  Sufficient dimension reduction (SDR) is an effective tool for regression
models, offering a viable approach to address and analyze the nonlinear nature
of regression problems. This paper introduces the itdr R package, a
comprehensive and user-friendly tool that introduces several functions based on
integral transformation methods for estimating SDR subspaces. In particular,
the itdr package incorporates two key methods, namely the Fourier method (FM)
and the convolution method (CM). These methods allow for estimating the SDR
subspaces, namely the central mean subspace (CMS) and the central subspace
(CS), in cases where the response is univariate. Furthermore, the itdr package
facilitates the recovery of the CMS through the iterative Hessian
transformation (IHT) method for univariate responses. Additionally, it enables
the recovery of the CS by employing various Fourier transformation strategies,
such as the inverse dimension reduction method, the minimum discrepancy
approach using Fourier transformation, and the Fourier transform sparse inverse
regression approach, specifically designed for cases with multivariate
responses. To demonstrate its capabilities, the itdr package is applied to five
different datasets. Furthermore, this package is the pioneering implementation
of integral transformation methods for estimating SDR subspaces, thus promising
significant advancements in SDR research.
