The sign rank test is taught in virtually all introductory Statistics classes. When teaching the sign rank test the students are told to ignore the ties. Ignoring ties that support the null hypothesis is not logical. ...The sign rank test is taught in virtually all introductory Statistics classes. When teaching the sign rank test the students are told to ignore the ties. Ignoring ties that support the null hypothesis is not logical. Why should valid data that support the null hypothesis be ignored? The approach taken here demonstrates a method for testing with ties included. A typical problem presentation in a text book would indicate that if you had ten ties in a sample of size fifty the tie scores would be excluded. However, the ten tie scores are a very valuable piece of statistical information which should not be ignored. The method demonstrated here shows that a different conclusion is reached in some cases when the ties are not excluded. Further many sign tests often will have ties because in some cases the data are not a cardinal number, but an ordinal number chosen from a set often results in ties. The alternative approach uses a one-tailed distribution and considers both +’s and -'s separated. A two-tailed test for equal variances is done with a one-tail of an F distribution. This alternate approach to the sign test allows the use of important statistical information which has been ignored with the traditional sign rank test.展开更多
This article is concerned with the high-dimensional location testing problem.For highdimensional settings,traditional multivariate-sign-based tests perform poorly or become infeasible since their Type I error rates ar...This article is concerned with the high-dimensional location testing problem.For highdimensional settings,traditional multivariate-sign-based tests perform poorly or become infeasible since their Type I error rates are far away from nominal levels.Several modifications have been proposed to address this challenging issue and shown to perform well.However,most of modified sign-based tests abandon all the correlation information,and this results in power loss in certain cases.We propose a projection weighted sign test to utilize the correlation information.Under mild conditions,we derive the optimal direction and weights with which the proposed projection test possesses asymptotically and locally best power under alternatives.Benefiting from using the sample-splitting idea for estimating the optimal direction,the proposed test is able to retain type-I error rates pretty well with asymptotic distributions,while it can be also highly competitive in terms of robustness.Its advantage relative to existing methods is demonstrated in numerical simulations and a real data example.展开更多
A maximum test in lieu of forcing a choice between the two dependent samples t-test and Wilcoxon signed-ranks test is proposed. The maximum test, which requires a new table of critical values, maintains nominal α whi...A maximum test in lieu of forcing a choice between the two dependent samples t-test and Wilcoxon signed-ranks test is proposed. The maximum test, which requires a new table of critical values, maintains nominal α while guaranteeing the maximum power of the two constituent tests. Critical values, obtained via Monte Carlo methods, are uniformly smaller than the Bonferroni-Dunn adjustment, giving it power superiority when testing for treatment alternatives of shift in location parameter when data are sampled from non-normal distributions.展开更多
We propose a new nonparametric test based on the rank difference between the paired sample for testing the equality of the marginal distributions from a bivariate distribution. We also consider a modification of the n...We propose a new nonparametric test based on the rank difference between the paired sample for testing the equality of the marginal distributions from a bivariate distribution. We also consider a modification of the novel nonparametric test based on the test proposed by Baumgartern, Weiβ, and Schindler (1998). An extensive numerical power comparison for various parametric and nonparametric tests was conducted under a wide range of bivariate distributions for small sample sizes. The two new nonparametric tests have comparable power to the paired t test for the data simulated from bivariate normal distributions, and are generally more powerful than the paired t test and other commonly used nonparametric tests in several important bivariate distributions.展开更多
小世界神经网络具有较快的收敛速度和优越的容错性,近年来得到广泛关注.然而,在网络构造过程中,随机重连可能造成重要信息丢失,进而导致网络精度下降.针对该问题,基于Watts-Strogatz(WS)型小世界神经网络,提出了一种基于突触巩固机制的...小世界神经网络具有较快的收敛速度和优越的容错性,近年来得到广泛关注.然而,在网络构造过程中,随机重连可能造成重要信息丢失,进而导致网络精度下降.针对该问题,基于Watts-Strogatz(WS)型小世界神经网络,提出了一种基于突触巩固机制的前馈小世界神经网络(Feedforward small-world neural network based on synaptic consolidation,FSWNN-SC).首先,使用网络正则化方法对规则前馈神经网络进行预训练,基于突触巩固机制,断开网络不重要的权值连接,保留重要的连接权值;其次,设计重连规则构造小世界神经网络,在保证网络小世界属性的同时实现网络稀疏化,并使用梯度下降算法训练网络;最后,通过4个UCI基准数据集和2个真实数据集进行模型性能测试,并使用Wilcoxon符号秩检验对对比模型进行显著性差异检验.实验结果表明:所提出的FSWNN-SC模型在获得紧凑的网络结构的同时,其精度显著优于规则前馈神经网络及其他WS型小世界神经网络.展开更多
文摘The sign rank test is taught in virtually all introductory Statistics classes. When teaching the sign rank test the students are told to ignore the ties. Ignoring ties that support the null hypothesis is not logical. Why should valid data that support the null hypothesis be ignored? The approach taken here demonstrates a method for testing with ties included. A typical problem presentation in a text book would indicate that if you had ten ties in a sample of size fifty the tie scores would be excluded. However, the ten tie scores are a very valuable piece of statistical information which should not be ignored. The method demonstrated here shows that a different conclusion is reached in some cases when the ties are not excluded. Further many sign tests often will have ties because in some cases the data are not a cardinal number, but an ordinal number chosen from a set often results in ties. The alternative approach uses a one-tailed distribution and considers both +’s and -'s separated. A two-tailed test for equal variances is done with a one-tail of an F distribution. This alternate approach to the sign test allows the use of important statistical information which has been ignored with the traditional sign rank test.
基金NNSF of China Grants(Grant Nos.11925106,11690015,11931001 and 11971247)NSF of Tianjin Grant(Grant Nos.18JCJQJC46000 and 18ZXZNGX00140)+1 种基金111 Project B20016National Science Foundation(Grant Nos.DMS 1820702,DMS 1953196 and DMS 2015539)。
文摘This article is concerned with the high-dimensional location testing problem.For highdimensional settings,traditional multivariate-sign-based tests perform poorly or become infeasible since their Type I error rates are far away from nominal levels.Several modifications have been proposed to address this challenging issue and shown to perform well.However,most of modified sign-based tests abandon all the correlation information,and this results in power loss in certain cases.We propose a projection weighted sign test to utilize the correlation information.Under mild conditions,we derive the optimal direction and weights with which the proposed projection test possesses asymptotically and locally best power under alternatives.Benefiting from using the sample-splitting idea for estimating the optimal direction,the proposed test is able to retain type-I error rates pretty well with asymptotic distributions,while it can be also highly competitive in terms of robustness.Its advantage relative to existing methods is demonstrated in numerical simulations and a real data example.
文摘A maximum test in lieu of forcing a choice between the two dependent samples t-test and Wilcoxon signed-ranks test is proposed. The maximum test, which requires a new table of critical values, maintains nominal α while guaranteeing the maximum power of the two constituent tests. Critical values, obtained via Monte Carlo methods, are uniformly smaller than the Bonferroni-Dunn adjustment, giving it power superiority when testing for treatment alternatives of shift in location parameter when data are sampled from non-normal distributions.
文摘We propose a new nonparametric test based on the rank difference between the paired sample for testing the equality of the marginal distributions from a bivariate distribution. We also consider a modification of the novel nonparametric test based on the test proposed by Baumgartern, Weiβ, and Schindler (1998). An extensive numerical power comparison for various parametric and nonparametric tests was conducted under a wide range of bivariate distributions for small sample sizes. The two new nonparametric tests have comparable power to the paired t test for the data simulated from bivariate normal distributions, and are generally more powerful than the paired t test and other commonly used nonparametric tests in several important bivariate distributions.
文摘小世界神经网络具有较快的收敛速度和优越的容错性,近年来得到广泛关注.然而,在网络构造过程中,随机重连可能造成重要信息丢失,进而导致网络精度下降.针对该问题,基于Watts-Strogatz(WS)型小世界神经网络,提出了一种基于突触巩固机制的前馈小世界神经网络(Feedforward small-world neural network based on synaptic consolidation,FSWNN-SC).首先,使用网络正则化方法对规则前馈神经网络进行预训练,基于突触巩固机制,断开网络不重要的权值连接,保留重要的连接权值;其次,设计重连规则构造小世界神经网络,在保证网络小世界属性的同时实现网络稀疏化,并使用梯度下降算法训练网络;最后,通过4个UCI基准数据集和2个真实数据集进行模型性能测试,并使用Wilcoxon符号秩检验对对比模型进行显著性差异检验.实验结果表明:所提出的FSWNN-SC模型在获得紧凑的网络结构的同时,其精度显著优于规则前馈神经网络及其他WS型小世界神经网络.
