| BERRY-ESSEEN BOUNDS OF ERROR VARIANCE ESTIMATION IN PARTLY LINEAR MODELS |
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| 引用本文： | Gao Jiti,Hong Shengyan,Liang Hua. BERRY-ESSEEN BOUNDS OF ERROR VARIANCE ESTIMATION IN PARTLY LINEAR MODELS[J]. 数学年刊B辑(英文版), 1996, 17(4): 477-490 |
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| 作者姓名： | Gao Jiti Hong Shengyan Liang Hua |
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| 作者单位： | [1]DepartmentofMathemaitcs,UniversityofScience＆TechnologyofChina,Hefei230026,China. [2]InstituteofSyatemsScience,AcademiaSinica,Beijing100080,China. [4]DepartmentofMathematics,UniversityofAnhui,Hefei230039,China. |
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| 基金项目： | ProjectsupportedbytheProbab .Lab .,Inst.ofApp .Math .,ChineseAcademyofSciencesandNationalNaturalSci enceFoundationofChina |
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| 摘 要： | §1.ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｓｉｄｅｒｔｈｅｍｏｄｅｌｇｉｖｅｎｂｙＹｉ=ｘｉτβ ｇ(ｔｉ) εｉ,ｉ=1,…,(1.1)ｗｈｅｒｅｘｉ=(ｘｉ1,…,ｘｉｐ)τ(ｐ1)ａｎｄｔｉ(ｔｉ∈[0,1])ａｒｅｋｎｏｗｎｄｅｓｉｇｎｐｏｉｎｔｓ,β=(β1,…,βｐ)τｉｓａｎｕｎｋｎｏｗｎｐａｒａｍｅｔｅｒｖｅｃｔｏｒａｎｄｇｉｓａｎｕｎｋｎｏｗｎｆｕｎｃｔｉｏｎ,ａｎｄεｉａｒｅｉ.ｉ.ｄ.ｒａｎｄｏｍｅｒｒｏｒｓｗｉｔｈｚｅｒｏ0ａｎｄｖａｒｉａｎｃｅσ2.Ｔｈｅｍｏｄｅｌｄｅｆｉｎｅｄｉｎ(1.1)ｂｅｌｏｎｇｓｔｏｔｈｅｃｌａｓｓ…
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| 关 键 词： | BERRY-ESSEEN边界 误差方差估计 部分线性模型 最小平方估计 |
| 收稿时间： | 1994-01-31 |
| 修稿时间： | 1995-05-24 |
BERRY-ESSEEN BOUNDS OF ERROR VARIANCE ESTIMATIONIN PARTLY LINEAR MODELS |
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| Gao Jiti,Hong Shengyan and Liang Hua. BERRY-ESSEEN BOUNDS OF ERROR VARIANCE ESTIMATIONIN PARTLY LINEAR MODELS[J]. Chinese Annals of Mathematics,Series B, 1996, 17(4): 477-490 |
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| Authors: | Gao Jiti Hong Shengyan Liang Hua |
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| Affiliation: | Department of Mathematics, University of Science & Technologyof China, Hefei 230026, China,Department of Mathematics, University of Anhui, Hefei 230039,China and Institute of Systems Science, Academia Sinica, Beijing 100080,China |
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| Abstract: | Consider the regression model $Y_i=x_i^taubeta+g(t_i)+varepsilon_i$ for $i=1,cdots, n.$ Here $(x_i, t_i)$ are known and nonrandom design points and $E_i$ are i.i.d. random errors. The family of nonparametric estimates $hat g_n(cdot)$ of $g(cdot)$ including some known estimates is proposed. Based on the model $Y_i=x_i^taubeta+hat g_n(t_i)+varepsilon_i,$ the Berry-Esseen bounds of the distribution of the least-squares estimator of $beta$ are investigated. |
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| Keywords: | Partly linear model Least-squares estimate Berry-Esseen bounds |
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