Directing Power Towards Conic Parameter Subspaces

07/11/2019
by   Nick Koning, et al.
0

For a high-dimensional parameter of interest, tests based on quadratic statistics are known to have low power against subsets of the parameter space (henceforth, parameter subspaces). In addition, they typically involve an inverse covariance matrix which is difficult to estimate in high-dimensional settings. I simultaneously address these two issues by proposing a novel test statistic that is large in a conic parameter subspace of interest. This test statistic generalizes the Wald statistic and nests many well-known test statistics. For a given parameter subspace, the statistic is free of tuning parameters and suitable for high-dimensional settings if the subspace is sufficiently small. It can be computed using regularized linear regression, where the type of regularization and the regularization parameters are completely determined by the parameter subspace of interest. I illustrate the statistic on subspaces that consist of sparse or nearly-sparse vectors, for which the computation corresponds to ℓ_0- and ℓ_1-regularized regression, respectively.

READ FULL TEXT
research
07/11/2019

Directing Power Towards Subspaces of the Alternative Hypothesis

This paper treats two problems in high-dimensional testing that have rec...
research
07/11/2019

Directing Power Towards Sub-Regions of the Alternative Hypothesis

In this paper, I propose a novel test statistic for testing hypotheses a...
research
08/29/2020

Efficiency Loss of Asymptotically Efficient Tests in an Instrumental Variables Regression

In an instrumental variable model, the score statistic can be stochastic...
research
03/29/2019

Ham-Sandwich cuts and center transversals in subspaces

The Ham-Sandwich theorem is a well-known result in geometry. It states t...
research
07/11/2019

Directing Power Towards Sub-Alternatives

This paper proposes a novel test statistic for testing a potentially hig...
research
05/19/2022

Interpolating Compressed Parameter Subspaces

Inspired by recent work on neural subspaces and mode connectivity, we re...
research
01/22/2023

Testing Many Zero Restrictions in a High Dimensional Linear Regression Setting

We propose a test of many zero parameter restrictions in a high dimensio...

Please sign up or login with your details

Forgot password? Click here to reset