Mixed models provide a wide range of applications including hierarchical modeling and longitudinal studies. The tests of variance component in mixed models have long been a methodological challenge because of its boun...Mixed models provide a wide range of applications including hierarchical modeling and longitudinal studies. The tests of variance component in mixed models have long been a methodological challenge because of its boundary conditions. It is well documented in literature that the traditional first-order methods: likelihood ratio statistic, Wald statistic and score statistic, provide an excessively conservative approximation to the null distribution. However, the magnitude of the conservativeness has not been thoroughly explored. In this paper, we propose a likelihood-based third-order method to the mixed models for testing the null hypothesis of zero and non-zero variance component. The proposed method dramatically improved the accuracy of the tests. Extensive simulations were carried out to demonstrate the accuracy of the proposed method in comparison with the standard first-order methods. The results show the conservativeness of the first order methods and the accuracy of the proposed method in approximating the p-values and confidence intervals even when the sample size is small.展开更多
Tibetan heritage buildings have a high historical and cultural value. They have endured adverse environmental loadings over hundreds of years without significant damage. However, there are few reports on their structu...Tibetan heritage buildings have a high historical and cultural value. They have endured adverse environmental loadings over hundreds of years without significant damage. However, there are few reports on their structural characteristics under normal environmental loadings and their behavior under dynamic loadings. In this research, a typical Tibetan wooden wall-frame building is selected to study its dynamic characteristics. Field measurements of the structure were conducted under environmental excitation to collect acceleration responses. The stochastic subspace identification （SSI） method was adopted to calculate the structural modal parameters and obtain the out-of-plane vibration characteristics of the slab and frames. The results indicated that the wall-frame structure had a lower out-of-plane stiffness and greater in-plane stiffness due to the presence of stone walls. Due to poor identified damping ratio estimates from the SSI method, a method based on the variance upper bound was proposed to complement the existing variance lower bound method for estimating the modal damping ratio to address the significant damping variability obtained from different points and measurements. The feasibility of the proposed method was illustrated with the measured data from the floor slab of the structure. The variance lower and upper bound methods both provided consistent results compared to those from the traditional SSI method.展开更多
This article proposes a new lack-of-test based on the weighted ratio of residuals and variances for partially linear regression models. The large and small sampling properties of the proposed test are established. The...This article proposes a new lack-of-test based on the weighted ratio of residuals and variances for partially linear regression models. The large and small sampling properties of the proposed test are established. The testing procedure is illustrated via several examples. Simulation studies show that the testing procedures are powerful even in small samples. An application of the test to a real data set is presented.展开更多
To test variance homogeneity,various likelihood-ratio based tests such as the Bartlett's test have been proposed.The null distributions of these tests were generally derived asymptotically or approximately.We re-e...To test variance homogeneity,various likelihood-ratio based tests such as the Bartlett's test have been proposed.The null distributions of these tests were generally derived asymptotically or approximately.We re-examine the restrictive maximum likelihood ratio(RELR)statistic,and sug-gest a Monte Carlo algorithm to compute its exact null distribution,and so its p-value.It is much easier to implement than most existing methods.Simulation studies indicate that the proposed procedure is also superior to its competitors in terms of type I error and powers.We analyse an environmental dataset for an illustration.展开更多
研究了无穷方差序列均值变点的检测问题.首先基于 CUSUM 函数,通过 Ratio 检验方法,构造无穷方差序列均值变点的比率检验统计量,其次证明了检验统计量在原假设和备择假设下的极限分布,最后数值模拟表明本方法对无穷方差序列均值变点检...研究了无穷方差序列均值变点的检测问题.首先基于 CUSUM 函数,通过 Ratio 检验方法,构造无穷方差序列均值变点的比率检验统计量,其次证明了检验统计量在原假设和备择假设下的极限分布,最后数值模拟表明本方法对无穷方差序列均值变点检测的有效性.展开更多
Anderson-Darling （AD） sensing, characteristic function （CF） sensing and order statistic （OS） sensing are three common spectrum sensing （SS） methods based on goodness of fit （GOF） testing. However, AD and OS ...Anderson-Darling （AD） sensing, characteristic function （CF） sensing and order statistic （OS） sensing are three common spectrum sensing （SS） methods based on goodness of fit （GOF） testing. However, AD and OS sensing needs the prior information of noise variance; CF and OS sensing have high computation complexity. To circumvent those difficulties, in this paper, the ratio of the mean square to variance （RM2V） of the samples, after deriving its probability density function （PDF）, is employed as a test statistic to detect the availability of the vacant spectrum in the cognitive radio （CR） system. Then a blind SS method based on RM2V is proposed, which is dubbed as RM2V sensing, and its exact theoretical threshold is obtained via the derived PDF of RM2V. The performance of RM2V sensing is evaluated by theoretical analysis and Monte Carlo simulations. Comparing with the conventional energy detection （ED）, AD, CF and OS sensing, RM2V sensing, with no need of noise variance, has advantages from the aspect of computation complexity and detection performance.展开更多
文摘Mixed models provide a wide range of applications including hierarchical modeling and longitudinal studies. The tests of variance component in mixed models have long been a methodological challenge because of its boundary conditions. It is well documented in literature that the traditional first-order methods: likelihood ratio statistic, Wald statistic and score statistic, provide an excessively conservative approximation to the null distribution. However, the magnitude of the conservativeness has not been thoroughly explored. In this paper, we propose a likelihood-based third-order method to the mixed models for testing the null hypothesis of zero and non-zero variance component. The proposed method dramatically improved the accuracy of the tests. Extensive simulations were carried out to demonstrate the accuracy of the proposed method in comparison with the standard first-order methods. The results show the conservativeness of the first order methods and the accuracy of the proposed method in approximating the p-values and confidence intervals even when the sample size is small.
基金National Natural Science Foundation of China under Grant No.51338001Natural Science Foundation of China under Grant Nos.51178028 and 51422801+2 种基金the Fundamental Research Funds for the Central Universities under Grant No.2014YJS087Program for New Century Excellent Talents in University under Grant No.NCET-11-0571111 Project of China under Grant No.B13002
文摘Tibetan heritage buildings have a high historical and cultural value. They have endured adverse environmental loadings over hundreds of years without significant damage. However, there are few reports on their structural characteristics under normal environmental loadings and their behavior under dynamic loadings. In this research, a typical Tibetan wooden wall-frame building is selected to study its dynamic characteristics. Field measurements of the structure were conducted under environmental excitation to collect acceleration responses. The stochastic subspace identification （SSI） method was adopted to calculate the structural modal parameters and obtain the out-of-plane vibration characteristics of the slab and frames. The results indicated that the wall-frame structure had a lower out-of-plane stiffness and greater in-plane stiffness due to the presence of stone walls. Due to poor identified damping ratio estimates from the SSI method, a method based on the variance upper bound was proposed to complement the existing variance lower bound method for estimating the modal damping ratio to address the significant damping variability obtained from different points and measurements. The feasibility of the proposed method was illustrated with the measured data from the floor slab of the structure. The variance lower and upper bound methods both provided consistent results compared to those from the traditional SSI method.
基金partially supported by the Major Project of Humanities Social Science Foundation of Ministry of Education under Grant No.08JJD910247Key Project of Chinese Ministry of Education under Grant No. 108120+3 种基金National Natural Science Foundation of China under Grant No.11271368Beijing Natural Science Foundation under Grant No.1102021the Fundamental Research Funds for the Central Universitiesthe Research Funds of Renmin University of China under Grant Nos.10XNL018 and 11XNH107
文摘This article proposes a new lack-of-test based on the weighted ratio of residuals and variances for partially linear regression models. The large and small sampling properties of the proposed test are established. The testing procedure is illustrated via several examples. Simulation studies show that the testing procedures are powerful even in small samples. An application of the test to a real data set is presented.
基金The research of Li was supported by Grant 11871294 from National Natural Science Foundation of ChinaLiang’s research was partially supported by NSF grant DMS-1620898.
文摘To test variance homogeneity,various likelihood-ratio based tests such as the Bartlett's test have been proposed.The null distributions of these tests were generally derived asymptotically or approximately.We re-examine the restrictive maximum likelihood ratio(RELR)statistic,and sug-gest a Monte Carlo algorithm to compute its exact null distribution,and so its p-value.It is much easier to implement than most existing methods.Simulation studies indicate that the proposed procedure is also superior to its competitors in terms of type I error and powers.We analyse an environmental dataset for an illustration.
基金supported by Natural Science Foundation of China(6127127661301091)Natural Science Foundation of Shaanxi Province(2014JM8299)
文摘Anderson-Darling （AD） sensing, characteristic function （CF） sensing and order statistic （OS） sensing are three common spectrum sensing （SS） methods based on goodness of fit （GOF） testing. However, AD and OS sensing needs the prior information of noise variance; CF and OS sensing have high computation complexity. To circumvent those difficulties, in this paper, the ratio of the mean square to variance （RM2V） of the samples, after deriving its probability density function （PDF）, is employed as a test statistic to detect the availability of the vacant spectrum in the cognitive radio （CR） system. Then a blind SS method based on RM2V is proposed, which is dubbed as RM2V sensing, and its exact theoretical threshold is obtained via the derived PDF of RM2V. The performance of RM2V sensing is evaluated by theoretical analysis and Monte Carlo simulations. Comparing with the conventional energy detection （ED）, AD, CF and OS sensing, RM2V sensing, with no need of noise variance, has advantages from the aspect of computation complexity and detection performance.
