Ching-Kang Ing

It has been shown that the error bound of the Lasso estimator attains the minimax optimal rate when the corresponding regression coefficients are sparse. The existing theory, however, is developed under fixed-design predictors with i.i.d. errors. Subsequent extensions to time-series predictors primarily focus on hard sparsity. This paper provides a unified treatment of the Lasso with time-series predictors under both hard and soft sparsity, with the latter allowing all regression coefficients to be nonzero. We first show that the key results continue to hold in the time-series setting. We then derive the convergence rate of the mean squared post-sample prediction error (MSPPE) for the Lasso predictor. Finally, for moderately dense coefficients, we show that the Lasso may require substantially fewer candidate variables to achieve the desired convergence rate. Monte Carlo simulations are conducted to evaluate the performance of the Lasso with time-series predictors.

Constructs multi-resolution thin-plate spline basis functions on the sphere for use in spatial regression and large-scale spatial prediction problems. Implements the basis system described in Huang, Huang, and Ing (2025) "Multi-Resolution Spatial Methods on the Sphere: Efficient Prediction for Global Data", Environmetrics, . Heavy computations are written in 'C++' via 'Rcpp' with optional 'OpenMP' parallelism.

Accurate spatial prediction on the sphere is fundamental for global environmental applications such as climate monitoring and oceanographic analysis. Existing approaches, however, often struggle to balance computational efficiency, predictive accuracy, and the ability to accommodate heterogeneous spatial structures. We propose a multi‐resolution spatial modeling framework that integrates thin‐plate spline (TPS) basis functions with Gaussian process modeling. The framework begins with a fixed‐effects representation based on a hierarchy of nearly orthogonal TPS basis functions ordered by smoothness, thereby providing a multi‐resolution decomposition of spatial variation. This allows large‐scale patterns to be captured efficiently while preserving interpretability. To represent localized dependencies, we extend the model with a random effect governed by a tapered Matérn covariance, which models fine‐scale structure while ensuring scalability through sparse matrix operations. Model complexity is adaptively controlled using the conditional Akaike information criterion (cAIC), which simultaneously selects the number of basis functions and determines the contribution of the Gaussian process component. Numerical experiments and a global sea surface temperature application show how our method balances predictive accuracy with computational feasibility, establishing its role as a powerful solution for large‐scale spatial modeling on the sphere.

This paper addresses an important gap in time series analysis by establishing rigorous results on prediction and model selection for weakly stationary processes with conditionally heteroscedastic errors, using mean squared prediction error (MSPE) as the evaluation metric. A key contribution is the derivation of a negative moment bound for the minimum eigenvalue of the sample autocovariance matrix. This result enables an explicit asymptotic decomposition of the MSPE for least squares predictors into interpretable components reflecting model complexity, misspecification, and time-varying volatility. Leveraging this decomposition, we develop a model selection criterion that consistently identifies the MSPE-optimal subset autoregressive model, even in the presence of conditional heteroscedasticity and model misspecification. Simulation studies support the theoretical developments and demonstrate the practical effectiveness of the proposed method.

We make some initial attempt to establish the theoretical and methodological foundation for the model-X knockoffs inference for time series data. We suggest the method of time series knockoffs inference (TSKI) by exploiting the ideas of subsampling and e-values to address the difficulty caused by the serial dependence. We also generalize the robust knockoffs inference in [4] to the time series setting to relax the assumption of known covariate distribution required by model-X knockoffs, since such an assumption is overly stringent for time series data. We establish sufficient conditions under which TSKI achieves the asymptotic false discovery rate (FDR) control. Our technical analysis reveals the effects of serial dependence and unknown covariate distribution on the FDR control. We conduct a power analysis of TSKI using the Lasso coefficient difference knockoff statistic under the generalized linear time series models. The finite-sample performance of TSKI is illustrated with several simulation examples and an economic inflation study.

The model-X knockoffs framework provides a flexible tool for achieving finite-sample false discovery rate (FDR) control in variable selection in arbitrary dimensions without assuming any dependence structure of the response on covariates. It also completely bypasses the use of conventional p-values, making it especially appealing in high-dimensional nonlinear models. Existing works have focused on the setting of independent and identically distributed observations. Yet time series data is prevalent in practical applications in various fields such as economics and social sciences. This motivates the study of model-X knockoffs inference for time series data. In this paper, we make some initial attempt to establish the theoretical and methodological foundation for the model-X knockoffs inference for time series data. We suggest the method of time series knockoffs inference (TSKI) by exploiting the ideas of subsampling and e-values to address the difficulty caused by the serial dependence. We also generalize the robust knockoffs inference to the time series setting and relax the assumption of known covariate distribution required by model-X knockoffs, because such an assumption is overly stringent for time series data. We establish sufficient conditions under which TSKI achieves the asymptotic FDR control. Our technical analysis reveals the effects of serial dependence and unknown covariate distribution on the FDR control. We conduct power analysis of TSKI using the Lasso coefficient difference knockoff statistic under linear time series models. The finite-sample performance of TSKI is illustrated with several simulation examples and an economic inflation study.

This paper studies an important sequential decision making problem known as the multi-armed stochastic bandit problem with covariates. Under a linear bandit framework with high-dimensional covariates, we propose a general multi-stage arm allocation algorithm that integrates both arm elimination and randomized assignment strategies. By employing a class of high-dimensional regression methods for coefficient estimation, the proposed algorithm is shown to have near optimal finite-time regret performance under a new study scope that requires neither a margin condition nor a reward gap condition for competitive arms. Based on the synergistically verified benefit of the margin, our algorithm exhibits adaptive performance that automatically adapts to the margin and gap conditions, and attains optimal regret rates simultaneously for both study scopes, without or with the margin, up to a logarithmic factor. Besides the desirable regret performance, the proposed algorithm simultaneously generates useful coefficient estimation output for competitive arms and is shown to achieve both estimation consistency and variable selection consistency. Promising empirical performance is demonstrated through extensive simulation and two real data evaluation examples.