some of the traditional order selection criteria. Comments are also made on the use of Yule–Walker as opposed to conditional least squares estimations for order selection.     

Resampling a coverage pattern

The possibility of resampling (bootstrapping) a spatial pattern is investigated. It is suggested that resampling provides a unified approach to consistemt inference in a wide range of coverage problems. Nevertheless, resampling distorts some of the interactions in the problem, and so introduces biases. The sizes of bias and standard deviation are investigated in the case of estimating sampling variance via resampling.     

农残水平测试中数据多态性分析及指定值估计研究

对全国农残水平测试中毒死蜱、氯氰菊酯数据进行统计分析,在数据统计分布特征研究基础上,使用内核密度估计进行数据多态性分析,使用bootstrap模拟取样法对数据样本值重复取样,以获得稳健的水平测试样品待测物含量代表值估计、标准误差及置信区间描述,证明以bootstrap模拟取样法获取的均值与标准偏差作为有限单次样本代表值是合理、有效的,解决了四分位稳健统计方法对非正态多态分布代表值估计不稳定问题及取样理论中取样样本数限制的瓶颈,为能力验证计划指定值的获取提供了一种新方法。     

On Testing for the Number of Components in a Mixed Poisson Model

Poisson mixtures are usually used to describe overdispersed data. Finite Poisson mixtures are used in many practical situations where often it is of interest to determine the number of components in the mixture. Identifying how many components comprise a mixture remains a difficult problem. The likelihood ratio test (LRT) is a general statistical procedure to use. Unfortunately, a number of specific problems arise and the classical theory fails to hold. In this paper a new procedure is proposed that is based on testing whether a new component can be added to a finite Poisson mixture which eventually leads to the number of components in the mixture. It is a sequential testing procedure based on the well known LRT that utilises a resampling technique to construct the distribution of the test statistic. The application of the procedure to real data reveals some interesting features of the distribution of the test statistic.     

矿产品水分含量代表值Bootstrap模拟取样估计

在对矿产品水分含量基础统计学特征描述的基础上,采用内核密度估计对水分含量数据多态性进行了分析,根据双态分布的特点,使用Bootstrap模拟取样方法对试验样本值模拟重复取样,以多次Bootstrap模拟取样的均值与标准偏差作为矿产品水分含量有限样本代表值及标准偏差的稳健估计,实践证明Bootstrap模拟取样估计对矿产品水分含量代表值的估计是有效的,该项研究为矿产品水分含量代表值的准确评估提供了一种新方法.     

Generating Replications of Chaotic Time Series

This paper addresses the problem of resampling chaotic time series. We propose a method based on resampling distances between nearest neighbours in phase space, so that the resampled time series present the original points differently positioned along the trajectory. This approach allows one to obtain time series with the same length of the original one, so that confidence intervals for Lyapunov exponents, correlation dimension and other invariants would be determined. For its generality this kind of resampling would be applicable to chaotic time series no matter the observations concern natural or life sciences. The method has been tested with common simulated chaotic systems with both clean and noisy data. Short and noisy time series, as the ones we simulated, typically occur in medicine, biology, and social sciences.     

Applications of the representative points in statistical simulations

The paper gives a new approach to statistical simulation and resampling by the use of number-theoretic methods and representative points. Resempling techniques take samples from an approximate population. The bootstrap suggests to use a random sample to form an approximate population. We propose to construct some approximate population distribution by the use of two kinds of representative points, and samples are taken from these approximate distributions. The statistical inference is based on those samples. The statistical inference in this paper involves estimation of mean, variance, skewness, kurtosis, quantile and density of the population distribution. Our results show that the new method can significantly improve the results by the use of Monte Carlo methods.