| 部分线性模型中估计的渐近正态性 |
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| 引用本文： | 高集体,陈希孺,赵林城. 部分线性模型中估计的渐近正态性[J]. 数学学报, 1994, 37(2): 256-268. DOI: cnki:ISSN:05831431.0.1994-02-014 |
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| 作者姓名： | 高集体 陈希孺 赵林城 |
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| 作者单位： | 中国科学技术大学数学系 |
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| 摘 要： | 考虑回归模型其中是未知函数，（ｘ＿ｉ，ｔ＿ｉ，ｕ＿ｉ）是固定非随机设计点列，β是待估参数，ｅ＿ｉ是随机误差。基于ｇ（·）及ｆ（·）的一类非参数估计（包括常见的核估计和近邻估计），我们构造了β的加权最小二乘估计，并证得了最小二乘估计和加权最小二乘估计的渐近正态性。
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| 关 键 词： | 部分线性模型，非参数估计，最小二乘估计，加权最小二乘估计，渐近正态性 |
| 收稿时间： | 1992-01-20 |
| 修稿时间： | 1993-04-14 |
Asymptotic Normality of a Class of Estimators in Partial Linear Models |
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| Goa Jiti, Chen Xiru, Zhao Lincheng. Asymptotic Normality of a Class of Estimators in Partial Linear Models[J]. Acta Mathematica Sinica, 1994, 37(2): 256-268. DOI: cnki:ISSN:05831431.0.1994-02-014 |
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| Authors: | Goa Jiti Chen Xiru Zhao Lincheng |
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| Affiliation: | Goa Jiti; Chen Xiru; Zhao Lincheng(Depedment of Mathematics, Univeroity of Science & Technology of china, Hefei,China) |
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| Abstract: | Consider the heteroscedastic regression,model y_i=x_iβ+g(t_i)+σ_ie_i forand i=1,2,…,n. Here the design points (x_i,t_i,u_i)are known and nonrandom,g and f areunknown functions, and e_i is an unobserued disturbahce. The family of nonparametric estimatesand including all known estimates is proposed,also proposed is a class of new nearestneighbor estimates of g and f.The least squares estimator β_n and the weighted least squaresestimator are obtained. Some asymptotically efficient estimates are also obtained. |
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| Keywords: | partial linear model.asymptotic normality nonparametric estimation least-squaresestimate weighted least-squares estimate |
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