Multivariate Nonparametric Regression by the Method of Sieves
Speaker: Tianyu Zhang
Abstract: Sieve estimators, or estimation using orthogonal function series, is a classical nonparametric statistical learning strategy (starting from the 80s). It is believed to be a nice idea when the covariates/ predictors are of very low dimension. However, in multivariate cases (say covariate dimension = 5), the direct extension of sieve estimators is usually thought to be not fruitful due to its high computational burden. In this talk, I will discuss how to effectively apply sieve estimators under multivariate tensor product models (including the relationship between these nonparametric spaces and classical Sobolev spaces). The proposed estimators can partially avoid the curse of dimensionality (statistically and computationally) under the more restrictive but still "interesting" nonparametric models. Check https://arxiv.org/abs/2206.02994 for more details.