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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 stochastic search of informative variables, have gained popularity. In this paper, we will study the asymptotic properties related to Bayesian model… (More)

- Guang Cheng, Hao Helen Zhang, Zuofeng Shang
- Annals of the Institute of Statistical…
- 2015

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)

- Zuofeng Shang, Murray K. Clayton
- Environmental and Ecological Statistics
- 2012

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)

In this paper, we explore statistical versus computational trade-off to address a basic question in the application of a distributed algorithm: what is the minimal computational cost in obtaining statistical optimality? In smoothing spline setup, we observe a phase transition phenomenon for the number of deployed machines that ends up being a simple proxy… (More)

- Zuofeng Shang, Guang Cheng
- 2012

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)

- Michael S. Becker, Zuofeng Shang
- The American Mathematical Monthly
- 2007

This paper attempts to solve a basic problem in distributed statistical inference: how many machines can we use in parallel computing? In kernel ridge regression, we address this question in two important settings: nonparametric estimation and hypothesis testing. Specifically, we find a range for the number of machines under which optimal estimation/testing… (More)

A common challenge in existing nonparametric inference is its high computational complexity when the volume of data is large. In this paper, we develop computationally efficient nonparametric testing by employing the strategy of random projection. Specifically, a distance-based test statistic is proposed, and further proven to be consistent and minimax… (More)

- SPLINE ESTIMATE, Zuofeng Shang, Guang Cheng
- 2013

This article presents methods for local and global inference for the smoothing spline estimation in a unified asymptotic framework. A functional Bahadur representation is developed as the theoretical foundation of this article, and is also of independent interest. Based on that, we establish four inter-connected procedures for inference: (i) Point-wise… (More)

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