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| 1 | GENERALIZED p-VALUES AND GENERALIZED CONFIDENCE INTERVALS FOR VARIANCE COMPONENTS IN GENERAL RANDOM EFFECT MODEL WITH BALANCED DATA显示文摘 | Rendao YE Songgui WANG | 2007 | Journal of Systems Science & Complexity2007，20，4： | 8 |
| 2 | A matrix version of the Wielandt inequality and its application to statistics显示文摘Suppose that A is an n×n positive definite Hemitain matrix. Let X and Y ben×p and n×q matrices(p+q≤n), such that X*Y=O. The following inequality is provedX*AY(YAY)-Y*AX≤((λ1-λn)/(λ1+λn)2)X*AX,where λ1 and λn are respectively the largest and smallest eigenvalues of A, and M- stands for a generalized inverse of M. This inequality is an extension of the well-known Wielandt inequality in which both X and Y are vectors. The inequality is utilized to obtain some interesting inequalities about covariance matrix and various correlation coefficients including the canonical correlation, multiple and simple correlation. | WANG Songgui Wai-Cheung IpDepartment of Applied Mathematics, Beijing Polytechnic University, Beijing 100022, China Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing 100080, China Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China | 1999 | Chinese Science Bulletin1999，44，2： | 7 |
| 3 | Simultaneous optimal estimates of fixed effects and variance components in the mixed model显示文摘For a general linear mixed model with two variance components, a set of simple conditions is obtained, under which, (i) the least squares estimate of the fixed effects and the analysis of variance (ANOVA) estimates of variance components are proved to be uniformly minimum variance unbiased estimates simultaneously; (ii) the exact confidence intervals of the fixed effects and uniformly optimal unbiased tests on variance components are given; (iii) the exact probability expression of ANOVA estimates of variance components taking negative value is obtained. | WU Mixia WANG Songgui | 2004 | Science China Mathematics2004，47，5： | 6 |
| 4 | A new method of spectral decomposition of covariance matrix in mixed effects models and its applications显示文摘For the mixed effects models with balanced data, a new ordering of design matrices of random effects is defined, and then a simple formula of the spectral decomposition of covariance matrix is obtained. To compare with the two methods in literature,the decomposition can not only give the actual number of all distinct eigenvalues and their expression, but also show clearly the relationship between the design matrices of random effects and the decomposition. These results can be applied to the problems for testifying the analysis of the variance estimate being a minimum variance unbiased under all random effects models and some mixed effects models with balanced data, for finding the explicit solution of maximum likelihood equations for the general mixed effects model and for showing the relationship between the spectral decomposition estimate and the analysis of variance estimate. | WU Mixia WANG Songgui | 2005 | Science China Mathematics2005，48，11： | 4 |
| 5 | Adaptive ridge predictor in finite populations显示文摘 | Wang Songgui | 1990 | Chinese Science Bulletin1990，，11： | 1 |
| 6 | A new estimate of the parameters in linear mixed model显示文摘 | WANG Songgui YIN Suju | 2002 | Science in China2002，45，10： | 1 |
| 7 | Consistent nonnegative estimates of variance components 显示文摘 | Xu Liwen Wang Songgui Shi Jianhong | 2010 | Acta Mathematica Applicate Sinica2010，2，： | 1 |
| 8 | On the measures of multicollineaxity in least squares regression 显示文摘 | WANG Songgui Tse Sinkeung Chow Sheinchung | 1990 | Statistics and Probability Letter1990，9，： | 1 |
| 9 | Kantoroyicg-tpye inequalities and the measures of inefficiency of the GLSE 显示文摘 | WANG Songgui HU Yang | 1989 | ACTA Mathematics Applicatae Sinica1989，5，4： | 1 |
| 10 | A new estimate of the parameters in linear mixed models显示文摘 | Wang Songgui Yin Suju | 2002 | Science in China Series A: Mathematics2002，，10： | 1 |
| 11 | The linear minimax estimator of stochastic regression coefficients and parameters under quadratic loss function显示文摘 | Xu liwen Wang songgui | 2005 | Chinese Annals of Mathematics Series A2005，26，： | 1 |
| 12 | J Constrained Kantorovich Inequalities and Relative Efficiency of Least Squares 显示文摘 | Wang Songgui Shao | 1992 | J Multi Analysis1992，42，： | 1 |
| 13 | Constrained Kantorovich Inequalities and relative efficiency of least squares显示文摘 | Wang Songgui Shao Jun | 1992 | J Multi Analysis1992，42，： | 1 |
| 14 | Kantorovich-tpye Inequalities and the Measures of Inefficiency of the GLSE 显示文摘 | Wang Songgui Yang Hu | 1989 | Acta Mathematicae Aoplicatae Sinica1989，5，： | 1 |
| 15 | Kantorovich-type inequalities and the measures of emciency of the GLSE显示文摘 | Wang Songgui Yang Hu | 1989 | Acta Mathematicae Aoplicatae Sinica1989，5，： | 1 |
| 16 | A new estimate of the parameters in linear mixed models显示文摘 | Wang Songgui Yin Suju | 2002 | Science in China Series A: Mathematics2002，，10： | 1 |
| 17 | The spectral decomposition of covariance matrices for the variance components models 显示文摘 | SHI JIANHONG WANG SONGGUI | 2006 | Journal of Multi- variate Analysis2006，97，： | 1 |
| 18 | A TEST FOR SPHERICITY OF ERRORS IN LINEAR MODELS显示文摘For a general linear model, spherical distributions are often considered whenerrors do not have normal distribution. Several authors[1-3] studied the least squaresand James-Stein estimations for a linear model whose errors follow multivariate t or moregeneral spherical distributions. In this paper the test problem for sphericity of errors isconsidered. We propose an exact test for the sphericity by using the conditional probabilityintegral transformation and another transformation. As an important special case, thecorresponding test statistics for multivariate t distribution are obtained. | WANG Songgui(Institute of Statistics, Beijing Polytechnic University, Beijing 100022, China)(Institute of Applied of Mathematics, Academia Sinica, Beijing 100080, China)YANG Zhenhai(Institute of Statistics, Beijing Polytechnic University, Beijing 100022, | 1997 | Systems Science and Mathematical Sciences1997，10，3： | 0 |
| 19 | IMPROVED ANOVAE OF THE COVARIANCE MATRIX IN GENERAL LINEAR MIXED MODELS显示文摘在这份报纸,估计协变性矩阵的问题一般来说线性的混合模型被考虑。评估者的一个新班被建议。这个新评估者在二摆平的损失功能下面统治变化估计的分析,这被显示出。最后,把建议评估者的表演与变化的分析的作比较的一些模拟结果估计被报导。模拟结果显示这个新评估者在大多数状况下面在风险提供实质的改进。 | Rendao YE Tiefeng MA Songgui WANG | 2011 | Journal of Systems Science & Complexity2011，24，1： | 0 |
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