数理统计方法在机械产品检测中的应用

机械产品加工的工艺过程是一个复杂的系统,工件的加工误差是许多随机因素作用的结果。应用数理统计方法对加工过程中工件的尺寸误差进行诊断分析,可以确定一批工件加工误差的总体规律,以便找出在工艺上控制误差的措施和解决问题的途径。     

Using Community Members to Collect Observational Data: Observer Training and Data Quality Assessment

ABSTRACT

This article highlights a structured approach to preparing community members for observational data collection in participatory research. Providing training related to the items that will be observed and conducting post-training assessments of observer accuracy and interrater reliability provides researchers with a measure of observer readiness to collect data. In addition, reassessing observer accuracy and interrater reliability at the end of data collection offers a measure of confidence in the data collection process. Discussion of this approach includes addressing survey items with low observer percentage agreement scores and training and evaluation strategies for intermittent and extended data collection periods.     

论二语产出的三个衡量维度——复杂性、准确性、流利性

二语研究领域目前普遍以复杂性、准确性和流利性三个维度来衡量学习者语言产出或水平。然而,这三个维度无论是在其操作化定义还是在其测量方式上都存在颇多的争议。随着二语研究成果的不断丰富,人们对于语言发展的特点有了更为深入的认识。二语研究者需要重新审视这三个维度的有效性和充分性,努力在一些关键概念上达成共识,同时进一步探讨衡量学习者语言发展的其它维度。     

On the distribution of the estimated mean from nonstandard mixtures of distributions

The distribution of the estimated mean of the nonstandard mixture of distributions that has a discrete probability mass at zero and a gamma distribution for positive values is derived. Furthermore, for the studied nonstandard mixture of distributions, the distribution of the standardized statistic (estimator - true mean)/standard deviation of estimator is derived. The results are used to study the accuracy of the confidence interval for the mean based on a large sample approximation. Quantiles for the standardized statistic are also calculated.     

Confidence Intervals for Linear Function of Variance Components in Two-Fold Nested Random Effects Model

In the article, we consider the unbalanced case of the two-way nested random effects model under partial balance. Using the method of generalized confidence intervals (GCIs) introduced in Weeranhandi (1993 Weeranhandi , S. ( 1993 ). Generalized confidence intervals . J. Amer. Statist. Assoc. 88 : 899 – 905 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar] 1995 Weeranhandi , S. ( 1995 ). Exact Statistical Methods for Data Analysis . New York : Springer-Verlag . [Google Scholar]), a new method is proposed for constructing confidence intervals on linear function of variance components. To compare the resulted intervals with the Modified Large Sample (MLS) intervals by Hernandez and Burdick (1993 Hernandez , R. P. , Burdick , R. K. ( 1993 ). Confidence intervals on the total variance in unbalanced two-fold nested designs . Biom. J. 35 : 515 – 522 .[Crossref] , [Google Scholar]), a simulation study is conducted. The results indicate that the proposed method performs better than the MLS method, especially for very unbalanced designs.     

The Effect of Mis-Specification Between the Lognormal and Weibull Distributions on the Interval Estimation of a Quantile for Complete Data

The lognormal and Weibull distributions are the most popular distributions for modeling lifetime data. In practical applications, they usually fit the data at hand well. However, their predictions may lead to large differences. The main purpose of the present article is to investigate the impacts of mis-specification between the lognormal and Weibull distributions on the interval estimation of a pth quantile of the distributions for complete data. The coverage probabilities of the confidence intervals (CIs) with mis-specification are evaluated. The results indicate that for both the lognormal and the Weibull distributions, the coverage probabilities are significantly influenced by mis-specification, especially for a small or a large p on lower or upper tail of the distributions. In addition, based on the coverage probabilities with correct and mis-specification, a maxmin criterion is proposed to make a choice between these two distributions. The numerical results indicate that for p ≤ 0.05 and 0.6 ≤ p ≤ 0.8, Weibull distribution is suggested to evaluate CIs of a pth quantile of the distributions, while, for 0.2 ≤ p ≤ 0.5 and p = 0.99, lognormal distribution is suggested to evaluate CIs of a pth quantile of the distributions. Besides, for p = 0.9 and 0.95, lognormal distribution is suggested if the sample size is large enough, while, for p = 0.1, Weibull distribution is suggested if the sample size is large enough. Finally, a simulation study is conducted to evaluate the efficiency of the proposed method.     

Improved Tolerance Factors for Multivariate Normal Distributions

The Q_os and Qm are two leading estimators of the probability of misclassification which are based on the asymptotic expansion of the the expected value of the Error Rate, P_i. The estimators are, however, not suitable for estimating the Error rates for certain ranges of the parameters p , n₁, n₂ and ß.We investigate the regions in which they produce unacceptable estimates , and show that the Q_os is, in general, better than the Q_m in producing acceptable estimates     

Confidence Interval of the Difference of Two Independent Binomial Proportions Using Weighted Profile Likelihood

Interval estimation of the difference of two independent binomial proportions is an important problem in many applied settings. Newcombe (1998 Newcombe , R. G. ( 1998 ). Interval estimation for the difference between independent proportions: comparison of seven methods . Statistics in Medicine 17 : 873 – 890 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) compared the performance of several existing asymptotic methods, and based on the results obtained, recommended a method known as Wilson's method, a modified version of a method originally proposed for single binomial proportion. In this article, we propose a method based on profile likelihood, where the likelihood is weighted by noninformative Jeffrey' prior. By doing extensive simulations, we find that the proposed method performs well compared to Wilson's method. A SAS/IML program implementing this method is also given with this article.     

Likelihood Ratio Tests for the Non Equivalence of Means

We derive likelihood ratio (LR) tests for the null hypothesis of equivalence that the normal means fall into a practical indifference zone. The LR test can easily be constructed and applied to k ≥ 2 treatments. Simulation results indicate that the LR test might be slightly anticonservative statistically, but when the sample sizes are large, it always produces the nominal level for mean configurations under the null hypothesis. More powerful than the studentized range test, the LR test is a straightforward application that requires only current existing statistical tables, with no complicated computations.     

The effect of temporal aggregation on the estimation accuracy of ARMA models

ABSTRACT

Autoregressive Moving Average (ARMA) time series model fitting is a procedure often based on aggregate data, where parameter estimation plays a key role. Therefore, we analyze the effect of temporal aggregation on the accuracy of parameter estimation of mixed ARMA and MA models. We derive the expressions required to compute the parameter values of the aggregate models as functions of the basic model parameters in order to compare their estimation accuracy. To this end, a simulation experiment shows that aggregation causes a severe accuracy loss that increases with the order of aggregation, leading to poor accuracy.