偏最小二乘法在函数型数据中的应用
Methodology and theory for partial least squares applied to functional data
摘要：
偏最小二乘方法最初用于估计多变量参数模型中的斜率参数。最近，它在函数数据文献中流行起来。在那里，斜率的偏最小二乘估计量用于构建线性预测模型，或作为将数据投影到一维量上的工具，用于进一步的统计分析。虽然偏最小二乘方法通常被认为是一个有吸引力的替代方案，预测到主成分的基础上，其属性是不太为人所知的比后者，主要是因为它的迭代性质。我们开发了一个明确的配方偏最小二乘函数数据，从而导致有见地的结果，并激发新的理论，证明一致性和建立收敛速度。
英文摘要：
The partial least squares procedure was originally developed to estimate the slope parameter in multivariate parametric models. More recently it has gained popularity in the functional data literature. There, the partial least squares estimator of slope is either used to construct linear predictive models, or as a tool to project the data onto a one-dimensional quantity that is employed for further statistical analysis. Although the partial least squares approach is often viewed as an attractive alternative to projections onto the principal component basis, its properties are less well known than those of the latter, mainly because of its iterative nature. We develop an explicit formulation of partial least squares for functional data, which leads to insightful results and motivates new theory, demonstrating consistency and establishing convergence rates.
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。
