具有AR(q)误差非线性回归模型的几何性质

数学季刊 ›› 2004, Vol. 19 ›› Issue (2): 146-154.

具有AR(q)误差非线性回归模型的几何性质

Department of Mathematics, Southeast University, Nanjing 210096, China; College of Information Science and Technology, Nanjing Forestry University, Nanjing 210037, China

收稿日期:2002-07-10 出版日期:2004-06-30 发布日期:2024-03-18
作者简介:LIU Ying-an(1965-),male,native of Shouxian,Anhui,an associate professor of Nanjing Forestry University,Ph.D.,engages in statistics;WEI Bo-cheng(1937-),male,native of Zhenjiang,Jiangsu,a professor of Southeast University,engages in statistics.
基金资助:
Supported by the NSSFC(02BTJ001)； Supported by the NSSFC(04BTJ002)； Supported by the Grant for Post-Doctorial Fellows in Southeast University；

Geometric Properties of AR(q) Nonlinear Regression Models

Department of Mathematics, Southeast University, Nanjing 210096, China; College of Information Science and Technology, Nanjing Forestry University, Nanjing 210037, China

Received:2002-07-10 Online:2004-06-30 Published:2024-03-18
About author:LIU Ying-an(1965-),male,native of Shouxian,Anhui,an associate professor of Nanjing Forestry University,Ph.D.,engages in statistics;WEI Bo-cheng(1937-),male,native of Zhenjiang,Jiangsu,a professor of Southeast University,engages in statistics.
Supported by:
Supported by the NSSFC(02BTJ001)； Supported by the NSSFC(04BTJ002)； Supported by the Grant for Post-Doctorial Fellows in Southeast University；

摘要/Abstract

摘要： This paper is devoted to a study of geometric properties of AR(q) nonlinear regression models. We present geometric frameworks for regression parameter space and autoregression parameter space respectively based on the weighted inner product by fisher information matrix. Several geometric properties related to statistical curvatures are given for the models. The results of this paper extended the work of Bates & Watts(1980,1988) [1,2] and Seber & Wild(1989) [3].

关键词: nonlinear , , regression , , model, AR(q)errors, geometric , , framework, statistical curvature, Fisher information matrix

Abstract: This paper is devoted to a study of geometric properties of AR(q) nonlinear regression models. We present geometric frameworks for regression parameter space and autoregression parameter space respectively based on the weighted inner product by fisher information matrix. Several geometric properties related to statistical curvatures are given for the models. The results of this paper extended the work of Bates & Watts(1980,1988) [1,2] and Seber & Wild(1989) [3].

Key words: nonlinear , , regression , , model, AR(q)errors, geometric , , framework, statistical curvature, Fisher information matrix

中图分类号:

刘应安, 韦博成. 具有AR(q)误差非线性回归模型的几何性质[J]. 数学季刊, 2004, 19(2): 146-154.

LIU Ying-an, WEI Bo-cheng . Geometric Properties of AR(q) Nonlinear Regression Models[J]. Chinese Quarterly Journal of Mathematics, 2004, 19(2): 146-154.

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