参数估计

When the underlying error term for tobit model is known to be normally distributed and homoskedasticity, maximum likelihood estimation is consistent and asymptotically normally distributed.

半参数估计是一种参数和非参数估计的混合，比相应的参数模型更能一致的估计参数，而且比非参数模型估计更精确，其优点是无需假定误差项分布，所以它对非正态和异方差是稳健的。

The examples indicate that the unknow parameters can be estimated faster and more accurately with the proposed objective function and SPSO, the solving procedure relies less on the augmented jacobian matrix, and the mean estimated values are close to the parameter truth values.

仿真算例表明：应用该文修正项和SPSO方法，能快速准确的估计线路参数，并提高参数估计精度和降低对量测系统参数可估计性的要求，估计均值更接近参数真值。

The examples indicate that the unkown line parameters can be estimated faster and more accurately with the proposed objective function and SPSO and the solving procedure relies less on the augmented jacobian matrix.

仿真算例表明：修正目标函数和SPSO算法能快速准确地估计线路参数，且可提高估计准确度和降低对量测系统参数可估计性的要求；取连续多次估计的均值，则可减小量测误差导致的参数估计偏差。

The performance function and constraint equation in calculus of variations were constructed by analyzing input and output equations of the system containing parameters to be estimated. The traditional parameter estimation problem could be transformed to that of least squares estimation.

通过分析包含待估参数的系统输入输出方程，构造变分法中的性能范函和约束方程，将传统的参数估计问题化为带约束条件的最小二乘估计问题；利用拉格朗日乘子法，分析参数估计方程，得到参数的最优估计。

In chapter 5,a knowledge-based correction term for the objective function of parameter estimation is proposed.The relationship between the function extreme points of state estimatin and parameter estimation is deduced.A strategy of projecting the parameter objective function from the augmented solution space to the parameter space is proposed and proved.

第五章分析了电力系统状态估计和参数估计的理论依据并指出传统解法的不足，提出基于经验知识的参数估计目标函数修正项，推导了状态估计和参数估计目标函数极值点的关系，由此提出并证明了新的基于垂直投影的估计策略。

A knowledge-based correction term in the objective function is proposed. The relationship between state estimatin and parameter estimation is analyzed. A strategy of projecting the objective function from the augmented solution space to the parameter space is proposed and proved.

该文提出基于经验知识的参数估计目标函数修正项，导出状态估计与参数估计目标函数极值的关系，由此提出将目标函数从增广解空间垂直投影到参数空间的估计策略，并指出参数估计偏差的成因。

In this method, the Maximum Likelihood Estimation and the Minimum Distance Estimation are integrated to settle the location parameter estimator.

针对三参数威布尔分布参数估计存在的问题，提出了参数复合估计法，将极大似然估计和最小距离估计有机结合，创造性地解决了位置参数估计问题。

Lagrange multiplication operator was used to analyze the parameter estimation equation for obtaining the optimized estimation of parameters. Computer simulation result showed that this method is better than traditional least squares estimation.

计算机仿真的结果表明，该优于传统的最小二乘估计法，获得的估计参数是渐进无偏的，获得的估计参数的辨识精度更高，该参数约束估计法在系统辨识和参数估计领域具有极其重要的实际应用价值。

The first one focuses upon the fundamental theory and methods of system identification, including the basic concepts of system description and identification,review of matrix theory, stochastic process and pulse response of linear systems; the first principle models for lumped and distributed parameter systems; modeling of bioreactions; auto regressive moving average model; weighted least square and regressive weighted least square for parameter estimation of ARMA model; Runge-Kutta and Simplex methods; an example of BPNN application; as well as Kalman Filter.

第一部分包括知识驱动建模、数据驱动建模、参数估计和状态估计的基础理论和方法。具体为：(1)系统辨识和系统描述的基本概念，包括矩阵论、随机过程、线性系统的脉冲响应函数等基础知识回顾；(2)基于动态物料和能量衡算的集总参数、分布参数对象的知识驱动建模方法；(3)生物反应系统的建模方法；(4)自回归移动平均模型；(5) ARMAX模型参数的加权最小二乘参数估计一次性算法和递推算法，相应的统计性质；(6)龙格库塔法和单纯形法；BP神经网络应用实例；(7)卡尔曼滤波器，及其与加权最小二乘参数估计递推算法的对比。

In conventional indirected parameter estimate, such as Weighted Least Square Method, the changing activity of the injected radiotracer is conventionally measured through multiple consecutive PET image reconstructions. The image of the radioactivity distribution in each frame is reconstructed independently and the whole set of frames is then used to estimate the distribution of the physiological parameter of interest by the application of an appropriate pharmacokinetic model to the time radioactivity curve either of appropriately selected functional regions or of each image element.

传统的间接参数估计方法如加权最小二乘参数估计方法(Weighted Least SquareMethod，WLS)，需要首先从测量数据重建出PET动态放射性活度图像，然后在这些时间上连续的重建图像应用适当的动力学模型上估计感兴趣的生理参数，然而PET重建图像中往往含有极大的噪声，这些噪声将影响参数估计的准确性。

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。