估计特征值集和特征值函数分布的带约束Bootstrap方法
Tie-respecting bootstrap methods for estimating distributions of sets and functions of eigenvalues
摘要：
Bootstrap方法被广泛用于分布估计，尽管在某些问题中它们的应用有困难。一个恰当的例子是，估计分布的特征值估计，或这些估计的功能，当一个或多个真正的特征值是绑。$m$ -out-of- $n$引导程序可用于处理这种一般类型的问题，但它对$m$的选择非常敏感。在本文中，我们提出了一种新的方法，领带诊断是用来确定领带的位置，并相应地调整参数估计。我们的领带诊断是由概率水平，$β$，这在原则上是一个类似的$m$在$m$ -出- $n$引导。然而，领带尊重引导（TRB）是非常强大的选择$β$。这使得TRB明显比$m$ -out-of- $n$引导程序更有吸引力，其中$m$的值对最终结果具有实质性影响。TRB可以非常普遍地使用;例如，用于检验关于由一组主成分解释的变异性比例的假设，或为其构建置信区域。它适用于有限维数据和函数数据。
英文摘要：
Bootstrap methods are widely used for distribution estimation, although in some problems they are applicable only with difficulty. A case in point is that of estimating the distributions of eigenvalue estimators, or of functions of those estimators, when one or more of the true eigenvalues are tied. The $m$-out-of-$n$ bootstrap can be used to deal with problems of this general type, but it is very sensitive to the choice of $m$. In this paper we propose a new approach, where a tie diagnostic is used to determine the locations of ties, and parameter estimates are adjusted accordingly. Our tie diagnostic is governed by a probability level, $β$, which in principle is an analogue of $m$ in the $m$-out-of-$n$ bootstrap. However, the tie-respecting bootstrap (TRB) is remarkably robust against the choice of $β$. This makes the TRB significantly more attractive than the $m$-out-of-$n$ bootstrap, where the value of $m$ has substantial influence on the final result. The TRB can be used very generally; for example, to test hypotheses about, or construct confidence regions for, the proportion of variability explained by a set of principal components. It is suitable for both finite-dimensional data and functional data.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
