测试伪随机数发生器(pseudo random number generator,PRNG)的性能是一个非常重要的问题,通常以能否通过检验均匀性和独立性的统计测试方法来衡量.1998年Rudnick和Sarnak提出了[0,1)上实数序列的泊松对相关(Poissonian pair correlation...测试伪随机数发生器(pseudo random number generator,PRNG)的性能是一个非常重要的问题,通常以能否通过检验均匀性和独立性的统计测试方法来衡量.1998年Rudnick和Sarnak提出了[0,1)上实数序列的泊松对相关(Poissonian pair correlations,PPC)的概念,独立且均匀分布的实数序列满足泊松对相关.该文基于泊松对相关的概念提出了一种测试(0,1)中伪随机数序列的一级统计测试方法,给出了收敛判别标准的选取方法,并对常见的PRNG(线性同余发生器、Mersenne Twister、Matlab.rand函数以及基于无理数π重叠产生的PRNG等)进行了测试,同时与卡方检验、序列检验、游程检验以及自相关检验进行比较.结果表明该测试方法不仅简单灵活、可操作性和可移植性较强,能有效地同时检验伪随机数序列的均匀性和独立性.展开更多
We consider the statistical inference for right-censored data when censoring indicators are missing but nonignorable, and propose an adjusted imputation product-limit estimator. The proposed estimator is shown to be c...We consider the statistical inference for right-censored data when censoring indicators are missing but nonignorable, and propose an adjusted imputation product-limit estimator. The proposed estimator is shown to be consistent and converges to a Gaussian process. Furthermore, we develop an empirical processbased testing method to check the MAR (missing at random) mechanism, and establish asymptotic properties for the proposed test statistic. To determine the critical value of the test, a consistent model-based bootstrap method is suggested. We conduct simulation studies to evaluate the numerical performance of the proposed method and compare it with existing methods. We also analyze a real data set from a breast cancer study for an illustration.展开更多
Second-order stochastic dominance plays an important role in reliability and various branches of economics such as finance and decision-making under risk, and statistical testing for the stochastic dominance is often ...Second-order stochastic dominance plays an important role in reliability and various branches of economics such as finance and decision-making under risk, and statistical testing for the stochastic dominance is often useful in practice. In this paper, we present a test of stochastic equality under the constraint of second-order stochastic dominance based on the theory of empirical processes. The asymptotic distribution of the test statistic is obtained, and a simple method to compute the critical value is derived. Simulation results and real data examples are presented to illustrate the proposed test method.展开更多
文摘测试伪随机数发生器(pseudo random number generator,PRNG)的性能是一个非常重要的问题,通常以能否通过检验均匀性和独立性的统计测试方法来衡量.1998年Rudnick和Sarnak提出了[0,1)上实数序列的泊松对相关(Poissonian pair correlations,PPC)的概念,独立且均匀分布的实数序列满足泊松对相关.该文基于泊松对相关的概念提出了一种测试(0,1)中伪随机数序列的一级统计测试方法,给出了收敛判别标准的选取方法,并对常见的PRNG(线性同余发生器、Mersenne Twister、Matlab.rand函数以及基于无理数π重叠产生的PRNG等)进行了测试,同时与卡方检验、序列检验、游程检验以及自相关检验进行比较.结果表明该测试方法不仅简单灵活、可操作性和可移植性较强,能有效地同时检验伪随机数序列的均匀性和独立性.
基金supported by National Natural Science Foundation of China (Grant Nos. 10901162 and 10926073)China Postdoctoral Science Foundation and Foundation of the Key Laboratory of Random Complex Structures and Data Science, Chinese Academy of Sciences+2 种基金supported by National Natural Science Foundation of China (Grant Nos. 10971007 and 11101015)the fund from the government of Beijing (Grant No. 2011D005015000007)supported by National Science Foundation of US (Grant Nos. DMS0806097 and DMS1007167)
文摘We consider the statistical inference for right-censored data when censoring indicators are missing but nonignorable, and propose an adjusted imputation product-limit estimator. The proposed estimator is shown to be consistent and converges to a Gaussian process. Furthermore, we develop an empirical processbased testing method to check the MAR (missing at random) mechanism, and establish asymptotic properties for the proposed test statistic. To determine the critical value of the test, a consistent model-based bootstrap method is suggested. We conduct simulation studies to evaluate the numerical performance of the proposed method and compare it with existing methods. We also analyze a real data set from a breast cancer study for an illustration.
基金This work is supported by Grants from the Natural Science Foundation of China （11271039） Specialized Research Fund for the Doctoral Program of Higher Education+2 种基金 Research Fund of Weifang University （2011Z24） Funding Project of Science and Technology Research Plan of Weifang City （201301019） The Natural Science Foundation of Shandong （ZR2013FL032）.
文摘Second-order stochastic dominance plays an important role in reliability and various branches of economics such as finance and decision-making under risk, and statistical testing for the stochastic dominance is often useful in practice. In this paper, we present a test of stochastic equality under the constraint of second-order stochastic dominance based on the theory of empirical processes. The asymptotic distribution of the test statistic is obtained, and a simple method to compute the critical value is derived. Simulation results and real data examples are presented to illustrate the proposed test method.
