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大样本平滑样条 ANOVA 模型的渐近与经验平滑参数选择AI 解读

Summary Large samples are generated routinely from various sources. Classic statistical models, such as smoothing spline ANOVA models, are not well equipped to analyse such large samples because of high computational costs. In particular, the daunting computational cost of selecting smoothing parameters renders smoothing spline ANOVA models impractical. In this article, we develop an asympirical, i.e., asymptotic and empirical, smoothing parameters selection method for…

通过空间填充基函数选择提高平滑样条近似效率AI 解读

Summary We consider the problem of approximating smoothing spline estimators in a nonparametric regression model. When applied to a sample of size $n$, the smoothing spline estimator can be expressed as a linear combination of $n$ basis functions, requiring $O(n^3)$ computational time when the number $d$ of predictors is two or more. Such a sizeable computational cost hinders the broad applicability of smoothing splines. In practice, the full-sample smoothing spline…

相关追踪：指数模型的前向逐步变量选择AI 解读

Summary A stepwise procedure, correlation pursuit (COP), is developed for variable selection under the sufficient dimension reduction framework, in which the response variable Y is influenced by the predictors X1,X2,…,Xp through an unknown function of a few linear combinations of them. Unlike linear stepwise regression, COP does not impose a special form of relationship (such as linear) between the response variable and the predictor variables. The COP procedure selects…

含多个协变量的大规模函数数据惩罚聚类AI 解读

In this article we propose a penalized clustering method for large-scale data with multiple covariates through a functional data approach. In our proposed method, responses and covariates are linked together through nonparametric multivariate functions (fixed effects), which have great flexibility in modeling various function features, such as jump points, branching, and periodicity. Functional ANOVA is used to further decompose multivariate functions in a reproducing kernel…