| 1. | The independence of two d - dimensional random vectors is tested by employing the linear rank statistics based on depth function
利用基于深度函数的线性秩统计量检验两d维随机向量的独立性。 |
| 2. | Then using one of these representations , we work out the p . d . f of the student statistic tn defined by some random vectors xn come from csd
且用其中一种表示法计算了一些中心相似分布下t统计量的分布密度。 |
| 3. | In this paper , sufficient conditions are given for applicability of the law of the iterated logarithm for self - normalized sums of independent random vectors
摘要本文给出了独立随机向量序列自正则和的重对数律成立的一个充分条件。 |
| 4. | The property of continuous function and the formula of probability addition to the convergence in probability of continuous function sequence of random vector is used
摘要将依概率收敛的一维随机变量序列的连续函数仍依概率收敛的结论推广到随机向量序列的情形。 |
| 5. | First , some inequalities of gram determinant and further , some estimates for correlation coefficient of a system of random vectors and its subsystems are obtained
本文首先给出了矩阵行列式的几个不等式，进一步，给出了多组随机变量及其子系统的相关度量的几个估计 |
| 6. | Based on the thought of extending the domain on which the random vector xn has uniform distribution to other sets , we construct the concept of center simila r distribution ( csd ) , and give some related theorems . also we get two representations of csd
而后我们基于将向量均匀分布的区域改变成其他形式集合的思想，提出了中心相似分布的概念和相关定理，相应的也给出了中心相似分布的两种表示法。 |
| 7. | On the strength of the square loss function , this part also defines the vector loss function and matrix loss function , and discusses the bayesian risk decision solutions about random vector parameter and random matrix parameter under these loss functions respectively . secondly , the bayesian inference theory about single equation model is explored
在单参数平方损失函数的基础上，定义了向量损失函数，利用向量化算子vec定义了矩阵损失函数，并讨论了这两类损失函数下随机向量参数和随机矩阵参数的贝叶斯风险决策解。 |
| 8. | 3 gray factor analysis ? common factor model let random vector be written as common factors , they are unobservable random variables . s1 , s2 , . . . sp are said to be specific factors . from ( i x ( ii ) , the common factors are independent with each other , st only act on yi , the aij of matrix is called loading of factor , a = ( aij ) is called the loading matrix of factors ; because cov
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| 9. | Anderson , amemiva and fujisawa et al scholars extended the growth curve model into the one with random effects and considered the likelihood ratio criterion ( lrc ) for its mean structure , where the random vectors follow normal distribution on the assumptions that random effects and random errors are mutually independent [ 1 ] [ 2 ]
Anderson ， amemiva和fujisawa等学者将gc模型推广为含有随机效应的增长曲线模型( thegrowthcurvemodelwithrandomeffects ) ，并在观察矩阵服从正态分布的条件下作了关于均值的广义线性假设似然比检验。 |
| 10. | In this paper , we use the main results of type 2 vdr to analyze the spherical symmetric distribution . we obtain the two equivalent representations of the spherical symmetric distribution . they are both a product of a positive random variable and a random vector with uniform distribution , and the domain of uniform distribution are both related with sphere
本文将第二类垂直密度表示的主要结论应用于球对称分布，得到了球对称分布的两种等价表示形式，它们都是一个正随机变量与一个均匀分布向量的乘积的形式，且均匀分布的区域都与球有关。 |
