STRONG CONSISTENCY AND ASYMPTOTIC NORMALITY OF /1 ESTIMATES OF THE AUTOREGRESSIVE MOVING-AVERAGE MODEL

Abstract. The strong consistency and central limit theorem for least absolute deviation estimates of the parameters in a scalar autoregressive-moving average model are established under general conditions on the innovations.     

抗震结构灰色可靠性初探

本文用灰色系统的观点和方法,探讨了在考虑地震载荷、场地分类以及结构抗力的灰色性的情况下的结构可靠性问题。为此,提出了灰色地震烈度,场地灰类、结构工作正常度以及结构灰色可靠度等概念及其计算方法。     

指数信号模型中参数估计的Bootstrap逼近

本文基于Prony方法和Bootstrap方法,解决了受抑制指数信号模型的辨识问题。给出了模型中参数的最小二乘估计的计算方法和逼近：为了使样本所在的区间有限,在保证模型相容的条件下,我们重新定义模型．证明了Bootstrap估计的相合性和渐近正态性,从而证明了我们这种方法的可行性：最后利用该方法给出模拟结果。并且和其他方法进行了比较。     

火焰原子吸收光谱测定聚乙烯包装材料中重金属的质控分析

评价了火焰原子吸收光谱法测定聚乙烯包装材料中重金属(以Pb计,下同)的不确定度,对食品包装材料的安全性评估提供理论支撑。实际检测数据通过了正态性验证,并在符合正态分布的前提下进行了质控分析,分别建立了单值(I)控制图、移动极差值(MR)控制图,结果显示测量系统的变异仅受随机误差影响,且有99.7%的正态分布数据落入控制限内,进一步验证了数据的正态性分布。绘制了指数加权移动平均值(EWMA)控制图,显示所测结果并未出现超限数据,且集中在中心线附近,说明测试结果具有较好的集中性。最终,在确信火焰原子吸收光谱法(FAAS)测定重金属的系统具有可信性和其偏倚可忽略不计的情况下,给出测试样本的评估参考量值为0.014 mg/L,并通过显著性t检验证明了方法测定过程中不存在系统误差。     

核能谱模拟的正态组合实现方法

结合核能谱的随机特性,探讨了核能谱的正态组合模拟方法。该方法将核能谱分解为正态分布函数的组合,进而转化为参数化模型,并对正态组合函数进行随机抽样以模拟原始能谱。该方法可以灵活地调整正态函数的个数和各正态函数的标准偏差,以满足模拟中对谱线平滑度、准确度的不同要求,是一种效果较好的参数化模拟方法。     

Asymptotic normality under transformations. A result with Bayesian applications

Summary A generalization is provided of the conditions to be satisfied in order to ensure asymptotic normality under transformations. From a Bayesian viewpoint, this result may be used to select an appropriate parameterization or to avoid additional calculations when the parameter of interest does not coincide with the usual parameter of the model.     

Formulas for calculating supremal controllable and normal sublanguages

Supremal controllable and normal sublanguages have been shown to play an important role in supervisor synthesis. In this paper, we discuss the computation of supremal controllable and normal sublanguages. We derive formulas for both supremal controllable sublanguages and supremal normal sublanguages when the languages involved are closed. As a result, those languages can be computed without applying recursive algorithms. We also discuss those aspects of these formulas.     

A Durbin–Watson serial correlation test for ARX processes via excited adaptive tracking

We propose a new statistical test for the residual autocorrelation in ARX adaptive tracking. The introduction of a persistent excitation in the adaptive tracking control allows us to build a bilateral statistical test based on the well-known Durbin–Watson statistic. We establish the almost sure convergence and the asymptotic normality for the Durbin–Watson statistic leading to a powerful serial correlation test. Numerical experiments illustrate the good performances of our statistical test procedure.     

An affine invariant multiple test procedure for assessing multivariate normality

A multiple test procedure for assessing multivariate normality (MVN) is proposed. The new test combines a finite set of affine invariant test statistics for MVN through an improved Bonferroni method. The usefulness of such an approach is illustrated by a multiple test including the Mardia and BHEP (Baringhaus-Henze-Epps-Pulley) tests that are among the most recommended procedures for testing MVN. A simulation study carried out for a wide range of alternative distributions, in order to analyze the finite sample power behavior of the proposed multiple test procedure, indicates that the new test demonstrates a good overall performance against other highly recommended MVN tests.     

EWMA Control Chart Performance with Estimated Parameters under Non‐normality

Exponentially weighted moving average (EWMA) control charts can be designed to detect shifts in the underlying process parameters quickly while enjoying robustness to non‐normality. Past studies have shown that performance of various EWMA control charts can be adversely affected when parameters are estimated or observations do not follow a normal distribution. To the best of our knowledge, simultaneous effect of parameter estimation and non‐normality has not been studied so far. In this paper, a Markov chain approach is used to model and evaluate performance of EWMA control charts when parameter estimation is subject to non‐normality using skewed and heavy‐tailed symmetric distributions. Using standard deviation of the run length (SDRL), average run length (ARL), and percentiles of run lengths for various phase I sample sizes, we show that larger phase I sample sizes do not necessarily lead to a better performance for non‐normal observations. Copyright © 2015 John Wiley & Sons, Ltd.