To understand any statistical tool requires not only an understanding of the relevant computational procedures but also an awareness of the assumptions upon which the procedures are based, and the effects of violation...To understand any statistical tool requires not only an understanding of the relevant computational procedures but also an awareness of the assumptions upon which the procedures are based, and the effects of violations of these assumptions. In our earlier articles (Laverty, Miket, & Kelly [1]) and (Laverty & Kelly, [2] [3]) we used Microsoft Excel to simulate both a Hidden Markov model and heteroskedastic models showing different realizations of these models and the performance of the techniques for identifying the underlying hidden states using simulated data. The advantage of using Excel is that the simulations are regenerated when the spreadsheet is recalculated allowing the user to observe the performance of the statistical technique under different realizations of the data. In this article we will show how to use Excel to generate data from a one-way ANOVA (Analysis of Variance) model and how the statistical methods behave both when the fundamental assumptions of the model hold and when these assumptions are violated. The purpose of this article is to provide tools for individuals to gain an intuitive understanding of these violations using this readily available program.展开更多
In a one-way analysis-of-variance(ANOVA)model,the number of pairwise comparisons can become large even with a moderate number of groups.Motivated by this,we consider a regime with a growing number of groups and prove ...In a one-way analysis-of-variance(ANOVA)model,the number of pairwise comparisons can become large even with a moderate number of groups.Motivated by this,we consider a regime with a growing number of groups and prove that,when testing pairwise comparisons,the Benjamini-Hochberg(BH)procedure can asymptotically control false discoveries,despite the fact that the involved t-statistics do not exhibit the wellknown positive dependence structure required for exact false discovery rate(FDR)control.Following Tukey's perspective that the di erence between the means of any two groups cannot be exactly zero,our main result provides control over the directional false discovery rate and directional false discovery proportion.A key technical contribution of our work is demonstrating that the dependence among the t-statistics is suciently weak to establish the convergence result typically required for asymptotic FDR control.Our analysis does not rely on conventional assumptions such as normality,variance homogeneity,or a balanced design,thereby o ering a theoretical foundation for applications in more general settings.展开更多
By introducing XOR operation and one-way function chains to group key management schemes based on the keys tree, a new group key management scheme based on the keys tree, XOR operation and one-way function chains is p...By introducing XOR operation and one-way function chains to group key management schemes based on the keys tree, a new group key management scheme based on the keys tree, XOR operation and one-way function chains is proposed. Initialization, member adding and member evicting operations are introduced. The new scheme is compared with three other group key management schemes which are based on the keys tree： SKDC, LKH, and OFF. As far as transmission, computation and storage costs are concerned, the performance of the new group key management scheme is the best. The security problem of the new scheme is analyzed. This new scheme provides backward and forward security, i.e.. newly admitted group members cannot read previous multicast messages and evicted members cannot read future multicast messages, even with collusion by many arbitrarily evicted members.展开更多
文摘To understand any statistical tool requires not only an understanding of the relevant computational procedures but also an awareness of the assumptions upon which the procedures are based, and the effects of violations of these assumptions. In our earlier articles (Laverty, Miket, & Kelly [1]) and (Laverty & Kelly, [2] [3]) we used Microsoft Excel to simulate both a Hidden Markov model and heteroskedastic models showing different realizations of these models and the performance of the techniques for identifying the underlying hidden states using simulated data. The advantage of using Excel is that the simulations are regenerated when the spreadsheet is recalculated allowing the user to observe the performance of the statistical technique under different realizations of the data. In this article we will show how to use Excel to generate data from a one-way ANOVA (Analysis of Variance) model and how the statistical methods behave both when the fundamental assumptions of the model hold and when these assumptions are violated. The purpose of this article is to provide tools for individuals to gain an intuitive understanding of these violations using this readily available program.
基金Weidong Liu was supported by National Natural Science Foundation of China(Grant No.11825104)Qi-Man Shao was supported by National Natural Science Foundation of China(Grant No.12031005)Shenzhen Outstanding Talents Training Fund of China.
文摘In a one-way analysis-of-variance(ANOVA)model,the number of pairwise comparisons can become large even with a moderate number of groups.Motivated by this,we consider a regime with a growing number of groups and prove that,when testing pairwise comparisons,the Benjamini-Hochberg(BH)procedure can asymptotically control false discoveries,despite the fact that the involved t-statistics do not exhibit the wellknown positive dependence structure required for exact false discovery rate(FDR)control.Following Tukey's perspective that the di erence between the means of any two groups cannot be exactly zero,our main result provides control over the directional false discovery rate and directional false discovery proportion.A key technical contribution of our work is demonstrating that the dependence among the t-statistics is suciently weak to establish the convergence result typically required for asymptotic FDR control.Our analysis does not rely on conventional assumptions such as normality,variance homogeneity,or a balanced design,thereby o ering a theoretical foundation for applications in more general settings.
文摘By introducing XOR operation and one-way function chains to group key management schemes based on the keys tree, a new group key management scheme based on the keys tree, XOR operation and one-way function chains is proposed. Initialization, member adding and member evicting operations are introduced. The new scheme is compared with three other group key management schemes which are based on the keys tree： SKDC, LKH, and OFF. As far as transmission, computation and storage costs are concerned, the performance of the new group key management scheme is the best. The security problem of the new scheme is analyzed. This new scheme provides backward and forward security, i.e.. newly admitted group members cannot read previous multicast messages and evicted members cannot read future multicast messages, even with collusion by many arbitrarily evicted members.
