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Linear models with a growing number of parameters have been widely used in modern statistics. One important problem about this kind of model is the variable selection issue. Bayesian approaches, which provide a stochas-tic search of informative variables, have gained popularity. In this paper, we will study the asymptotic properties related to Bayesian(More)
We consider model selection and estimation for partial spline models and propose a new regularization method in the context of smoothing splines. The regularization method has a simple yet elegant form, consisting of roughness penalty on the nonparametric component and shrinkage penalty on the parametric components, which can achieve function smoothing and(More)
This article presents the first comprehensive studies on the local and global inferences for the smoothing spline estimate in a unified asymptotic framework. The novel functional Bahadur representation is developed as the theoretical foundation of this article, and is also of independent interest. Based on that, we establish four interconnected inference(More)
Spatial concurrent linear models, in which the model coefficients are spatial processes varying at a local level, are flexible and useful tools for analyzing spatial data. One approach places stationary Gaussian process priors on the spatial processes, but in applications the data may display strong nonstationary patterns. In this article, we propose a(More)
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