On Statistical Inference with High Dimensional Sparse CCA

Citation:

Nilanjana Laha, Nathan Huey, Brent Coull, and Rajarshi Mukherjee. 9/24/2021. “On Statistical Inference with High Dimensional Sparse CCA.” arXiv.org. Publisher's Version

Abstract:

We consider asymptotically exact inference on the leading canonical correlation directions and strengths between two high dimensional vectors under sparsity restrictions. In this regard, our main contribution is the development of a loss function, based on which, one can operationalize a one-step bias-correction on reasonable initial estimators. Our analytic results in this regard are adaptive over suitable structural restrictions of the high dimensional nuisance parameters, which, in this set-up, correspond to the covariance matrices of the variables of interest. We further supplement the theoretical guarantees behind our procedures with extensive numerical studies.

Notes:

 Link to our R package, which implements our method.

https://github.com/nilanjanalaha/de.bias.CCA

Last updated on 11/01/2021