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非参数混合效应模型中的最优平滑AI 解读

Mixed-effect models are widely used for the analysis of correlated data such as longitudinal data and repeated measures. In this article, we study an approach to the nonparametric estimation of mixed-effect models. We consider models with parametric random effects and flexible fixed effects, and employ the penalized least squares method to estimate the models. The issue to be addressed is the selection of smoothing parameters through the generalized cross-validation method,…

平滑样条高斯回归：通过有效近似实现更可扩展的计算AI 解读

Summary Smoothing splines via the penalized least squares method provide versatile and effective nonparametric models for regression with Gaussian responses. The computation of smoothing splines is generally of the order O(n3), n being the sample size, which severely limits its practical applicability. We study more scalable computation of smoothing spline regression via certain low dimensional approximations that are asymptotically as efficient. A simple algorithm is…

平滑样条密度估计：无量纲自动算法AI 解读

As a sequel to an earlier article by Gu and Qiu, this article describes and illustrates a dimensionless automatic algorithm for nonparametric probability density estimation using smoothing splines. The algorithm is designed to calculate an adaptive finite dimensional solution to the penalized likelihood problem, which was shown by Gu and Qiu to share the same asymptotic convergence rates as the nonadaptive infinite dimensional solution. The smoothing parameter is updated…

平滑样条密度估计：理论AI 解读

In this article, a class of penalized likelihood probability density estimators is proposed and studied. The true log density is assumed to be a member of a reproducing kernel Hilbert space on a finite domain, not necessarily univariate, and the estimator is defined as the unique unconstrained minimizer of a penalized log likelihood functional in such a space. Under mild conditions, the existence of the estimator and the rate of convergence of the estimator in terms of the…

采用张量积薄板样条的半参数方差分析AI 解读

SUMMARY We consider fitting multivariate models to response data based on analysis-of-variance (ANOVA)-like decompositions of functions of several variables, f(t 1,..., td) = C + σα f α(ta + σα < β f αβ(t α, t β) + · · · · A theory for fitting (some components of) these models with polynomial smoothing splines exists when each tα is in a subset of the real line. In this case the various estimated components turn out to be certain tensor sums and products of polynomial…

含加性项的非参数回归模型诊断AI 解读

Recent developments of multivariate smoothing methods provide a rich collection of feasible models for nonparametric multivariate data analysis. Among the most interpretable are models with additive terms. Construction of various models and algorithms for computing the models have been the main concern of the existing literature in this area. Few results are available on the validation of computed fits, and many applications of nonparametric methods unfortunately end up…

非高斯回归模型中的自适应样条平滑AI 解读

A convenient and efficient algorithm for penalized likelihood smoothing spline regression is proposed and illustrated. The amount of smoothing is tuned adaptively via the generalized cross-validation method. Under certain conditions, the method is shown to approximately minimize the expected Kullback-Leibler discrepancy in modeling one-parameter exponential family observations through the canonical parameter. The algorithm is applied to fit logistic models using interaction…

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