方差矩阵

This thesis has mainly contributed two results in theory: one is that the covariance matrix is not positive definitive if the number of sampling is least than the number of variables, the other is that the covariance matrix of discrete sample is positive definitive if and only if the sum of every random column vector of data matrix is non I-linear combination.

本论文在理论上，主要得出两个新的结果：ⅰ抽样调查中，若样本的个数少于变量的个数则样本协方差矩阵恒为非正定；ⅱ离散型样本协方差矩阵正定的充要条件是样本资料阵的各随机列向量是非I-线性组合。

Collocation needs to know the covariance matrix of the signal vector,which is usually evaluated by a chosen covariance function and corresponding coefficient fitting.

拟合推估解算必须首先求得信号向量的方差协方差矩阵，该协方差矩阵一般通过选定的协方差函数，并通过已测点数据进行拟合得到。

In a special case of 2 dimensional variables, the probability of the positive definitiveness of the discrete sample covariance matrix is given in term of sample size and variable dimension. Based on the results, the optimal sample size is provided in this thesis.

推出了离散型样本协方差矩阵正定的充要条件，得到了求离散型样本协方差矩阵正定概率的模型，建立了特殊情况下的抽样优化模型。

Unlike the previous method, however, the proposed algorithm obtains the new transformed matrix by taking the conjugate operation to the forward and backward spatial smoothing covariance matrix of the received data, so that the modified covariance differencing matrix which is a Hermitian matrix of zero real part can lower the computation load effectively during the eigenvalue decomposition.

不同于以前的算法，提出的算法通过对接收数据的前后向空间平滑协方差矩阵进行共轭运算得到新的变换矩阵，因此修正后的协方差差分矩阵是个实部为零的厄米特矩阵，从而有效地降低了特征分解过程的计算量。

METHODS: Both diastolic and systolic blood pressures repeated measures data, collected from 120 drug abusers after taking two kinds of medicine (Drug A: Xiaoyinfuzheng, Drug B: Kelening), were analyzed by multivariate random coefficients model. The fixed effect parameters matrix x of model coefficients were estimated by using least squares estimation method, the effects between treatment groups were compared and the variancecovariance matrices of random effect were also estimated.

对两种药物（A药：消瘾扶正胶囊，B药：可乐宁）治疗120例患者后的舒张压和收缩压重复观测数据进行多变量随机系数模型分析，对模型系数的固定效应参数矩阵ξ作最小二乘估计并进行组间比较，同时估计随机效应的方差协方差矩阵，分析方法用SAS/IML软件编程得以实现。

METHODS: Both diastolic and systolic blood pressures repeated measures data, collected from 120 drug abusers after taking two kinds of medicine (Drug A: Xiaoyinfuzheng, Drug B: Kelening), were analyzed by multivariate random coefficients model. The fixed effect parameters matrix x of model coefficients were estimated by using least squares estimation method, thelunwen114 effects between treatment groups were compared and the variancecovariance matrices of random effect were also estimated. Related analysis methods were programmed with SAS/IML code.

对两种药物（A药：消瘾扶正胶囊，B药：可乐宁）治疗120例患者后的舒张压和收缩压重复观测数据进行多变量随机系数模型分析，对模型系数的固定效应参数矩阵ξ作最小二乘估计并进行组间比较，同时估计随机效应的方差协方差矩阵，分析方法用SAS/IML软件编程得以实现。

For these important and practical problems,sample covariance matrix is an important statistic because many important statistics are functionals of it.When we make statistical inferences,such as estimations and/or hypothesis tests,the sample covariance matrices must be investigated.

以上诸多方面在做估计和假设检验过程中，无不用到大维随机矩阵的处理，尤其是大维样本协方差矩阵的相关性质，因为多元分析中许多重要的统计量都可以表示成样本协方差矩阵的函数。

Five ways on comparing covariance matrix are applied to the Shanghai 50 Indexes Stock Exchange, which are sample covariance matrix, scalar matrix, two-parameter covariance matrix, single index matrix, constant correlation matrix. We adopt principal components method and Markowitz portfolio method to measure stock market risk using VaR, getting the effect of measuring market risk. The result shows that sample covariance matrix and two-parameter covariance matrix could measure market risk more effectively.

本文以上证50指数数据为样本，采用样本协方差矩阵、数量矩阵、两参数模型矩阵、单指数模型矩阵、常量相关矩阵作为与股票相关的协方差矩阵，结合投资策略选择的主成分方法和Markowitz最优投资组合方法，计算VaR以度量市场风险，并比较了五种协方差矩阵度量市场风险的效果，结果表明，在主成分方法中，样本协方差矩阵和两参数矩阵方法能有效的度量市场风险。

On the ground that the covariance between the disturbing gravity field elements is not isotropic, the covariance matrix has a complicated structure (its submatrix being not repetitive Toeplitz matrix) and thus its degree cannot be degraded with transformation matrix method, so it cannot be put into practice. So far, the application of least squares collocation to the modeling and data processing of the horizontal disturbing gravity field observations has not been found in literature.

由于水平扰动场元之间的协方差并非各向同性，导致协方差矩阵结构复杂(子矩阵不是 Toeplitz 循环阵)，不能利用变换矩阵将其降阶，无法付诸实践，迄今尚无最小二乘配置理论应用于水平扰动场元观测量的模型化公式和数据处理方法。

The first method used not only the row element but also the column element of covariance matrix to structure a toeplitz matrix; this process accomplishes the function of forward/backward spatial smoothing for multipath signals.

第一种改进的方法不但利用了阵列输出协方差矩阵的行元素，而且还利用了阵列输出协方差矩阵的列元素构造Toeplitz矩阵，实现了前、后向空间平滑解相干的功能。

In the United States, chronic alcoholism and hepatitis C are the most common ones.

在美国，慢性酒精中毒，肝炎是最常见的。

If you have any questions, you can contact me anytime.

如果有任何问题，你可以随时联系我。