协方差

Robust estimation, RLS Estimation, M estimation, Independent observations, Correlated observations, Function model, Random model, Outliers analysis, Outliers Confirmation, Outliers Disposal, Infectant Distribution, Equivalent weights, Equivalent variance-covariance

稳健估计，稳健最小二乘估计， M 估计，独立观测，相关观测，函数模型，随机模型，粗差分析，粗差定位，粗差处理，污染分布，等价权，等价方差-协方差

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。

Estimation of parameters for general liner functional model with singular covariance. First, the Rao decomposition of the sample variance and the known singular measure error variance are presented and then the square measure error with singular variance and the standardized condition are got.

首先讨论了样本协方差与已知的奇异度量误差方差的Rao分解，给出了含有奇异方差广义逆的二次度量误差和模型的标准化条件，证明了二次度量误差与广义逆的选取无关。

The algorithms estimate the DOA of the broadband distributed source fron the secondary diagonal elements of the covariance matrices generated from every frequency domain of the received broadband signal s, thus avoiding unwrapping of phases.

该类算法首先将阵列接收的宽带信号变换到频率域，然后对于每个频率形成阵列接收信号协方差阵，最后由该协方差阵的次对角线元素估计宽带分布源的到达角，其主要特点是避免了相位展开。

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。

After studying this phenomenon, the author finds that, the covariance matrix of the complex expressions of horizontal gradients of the disturbing gravity field elements has a structure of blockwise repetitive Toeplitz matrix, though the covariance within the disturbing gravity field elements is still anisotropic. Therefore, the collocation problem of the complex combination of horizontal components is similar to that of gravity anomaly, which makes the degradation be able to be completed by FFT transformation matrix.

作者研究发现，利用水平梯度的复组合，即复数表示后，扰动重力场元复组合之间的协方差函数尽管还是各向异性，但它们对应的协方差矩阵却具有分块 Toeplitz 循环阵的结构，因而水平分量复组合的配置问题与重力异常的配置问题相似，可以利用傅立叶变换矩阵进行降阶处理。

In this paper we assume the expected returns of the risky and risk-free assets as well as the covariance matrix of the risky assets are not exactly known, but defined by some known elements, which form the vertices of this polytope. Robust optimal portfolio problems are proposed in the market with and without risk-free asset. And the analytical solutions are given out when the covariance matrix of the risky assets are exactly known.

本文假设风险资产和无风险资产的收益以及风险资产的协方差矩阵不是完全确定的，其相关参数属于某个已知的凸多面体，分别在市场不存在和存在无风险资产的情况下定义了稳健最优投资组合问题，并在协方差矩阵确定的情况下给出了问题的解析解。

In this paper a new method is proposed in order to suppress the coherent interference. First, utilizing the interpolate method, the real array can be virtually shifted under coherent interference, several covariance matrice are gererated after the virtual shifting. By averaging the previous results, a new covariance matrix is obtained. It is a full rank matrix.

提出一种新的相干波束形成方法，利用内插变换对相干背景下的真实阵列进行虚拟平移，得到多个虚拟平移后的信号协方差矩阵；对其进行平均后，所得到的相干信号协方差矩阵具有满秩性。

First, utilizing the interpolate method, the real array can be virtually shifted under coherent interference, several covariance matrice are gererated after the virtual shifting. By averaging the previous results, a new covariance matrix is obtained. It is a full rank matrix.

软件简介：提出一种新的相干波束形成方法，利用内插变换对相干背景下的真实阵列进行虚拟平移，得到多个虚拟平移后的信号协方差矩阵；对其进行平均后，所得到的相干信号协方差矩阵具有满秩性。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。