An implicit function approach to constrained optimization with applications to asymptotic expansions
An implicit function approach to constrained optimization with applications to asymptotic expansions
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约束优化的隐式函数方法及其在渐近展开中的应用
DOI：
10.1016/j.jmva.2007.01.005
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发表时间：
2008
影响因子：
1.6
通讯作者：
R. J. Boik
中科院分区：
文献类型：
--
作者：
R. J. Boik
本文对向量值自变量的标量值函数构造了一个无约束泰勒级数展开式，该展开式受非线性等式约束。扩展是可能的，首先重新参数化的约束参数方面的识别和隐式参数，然后扩展的功能，仅在识别的参数。给出了函数关于所识别参数的导数的矩阵表达式。利用该展开式构造了一个无约束牛顿算法，用于求解约束函数的优化问题。统计模型中的参数通常是通过求解统计估计方程来估计的。它显示了如何无约束牛顿算法可以用来解决约束估计方程。此外，无约束泰勒级数适用于构造有约束估计量的标量函数的Edgeworth展开。埃奇沃思展开说明最大似然估计在一个探索性的因子分析模型，其中一个斜旋转后，凯泽行归一化的因子加载矩阵。模拟研究表明，两项Edgeworth近似的优越性相比，渐近正态近似时，从多元正态或非正态分布采样。
In this article, an unconstrained Taylor series expansion is constructed for scalar-valued functions of vector-valued arguments that are subject to nonlinear equality constraints. The expansion is made possible by first reparameterizing the constrained argument in terms of identified and implicit parameters and then expanding the function solely in terms of the identified parameters. Matrix expressions are given for the derivatives of the function with respect to the identified parameters. The expansion is employed to construct an unconstrained Newton algorithm for optimizing the function subject to constraints. Parameters in statistical models often are estimated by solving statistical estimating equations. It is shown how the unconstrained Newton algorithm can be employed to solve constrained estimating equations. Also, the unconstrained Taylor series is adapted to construct Edgeworth expansions of scalar functions of the constrained estimators. The Edgeworth expansion is illustrated on maximum likelihood estimators in an exploratory factor analysis model in which an oblique rotation is applied after Kaiser row-normalization of the factor loading matrix. A simulation study illustrates the superiority of the two-term Edgeworth approximation compared to the asymptotic normal approximation when sampling from multivariate normal or nonnormal distributions.
结构方程建模中最小二乘估计量的渐近偏差。
DOI：
--
发表时间：
2004
期刊：
Advances in psychology research (Shohov, S.P.(Ed.)) Vol.27
影响因子：
--
作者：
Ogasawara;H.
通讯作者：
H.