(中國科學(xué)院測量與地球物理研究所， 武漢 430077)
摘 要: 在分析了向量空間中最小二乘原理的基礎(chǔ)上，依據(jù)Hilbert空間的可分性，提出并論證了值域空間的正交分解定理及其推論，從而揭示了從觀測向量空間到值域空間的投影算子的特性， 提出了參數(shù)分組估計(jì)方法和相應(yīng)的估計(jì)公式，為研究參數(shù)向量間復(fù)共線性影響最小二乘估計(jì)質(zhì)量提供了一種有效的方法。
關(guān)鍵字: 關(guān)鍵詞: Hilbert空間 投影算子 參數(shù)估計(jì)
（Institute of Measure and Geophysics, Chinese Academy of Sciences,Wuhan 430077, P. R. China）
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.
Key words: Hilbert space projection operator parameter estimate
