1 research outputs found
Wavelet regression and additive models for irregularly spaced data
We present a novel approach for nonparametric regression using wavelet basis
functions. Our proposal, , 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 to
existing methods