标题： 小波回归和不规则间距数据的加法模型 显示英文标题

标题： Wavelet regression and additive models for irregularly spaced data

摘要： 我们提出了一种使用小波基函数的非参数回归新方法。 我们的方法，$\texttt{waveMesh}$，可以应用于非等距数据，样本量不一定是2的幂次。 我们开发了一种高效的近端梯度下降算法来计算估计量，并建立了自适应最小最大收敛速率。 我们方法的主要优势在于它可以自然地扩展到加法和稀疏加法模型，适用于潜在大量协变量的情况。 我们在稀疏加法模型下弱兼容性条件下证明了最小最大最优收敛速率。 当协变量数量较小时，兼容性条件成立。 此外，我们还建立了当该条件不满足时的收敛速率。 我们通过实证研究补充了理论结果，将$\texttt{waveMesh}$与现有方法进行了比较。 显示英文摘要

摘要： 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.