Optimal testing in a three way anova model

We consider likelihood ratio, score and Wald tests for a three-way random effects ANOVA model. Competitor tests are compared using criteria such as small sample power, asymptotic relative efficiency, and convenient null distribution. The final choice is between a new test and two tests long used in practice.     

Use of the Correlation Coefficient with Normal Probability Plots

The use of the correlation coefficient is suggested as a technique for summarizing and objectively evaluating the information contained in probability plots. Goodness-of-fit tests are constructed using this technique for several commonly used plotting positions for the normal distribution. Empirical sampling methods are used to construct the null distribution for these tests, which are then compared on the basis of power against certain nonnormal alternatives. Commonly used regression tests of fit are also included in the comparisons. The results indicate that use of the plotting position p_i = (i - .375)/(n + .25) yields a competitive regression test of fit for normality.     

Comparison of ANOVA-F and ANOM tests with regard to type I error rate and test power

A Monte Carlo simulation was conducted to compare the type I error rate and test power of the analysis of means (ANOM) test to the one-way analysis of variance F-test (ANOVA-F). Simulation results showed that as long as the homogeneity of the variance assumption was satisfied, regardless of the shape of the distribution, number of group and the combination of observations, both ANOVA-F and ANOM test have displayed similar type I error rates. However, both tests have been negatively affected from the heterogeneity of the variances. This case became more obvious when the variance ratios increased. The test power values of both tests changed with respect to the effect size (Δ), variance ratio and sample size combinations. As long as the variances are homogeneous, ANOVA-F and ANOM test have similar powers except unbalanced cases. Under unbalanced conditions, the ANOVA-F was observed to be powerful than the ANOM-test. On the other hand, an increase in total number of observations caused the power values of ANOVA-F and ANOM test approach to each other. The relations between effect size (Δ) and the variance ratios affected the test power, especially when the sample sizes are not equal. As ANOVA-F has become to be superior in some of the experimental conditions being considered, ANOM is superior in the others. However, generally, when the populations with large mean have larger variances as well, ANOM test has been seen to be superior. On the other hand, when the populations with large mean have small variances, generally, ANOVA-F has observed to be superior. The situation became clearer when the number of the groups is 4 or 5.     

农业强国建设及其关联问题

加快建设农业强国,要高度重视保障粮食和重要农产品稳定安全供给的重要性和紧迫性,但这是建设农业强国的底线要求,不是全部主要任务。保障粮食和重要农产品稳定安全供给是个系统工程,不可顾此失彼,要注意强化产业链供应链思维。通过分析巴西在保障粮食安全问题上的教训提出：解决粮食安全问题不仅“饭碗应该主要装中国粮”,还要注意这些粮源必须“自主可控”;加快建设农业强国必须同巩固拓展脱贫攻坚成果、促进工农城乡收入差距合理化结合起来;推进农业组织结构创新要注意依托双层经营体制发展农业,带动小农户合作经营、共同增收。当前加快建设农业强国时不我待,要注意推进相关研究强化包容互动。     

农业农村创新与创业联动机制研究

破除全面推进乡村振兴的创新瓶颈,关键是解决各自为战、低水平重复、转化率不高等导致的创新体系整体效能不高问题。中国农业农村发展的特殊性使其创新体系分为创新生产、成果转化、应用推广三个相对独立的环节。创新体系整体效能不高的根源是三个环节衔接不畅,不同主体逻辑分化导致的部分环节“自我循环”、创新链条短化,叠加小农户创新需求难以表达、创新服务供给成本高,使创新供给与需求不匹配。如果不建立创新供给与需求的内在联系,强调创新供给的资源投入,可能造成更多的资源沉淀和投入浪费。农业农村创业迅速发展形成了大量具有创新内生需求的主体和乡村全面振兴人才,有助于打开创新“自我循环”,畅通创新要素循环流动通道,促进农业农村创新均衡发展。从完善创新体系的需求出发,以联动创业与创新为探索方向,以高质量创业补齐创新体系短板,是增强农业农村创新动能的有效机制。要把创新导向和创新价值的创业纳入农业农村创新体系,统筹生计型创业和创新型创业,建立创新型创业的孵化和服务体系,优化乡村营商和发展环境,推动农业农村创业与创新的融合发展。     

Exceedance probabilities for parametric control charts

Common control charts assume normality and known parameters. Quite often, these assumptions are not valid and large relative errors result in the usual performance characteristics such as the false alarm rate or the average run length. A fully nonparametric approach can form an attractive alternative but requires more Phase I observations than usually available. Sufficiently general parametric families then provide realistic intermediate models. In this article, the performance of charts based on such families is considered. Exceedance probabilities of the resulting stochastic performance characteristics during in-control are studied. Corrections are derived to ensure that such probabilities stay within prescribed bounds. Attention is also devoted to the impact of the corrections for an out-of-control process. Simulations are presented both to illustrate and to demonstrate that the approximations obtained are sufficiently accurate for practical usage.     

Convergence of non-linear functionals of smoothed empirical processes and kernel density estimates

We consider regularizations by convolution of the empirical process and study the asymptotic behaviour of non-linear functionals of this process. Using a result for the same type of non-linear functionals of the Brownian bridge, shown in a previous paper [4], and a strong approximation theorem, we prove several results for the p-deviation in estimation of the derivatives of the density. We also study the asymptotic behaviour of the number of crossings of the smoothed empirical process defined by Yukich [17] and of a modified version of the Kullback deviation.     

Consistency of maximum likelihood estimators in a large class of deconvolution models

We consider the maximum likelihood estimator $\hat{F}_n$ of a distribution function in a class of deconvolution models where the known density of the noise variable is of bounded variation. This class of noise densities contains in particular bounded, decreasing densities. The estimator $\hat{F}_n$ is defined, characterized in terms of Fenchel optimality conditions and computed. Under appropriate conditions, various consistency results for $\hat{F}_n$ are derived, including uniform strong consistency. The Canadian Journal of Statistics 41: 98–110; 2013 © 2012 Statistical Society of Canada     

Powers of Discrete Goodness-of-Fit Test Statistics for a Uniform Null Against a Selection of Alternative Distributions

The comparative powers of six discrete goodness-of-fit test statistics for a uniform null distribution against a variety of fully specified alternative distributions are discussed. The results suggest that the test statistics based on the empirical distribution function for ordinal data (Kolmogorov–Smirnov, Cramér–von Mises, and Anderson–Darling) are generally more powerful for trend alternative distributions. The test statistics for nominal (Pearson's chi-square and the nominal Kolmogorov–Smirnov) and circular data (Watson's test statistic) are shown to be generally more powerful for the investigated triangular (∨), flat (or platykurtic type), sharp (or leptokurtic type), and bimodal alternative distributions.     

Control charts for location based on different sampling schemes

Control charts are the most important statistical process control tool for monitoring variations in a process. A number of articles are available in the literature for the X? control chart based on simple random sampling, ranked set sampling, median-ranked set sampling (MRSS), extreme-ranked set sampling, double-ranked set sampling, double median-ranked set sampling and median double-ranked set sampling. In this study, we highlight some limitations of the existing ranked set charting structures. Besides, we propose different runs rules-based control charting structures under a variety of sampling strategies. We evaluate the performance of the control charting structures using power curves as a performance criterion. We observe that the proposed merger of varying runs rules schemes with different sampling strategies improve significantly the detection ability of location control charting structures. More specifically, the MRSS performs the best under both single- and double-ranked set strategies with varying runs rules schemes. We also include a real-life example to explain the proposal and highlight its significance for practical data sets.