Evidential inference for diffusion-type processes

This article analyses diffusion-type processes from a new point-of-view. Consider two statistical hypotheses on a diffusion process. We do not use a classical test to reject or accept one hypothesis using the Neyman–Pearson procedure and do not involve Bayesian approach. As an alternative, we propose using a likelihood paradigm to characterizing the statistical evidence in support of these hypotheses. The method is based on evidential inference introduced and described by Royall [Royall R. Statistical evidence: a likelihood paradigm. London: Chapman and Hall; 1997]. In this paper, we extend the theory of Royall to the case when data are observations from a diffusion-type process instead of iid observations. The empirical distribution of likelihood ratio is used to formulate the probability of strong, misleading and weak evidences. Since the strength of evidence can be affected by the sampling characteristics, we present a simulation study that demonstrates these effects. Also we try to control misleading evidence and reduce them by adjusting these characteristics. As an illustration, we apply the method to the Microsoft stock prices.     

A simple algorithm for calculating values for folded normal distribution

Folded normal distribution originates from the modulus of normal distribution. In the present article, we have formulated the cumulative distribution function (cdf) of a folded normal distribution in terms of standard normal cdf and the parameters of the mother normal distribution. Although cdf values of folded normal distribution were earlier tabulated in the literature, we have shown that those values are valid for very particular situations. We have also provided a simple approach to obtain values of the parameters of the mother normal distribution from those of the folded normal distribution. These results find ample application in practice, for example, in obtaining the so-called upper and lower α-points of folded normal distribution, which, in turn, is useful in testing of the hypothesis relating to folded normal distribution and in designing process capability control chart of some process capability indices. A thorough study has been made to compare the performance of the newly developed theory to the existing ones. Some simulated as well as real-life examples have been discussed to supplement the theory developed in this article. Codes (generated by R software) for the theory developed in this article are also presented for the ease of application.     

Economic and economic statistical designs for three-level control charts

In some situations, an appropriate quality measure uses three or more discrete levels to classify a product characteristic. For these situations, some control charts have been developed based on statistical criteria regardless of economic considerations. In this paper, we develop economic and economic statistical designs (ESD) for 3-level control charts. We apply the cost model proposed by Costa and Rahim.[Economic design of X charts with variable parameters: the Markov chain approach, J Appl Stat 28 (2001), 875–885] Furthermore, we assume that the length of time that the process remains in control is exponentially distributed which allows us to apply the Markov chain approach for developing the cost model. We apply a genetic algorithm to determine the optimal values of model parameters by minimizing the cost function. A numerical example is provided to illustrate the performance of the proposed models and to compare the cost of the pure economic and ESD for three-level control charts. A sensitivity analysis is also conducted in this numerical example.     

Sample size determination for estimating multivariate process capability indices based on lower confidence limits

With the advent of modern technology, manufacturing processes have become very sophisticated; a single quality characteristic can no longer reflect a product's quality. In order to establish performance measures for evaluating the capability of a multivariate manufacturing process, several new multivariate capability (NMC) indices, such as NMC _p and NMC _pm , have been developed over the past few years. However, the sample size determination for multivariate process capability indices has not been thoroughly considered in previous studies. Generally, the larger the sample size, the more accurate an estimation will be. However, too large a sample size may result in excessive costs. Hence, the trade-off between sample size and precision in estimation is a critical issue. In this paper, the lower confidence limits of NMC _p and NMC _pm indices are used to determine the appropriate sample size. Moreover, a procedure for conducting the multivariate process capability study is provided. Finally, two numerical examples are given to demonstrate that the proper determination of sample size for multivariate process indices can achieve a good balance between sampling costs and estimation precision.     

Robustness to non-normality and autocorrelation of individuals control charts

This paper studies the effects of non-normality and autocorrelation on the performances of various individuals control charts for monitoring the process mean and/or variance. The traditional Shewhart X chart and moving range (MR) chart are investigated as well as several types of exponentially weighted moving average (EWMA) charts and combinations of control charts involving these EWMA charts. It is shown that the combination of the X and MR charts will not detect small and moderate parameter shifts as fast as combinations involving the EWMA charts, and that the performana of the X and MR charts is very sensitive to the normality assumption. It is also shown that certain combinations of EWMA charts can be designed to be robust to non-normality and very effective at detecting small and moderate shifts in the process mean and/or variance. Although autocorrelation can have a significant effect on the in-control performances of these combinations of EWMA charts, their relative out-of-control performances under independence are generally maintained for low to moderate levels of autocorrelation.     

对应分析统计检验体系探讨

对应分析因其结果的易读性,近些年得到了越来越广泛的应用。为了更好地应用对应分析,提出建立对应分析统计检验体系,包括对应分析适用性的统计检验以及对应分析效果的检验,同时还提出应用对应分析时应注意的其它问题。     

宏观经济统计数据质量的静态诊断

统计数据的真实性是统计的生命线,统计数据质量的高低直接影响统计信息的有用性及价值大小。统计数据质量是当今各级政府和公众关注的热点问题,也是学者研究的重点课题。本研究运用全国31个省市的截面数据,构建了基于区域宏观经济系统的联立方程定量诊断模型,依据此模型对陕西省的地区生产总值、财政收入、居民消费水平和固定资产投资指标进行诊断示范,结果显示构造的定量诊断模型对于区域宏观统计数据质量诊断效果良好。     

统计调查课程的现状与调整思路

文章从统计调查课程设置的现状出发,介绍了当前随着社会经济的发展和统计调查方法体系的改革,统计调查理论体系以及统计调查课程设置的不足,叙述了统计调查课程调整的思路。要实施这个思路,必须重视统计调查对象内容的变化,并注重借鉴国外成熟的经验。为适应形势的发展,随着现行统计调查方法体系的调整与完善,对统计调查课程也要作相应的调整。     

Target detection from a classical and a Bayesian viewpoint

Two approaches have been used for designing spatial surveys to detect a target. The classical approach controls the probability of missing a target that exists; a Bayesian approach controls the probability that a target exists given that none was seen. In both cases, information about the likely size of the target can reduce sampling requirements. In this paper, previous results are summarized and then used to assess the risk that Roman remains could be present at sites scheduled for development in Greater London.     

明、清及民国广东县志“风俗”门目研究

文章对369部广东县志的风俗门目进行统计分析和研究。首先分析了广东县志风俗门目载述概况;其次对广东县志风俗门目设置进行统计分析。通过统计分析发现广东县志旧志的风俗门目的特征是载述范围广、载述门目众多、门目名称大量存在同义词的现象。