The scalar-on-function regression model has become a popular analysis tool to explore the relationship between a scalar response and multiple functional predictors. Most of the existing approaches to estimate this model are based on the least-squares estimator, which can be seriously affected by outliers in empirical datasets. When outliers are present in the data, it is known that the least-squares-based estimates may not be reliable. This paper proposes a robust functional partial least squares method, allowing a robust estimate of the regression coefficients in a scalar-on-multiple-function regression model. In our method, the functional partial least squares components are computed via the partial robust M-regression. The predictive performance of the proposed method is evaluated using several Monte Carlo experiments and two chemometric datasets: glucose concentration spectrometric data and sugar process data. The results produced by the proposed method are compared favorably with some of the classical functional or multivariate partial least squares and functional principal component analysis methods.
Sign-constrained least squares estimation for high-dimensional regression
高维回归问题的正则化方案很多。大多数需要使用模型选择标准或交叉验证方案来选择调优参数。我们表明，一个简单的非负或符号约束最小二乘是一个非常简单和有效的正则化技术，为某一类高维回归问题。符号约束必须通过先验知识或初始估计器导出，但不需要进一步的调整或交叉验证。成功取决于在实践中容易检验的条件。我们的结果的一个充分条件是，大多数变量具有相同的符号约束是正相关的。对于稀疏最优预报，证明了回归系数的L1-误差的非渐近界。不使用任何进一步的正则化，只要\log（p）s/n -> 0 for n -> \infty，就可以一致地估计回归向量，其中s是最佳回归向量的稀疏度，p是变量的数量，n是样本量。网络断层扫描被证明是一个应用程序，其中成功的非负最小二乘的必要条件自然满足和经验结果证实了稀疏恢复的符号约束的有效性。
Partial Trace Regression and Low-Rank Kraus Decomposition
Aix-Marseille University（艾克斯-马赛大学）；CNRS（法国国家科学研究中心）；LIS（计算机科学与系统实验室）；Helsinki Institute for Information Technology HIIT（赫尔辛基信息技术研究所）；Aalto University（阿尔托大学）；Université Rouen Normandie（鲁昂诺曼底大学）；LITIS（信息处理与系统实验室）；Criteo AI Lab（Criteo人工智能实验室）
A partial least squares approach for function-on-function interaction regression
A partial least squares regression is proposed for estimating the function-on-function regression model where a functional response and multiple functional predictors consist of random curves with quadratic and interaction effects. The direct estimation of a function-on-function regression model is usually an ill-posed problem. To overcome this difficulty, in practice, the functional data that belong to the infinite-dimensional space are generally projected into a finite-dimensional space of basis functions. The function-on-function regression model is converted to a multivariate regression mo…
On function-on-function regression: Partial least squares approach
Functional data analysis tools, such as function-on-function regression models, have received considerable attention in various scientific fields because of their observed high-dimensional and complex data structures. Several statistical procedures, including least squares, maximum likelihood , and maximum penalized likelihood, have been proposed to estimate such function-on-function regression models. However, these estimation techniques produce unstable estimates in the case of degenerate functional data or are computationally intensive. To overcome these issues, we proposed a partial least …
In this paper, a functional partial quantile regression approach, a quantile regression analog of the functional partial least squares regression, is proposed to estimate the function-on-function linear quantile regression model. A partial quantile covariance function is first used to extract the functional partial quantile regression basis functions. The extracted basis functions are then used to obtain the functional partial quantile regression components and estimate the final model. In our proposal, the functional forms of the discretely observed random variables are first constructed via …
Bayesian bandwidth estimation and semi-metric selection for a functional partial linear model with unknown error density
This study examines the optimal selections of bandwidth and semi-metric for a functional partial linear model . Our proposed method begins by estimating the unknown error density using a kernel density estimator of residuals, where the regression function , consisting of parametric and nonparametric components, can be estimated by functional principal component and functional Nadayara-Watson estimators. The estimation accuracy of the regression function and error density crucially depends on the optimal estimations of bandwidth and semi-metric. A Bayesian method is utilized to simultaneously e…
