Estimation of a structural parameter in the presence of a large number of nuisance parameters
Estimation of a structural parameter in the presence of a large number of nuisance parameters
复制标题
存在大量干扰参数时结构参数的估计
DOI：
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复制
发表时间：
1984
期刊：
影响因子：
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通讯作者：
S. Amari
中科院分区：
文献类型：
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作者：
M. Kumon;S. Amari
摘要当干扰参数的数量与样本量成比例增加时，Cramer-Rao界不一定给出结构参数估计量的渐近方差的可达到的下限。本文提出了一个新的下限下的标准称为信息一致性。该界限表示为部分信息和某个非负项之和的倒数，该非负项由微分几何考虑导出。当最优估计函数存在时，也得到了满足该下界的最优估计函数的分解形式。第一项是修正的得分函数，第二项是，粗略地说，由一些随机变量的混合协变导数的正态分量给出。此外，这些结果的特殊版本给出了简洁的形式，这些然后应用于阐明一些例子的有效性。
SUMMARY When the number of nuisance parameters increases in proportion to the sample size, the Cramer-Rao bound does not necessarily give an attainable lower bound for the asymptotic variance of an estimator of the structural parameter. The present paper presents a new lower bound under a criterion called information uniformity. The bound is expressed as the inverse of the sum of the partial information and a certain nonnegative term, which is derived by differential-geometrical considerations. The optimal estimating function meeting this lower bound, when it exists, is also obtained in a decomposed form. The first term is the modified score function, and the second term is, roughly speaking, given by the normal component of the mixture covariant derivative of some random variable. Furthermore, special versions of these results are given in concise form, and these are then applied to elucidate the efficiency of some examples.