Estimating semiparametric models with complex spatiotemporal dependence

This Github page provides code and data for reproducing the results in the manuscript: ``Estimating semiparametric models with complex spatiotemporal dependence'' by Y. Chen, T. Chu, C. Zhou, Y. Shen, and H. Huang.

Summary

For spatiotemporally dependent data, the naive incorporation of complex dependence structures into nonparametric or semiparametric estimation procedures may lead to unreliable or undesirable inferences. As a result, many existing semiparametric approaches either completely ignore or inadequately account for spatiotemporal dependence during statistical inference, potentially resulting in efficiency losses and additional methodological challenges in improving prediction accuracy and interpretability. To address these issues, we propose a novel K-nearest-neighbor weighted local linear regression framework that properly incorporates spatiotemporal dependence into the estimation equations for both parametric and nonparametric components. In addition, the proposed approach does not require the assumption of non-stationarity of the space-time covariance, which makes the modeling more flexible. Under an increasing-domain asymptotic framework, we show that the bias and efficiency of the nonparametric estimator can be significantly improved, while the parametric counterpart achieves consistency and attains optimal efficiency under Gaussian settings. Simulation studies further demonstrate the finite-sample performance and robustness of the proposed methods, even when the covariance or data-generating process is misspecified. An application of air pollution data illustrates its practical effectiveness.

Software package

We developed an R package to implement the proposed K-nearest-neighbor weighted local linear regression (KNN-WLLR) in knnWLLR; see knnWLLR_1.0.zip. All simulation code can be found in the R folder to facilitate reproducibility.

Simulation results

Figure 1 provides a thorough insight into the performance of each method by showing trajectory plots of the absolute bias, standard deviation, and MSE at each sampling point when estimating the nonparametric functions. Our proposed KNN-WLLR consistently outperforms the competing methods across all three metrics at nearly all sampling points.

Figure 1: Pointwise absolute bias, standard deviation and mean square error for each method in estimating nonparametric functions.

Real data analysis

We analyze daily concentration data of PM2.5 in China's BTH region from November 1 to November 30, 2015. The PM2.5 concentrations are from two sources: (i) readings at 68 spatially sparse monitoring sites and (ii) outputs of the Community Multiscale Air Quality (CMAQ) model, a widely used numerical modeling system. The detailed description of the data can be found in the paper and the paper. These data are publicly available on GitHub. Nonstationary patterns in space and time are observed based on the estimated covariance via the machine learning method.

Figure 1: Spatiotemporal covariance estimated via the deeper learning method.