值域空间的正交分解与参数分组估计

来源期刊：中国有色金属学报1998年第3期

论文作者：卢秀山 欧吉坤

文章页码：541 - 546

关键词：Hilbert空间； 投影算子； 参数估计

Key words：Hilbert space； projection operator； parameter estimate

摘    要：在分析了向量空间中最小二乘原理的基础上，依据Hilbert空间的可分性，提出并论证了值域空间的正交分解定理及其推论，从而揭示了从观测向量空间到值域空间的投影算子的特性， 提出了参数分组估计方法和相应的估计公式，为研究参数向量间复共线性影响最小二乘估计质量提供了一种有效的方法。

Abstract: Having briefly introduced the principle of least-squares in vector space, based on the resolvable character of limited dimensions Hilbert space, the mutual orthogonal resolution theorem of value domain space and its deduction have been offered and demonstrated. Therefore, it revealed the specific property of projection operator which projects observation vectors from observation vector space to corresponding value domain space. According to the theorem and its deduction, the method of parameter grouped estimate as well as relevant estimate formula has been advanced. It provided one kind of effective method by which to study that the multicollinearty among the parameter vectors could effect the qualities of least-squares estimation.