弱平稳序列 meaning in English
weakly stationary sequence
Examples
- This dissertation deals with how to estimate parameters of a model of multivariable weak stable auto - regression equation on time series ( marked by ar ( p ) ) and formulizes properties of them
本文系统地研究了多元弱平稳序列自回归模型ar ( p )的参数估计方法及性状。 - A important result is the one - orde r expression of ar ( p ) yt = dyt - 1 + e , from paralleling a high - order differential equation transformation into a one - order differential equation system , the one - order expression exposes that the ar ( p ) is only a certain more - multivariable power series process and , if a process is described as an ar ( p ) , the sufficient and necessary condition is the spectrum norm a of the coefficient matrix d less than one . simplification of ar ( p ) not only brings about orthogonal f ( h ) but also provides global foretelling formula
作者用高阶微分方程化一阶微分方程组的方法，获得多元弱平稳序列p阶自回归模型的一步滑动平均表达式，证明了ar ( p )的是一个更高维的幂级数的线性过程，从而，说明了ar ( p )关于序列依概率成立的充要条件是：该模型更高维的幂级数的线性过程的表达式中系数矩阵d的谱范数1 。 - It comes up with a new notion , d - solution , which is applied to the distance estimation , by virtue of hilbert space ; furthermore , the dissertation has gained a necessary condition which is identity of minimum mean - square value in linear function classes , so that d - solution extends minimum mean - square value within the domain of nonlinear function equation or equation system ; and , the dissertation studies in detail the classical moment estimation and maximal likelihood estimation on the parameters of ar ( p ) , a series of theorems in the estimation section shows the moment estimators are consistent on the ground of large samples jikewise , those distribution functions of the estimated parameters accord to maximum likelihood estimation converge gauss distribution if the white noise is gaussan
首先，借助hilbert空间理论，提出了距离估计的d -解，给出了d -解的必要条件，这个条件在线性函数类里即是极小二乘估计法， d -解的必要条件满足的方程实质上将极小二乘估计法推广到多函数及非线性函数类。再而，详细地研究了多元弱平稳序列自回归模型ar ( p )的参数经典的矩的替代估计和极大似然估计，获得矩的替代估计的一致性的结果。对基于gauss白噪声假设多元弱平稳序列自回归模型的均值、白噪声的协方差阵的极大似然估计都有依分布收敛到多元正态分布的统计性质。