Skip to main content

Testing against a high dimensional alternative

Buy Article:

$43.00 plus tax (Refund Policy)

Summary. 

As the dimensionality of the alternative hypothesis increases, the power of classical tests tends to diminish quite rapidly. This is especially true for high dimensional data in which there are more parameters than observations. We discuss a score test on a hyperparameter in an empirical Bayesian model as an alternative to classical tests. It gives a general test statistic which can be used to test a point null hypothesis against a high dimensional alternative, even when the number of parameters exceeds the number of samples. This test will be shown to have optimal power on average in a neighbourhood of the null hypothesis, which makes it a proper generalization of the locally most powerful test to multiple dimensions. To illustrate this new locally most powerful test we investigate the case of testing the global null hypothesis in a linear regression model in more detail. The score test is shown to have significantly more power than the F-test whenever under the alternative the large variance principal components of the design matrix explain substantially more of the variance of the outcome than do the small variance principal components. The score test is also useful for detecting sparse alternatives in truly high dimensional data, where its power is comparable with the test based on the maximum absolute t-statistic.
No References
No Citations
No Supplementary Data
No Article Media
No Metrics

Keywords: Empirical Bayes modelling; F-test; High dimensional data; Hypothesis testing; Locally most powerful test; Power; Score test

Document Type: Research Article

Affiliations: Leiden University, the Netherlands

Publication date: 2006-06-01

  • Access Key
  • Free content
  • Partial Free content
  • New content
  • Open access content
  • Partial Open access content
  • Subscribed content
  • Partial Subscribed content
  • Free trial content
Cookie Policy
X
Cookie Policy
Ingenta Connect website makes use of cookies so as to keep track of data that you have filled in. I am Happy with this Find out more