一类新半参数回归模型参数估计的强收敛速度
摘要
本文讨论了一类新的半参数回归模型，在一组比较基本的条件下，得到了估计量的较好的一致强收敛速度。全文共分两章。
文章的第一章简要介绍文章的有关背景，半参数回归模型在国内外发展的有关现状，本文所要解决的主要问题及其意义。第二章共分六节。第一节为引言，提出本文所讨论的模型。第二节介绍了估计量的构造及文章所需的假设条件。第三节给出了本文的主要结果,即各估计量的一致强收敛速度。第四节和第五节利用有关假设条件分别证明了引理和定理。第六节为文章的注记，指出了就目前而言，本文的结果是最好的。
In this paper, we have considered a new class of semiparametric regression model Under some mild conditions we have obtained better uniformly strong convergence rates for the proposed estimators. The paper consists of two chapters.
In the first chapter, we have introduced the background of this paper, the development of Semiparametric regression model, the questions we were going to discuss, and its profound meaning. The second chapter consists of six sections. The first section is introduction, where we have brought forward the model we should discuss. In the second section, we have introduced the formation for the estimators and the proposed conditions that the paper needed . In the third section, we have presented the main result of the paper, namely the uniformly strong convergence rates for each estimator. In the fourth and fifth sections, by utilizing some relating proposed conditions we have proved the lemmas and theorems respectively. In the sixth footnote section of the paper, it pointed out that as far as the present, the outcome in the paper was the best.
文章的第一章简要介绍文章的有关背景，半参数回归模型在国内外发展的有关现状，本文所要解决的主要问题及其意义。第二章共分六节。第一节为引言，提出本文所讨论的模型。第二节介绍了估计量的构造及文章所需的假设条件。第三节给出了本文的主要结果,即各估计量的一致强收敛速度。第四节和第五节利用有关假设条件分别证明了引理和定理。第六节为文章的注记，指出了就目前而言，本文的结果是最好的。
In this paper, we have considered a new class of semiparametric regression model Under some mild conditions we have obtained better uniformly strong convergence rates for the proposed estimators. The paper consists of two chapters.
In the first chapter, we have introduced the background of this paper, the development of Semiparametric regression model, the questions we were going to discuss, and its profound meaning. The second chapter consists of six sections. The first section is introduction, where we have brought forward the model we should discuss. In the second section, we have introduced the formation for the estimators and the proposed conditions that the paper needed . In the third section, we have presented the main result of the paper, namely the uniformly strong convergence rates for each estimator. In the fourth and fifth sections, by utilizing some relating proposed conditions we have proved the lemmas and theorems respectively. In the sixth footnote section of the paper, it pointed out that as far as the present, the outcome in the paper was the best.
引文
[1] heckman, N.,Spline smoothng in a partly linear model,J.roy.statist. soc. ser.,
soc.ser.,B48(1986)，244-248
[2] Rice,J.,Convergence rates for partially splined models Statist.& Propab.Lett.,
4.(1986),203-206
[3] Chen,H.,Convergence rates for parametric components in a partly linear
model,Ann.Statist.,16(1988),136-146
[4] Speckman,P,,Kernel smoothing partial linear models,J.Roy. Statist.Soc.Ser.,
B50(1988),413-436
[5] Robinson,P.,Root-N-Consistent semiparametric regression,Econometric,
56(1988),931-954
[6] Gao,J.T.A large sample theory in semiparametric regression models.Ph.D.
Thesis Graduate school at the university of Science & Technology of China,
Hefei,Anhui.P.R.China
[7] Stone,C.J.(1985),Ann.Statist.,13(689-705)
[8] Hastie,T.and R.Tibshirani(1986),Statist.Sci.,1(197-318)
[9] Buja,A.. T.Hastie and R.Tibshirani.(1989),Ann.Statist,17(453-555)
[10] Gao,J.T(1991),J.China.Univ.Sci.S Tech.,2(1992),131-137
[11] Gao.J.T,Ph.D.Thesis,Department of Mathematics,Univ.Sci.S Tech.China,
1992
[12] Liang,H.,Ph.D.Thesis,Institute of System Science,Academic Sinica
[13] Gao,J.T,Chin.Aun.of Mutn.accepted for publication
[14] Li,K.C.(1989),Ann.Statist.,17(1009-1052)
[15] 卢昆亮，密度的混合偏导数的核估计及其收敛速度。系统科学与数学2
（3）（1982），220－226
[16] Farrel,R.H,Ann.Math.Statist,43(1972),170
[17] 陈希孺，密度核估计的一致收敛速度。系统科学与数学 3（4）（1983），263－272
soc.ser.,B48(1986)，244-248
[2] Rice,J.,Convergence rates for partially splined models Statist.& Propab.Lett.,
4.(1986),203-206
[3] Chen,H.,Convergence rates for parametric components in a partly linear
model,Ann.Statist.,16(1988),136-146
[4] Speckman,P,,Kernel smoothing partial linear models,J.Roy. Statist.Soc.Ser.,
B50(1988),413-436
[5] Robinson,P.,Root-N-Consistent semiparametric regression,Econometric,
56(1988),931-954
[6] Gao,J.T.A large sample theory in semiparametric regression models.Ph.D.
Thesis Graduate school at the university of Science & Technology of China,
Hefei,Anhui.P.R.China
[7] Stone,C.J.(1985),Ann.Statist.,13(689-705)
[8] Hastie,T.and R.Tibshirani(1986),Statist.Sci.,1(197-318)
[9] Buja,A.. T.Hastie and R.Tibshirani.(1989),Ann.Statist,17(453-555)
[10] Gao,J.T(1991),J.China.Univ.Sci.S Tech.,2(1992),131-137
[11] Gao.J.T,Ph.D.Thesis,Department of Mathematics,Univ.Sci.S Tech.China,
1992
[12] Liang,H.,Ph.D.Thesis,Institute of System Science,Academic Sinica
[13] Gao,J.T,Chin.Aun.of Mutn.accepted for publication
[14] Li,K.C.(1989),Ann.Statist.,17(1009-1052)
[15] 卢昆亮，密度的混合偏导数的核估计及其收敛速度。系统科学与数学2
（3）（1982），220－226
[16] Farrel,R.H,Ann.Math.Statist,43(1972),170
[17] 陈希孺，密度核估计的一致收敛速度。系统科学与数学 3（4）（1983），263－272