Testing against a high dimensional alternative Export

@article{citeulike:637814, abstract = {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.}, author = {Goeman, Jelle J. and van de Geer, Sara A. and van Houwelingen, Hans C.}, citeulike-article-id = {637814}, citeulike-linkout-0 = {http://dx.doi.org/10.1111/j.1467-9868.2006.00551.x}, citeulike-linkout-1 = {http://www.ingentaconnect.com/content/bpl/rssb/2006/00000068/00000003/art00006}, comment = {The authors consider testing against a broad range of alternatives where "interesting" alternatives are suggested by the prior distributions of the parameters.}, doi = {10.1111/j.1467-9868.2006.00551.x}, issn = {1369-7412}, journal = {Journal of the Royal Statistical Society: Series B (Statistical Methodology)}, keywords = {bayesian, data\_mining, empirical\_bayes}, month = {June}, number = {3}, pages = {477--493}, posted-at = {2006-06-28 19:30:49}, priority = {2}, publisher = {Blackwell Publishing}, title = {Testing against a high dimensional alternative}, url = {http://dx.doi.org/10.1111/j.1467-9868.2006.00551.x}, volume = {68}, year = {2006} }

TY - JOUR ID - citeulike:637814 L3 - citeulike-article-id:637814 N2 - 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. IS - 3 JF - Journal of the Royal Statistical Society: Series B (Statistical Methodology) SN - 1369-7412 EP - 493 TI - Testing against a high dimensional alternative PB - Blackwell Publishing VL - 68 SP - 477 KW - bayesian KW - data_mining KW - empirical_bayes N1 - The authors consider testing against a broad range of alternatives where "interesting" alternatives are suggested by the prior distributions of the parameters. AU - Goeman, Jelle AU - van de Geer, Sara AU - van Houwelingen, Hans PY - 2006/06// UR - http://dx.doi.org/10.1111/j.1467-9868.2006.00551.x ER -