Interquantile shrinkage in spatial additive autoregressive models

In this paper, we study the commonness of nonparametric component functions at different quantile levels in spatial additive autoregressive models. We propose two fused adaptive group LASSO penalties to shrink the difference of functions between neighbouring quantile levels. Using these methods, we can estimate the nonparametric functions and identify the quantile regions where functions are unvarying simultaneously. Therefore, when there exists a quantity-level region where the functions are unvarying, its performance is expected to be better than the conventional spatial quantile additive autoregressive model. Under some regularity conditions, the proposed penalized estimators can reach the optimal rate of convergence in theory and also recognize the true varying/unvarying regions accurately. At the same time, our proposed method shows good numerical results in simulated and real datasets.