Wavelet regression and additive models for irregularly spaced data
This work addresses regression challenges in data with irregular spacing for statisticians and data scientists, offering incremental improvements in method flexibility.
The authors tackled nonparametric regression for irregularly spaced data by developing waveMesh, a wavelet-based method that achieves adaptive minimax convergence rates and extends to additive models, with empirical studies showing competitive performance.
We present a novel approach for nonparametric regression using wavelet basis functions. Our proposal, $\texttt{waveMesh}$, can be applied to non-equispaced data with sample size not necessarily a power of 2. We develop an efficient proximal gradient descent algorithm for computing the estimator and establish adaptive minimax convergence rates. The main appeal of our approach is that it naturally extends to additive and sparse additive models for a potentially large number of covariates. We prove minimax optimal convergence rates under a weak compatibility condition for sparse additive models. The compatibility condition holds when we have a small number of covariates. Additionally, we establish convergence rates for when the condition is not met. We complement our theoretical results with empirical studies comparing $\texttt{waveMesh}$ to existing methods.