A0640
Title: Inference in nonstationary random fields and rates of convergence of threshold variance estimation under sparsity
Authors: Ansgar Steland - RWTH Aachen University (Germany) [presenting]
Abstract: Inference in nonlinear random fields is studied under nonstationarity. The results include a functional central limit theorem for the smoothed spatial partial sum process indexed by classes of sets satisfying a weak entropy condition satisfied by various relevant classes arising in statistics and machine learning. For statistical applications, consistent estimation of the asymptotic variance is needed. The aim is to study (soft-) threshold estimation under a wide class of fields under sparse dependence by establishing nonasymptotic rates of convergence. The results reveal that thresholding is superior under sublinear growth of the non-vanishing spatial covariances over increasing rectangles. Those results also cover estimation from residuals. Applications to hypothesis testing in images, e.g., to detect cancer, regression models with external regressors, and sparse convolutional network layers are discussed.
