Browsing by Author "Liu, Ruiqi"

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    Optimal nonparametric inference via deep neural network
    (Elsevier, 2022-01) Liu, Ruiqi; Boukai, Ben; Shang, Zuofeng; Mathematical Sciences, School of Science
    Deep neural network is a state-of-art method in modern science and technology. Much statistical literature have been devoted to understanding its performance in nonparametric estimation, whereas the results are suboptimal due to a redundant logarithmic sacrifice. In this paper, we show that such log-factors are not necessary. We derive upper bounds for the L2 minimax risk in nonparametric estimation. Sufficient conditions on network architectures are provided such that the upper bounds become optimal (without log-sacrifice). Our proof relies on an explicitly constructed network estimator based on tensor product B-splines. We also derive asymptotic distributions for the constructed network and a relating hypothesis testing procedure. The testing procedure is further proved as minimax optimal under suitable network architectures.
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    Statistical Inference on Panel Data Models: A Kernel Ridge Regression Method
    (Taylor & Francis, 2021) Zhao, Shunan; Liu, Ruiqi; Shang, Zuofeng; Mathematical Sciences, School of Science
    We propose statistical inferential procedures for nonparametric panel data models with interactive fixed effects in a kernel ridge regression framework. Compared with the traditional sieve methods, our method is automatic in the sense that it does not require the choice of basis functions and truncation parameters. The model complexity is controlled by a continuous regularization parameter which can be automatically selected by the generalized cross-validation. Based on the empirical process theory and functional analysis tools, we derive the joint asymptotic distributions for the estimators in the heterogeneous setting. These joint asymptotic results are then used to construct the confidence intervals for the regression means and the prediction intervals for future observations, both being the first provably valid intervals in literature. The marginal asymptotic normality of the functional estimators in a homogeneous setting is also obtained. Our estimators can also be readily modified and applied to other widely used semiparametric models, such as partially linear models. Simulation and real data analyses demonstrate the advantages of our method.