Variable Selection via Adaptive False Negative Control in Linear Regression
arXiv:1804.07416
Abstract
Variable selection methods have been developed in linear regression to provide sparse solutions. Recent studies have focused on further interpretations on the sparse solutions in terms of false positive control. In this paper, we consider false negative control for variable selection with the goal to efficiently select a high proportion of relevant predictors. Different from existing studies in power analysis and sure screening, we propose to directly estimate the false negative proportion (FNP) of a decision rule and select the smallest subset of predictors that has the estimated FNP less than a user-specified control level. The proposed method is adaptive to the user-specified control level on FNP by selecting less candidates if a higher level is implemented. On the other hand, when data has stronger effect size or larger sample size, the proposed method controls FNP more efficiently with less false positives. New analytic techniques are developed to cope with the major challenge of FNP control when relevant predictors cannot be consistently separated from irrelevant ones. Our numerical results are in line with the theoretical findings.
arXiv comment27 pages and 1 figure; to appear in Electronic Journal of Statistics
References in corpus (9)
- Higher criticism for detecting sparse heterogeneous mixtures
- Confidence Intervals and Hypothesis Testing for High-Dimensional Regression
- SLOPE - Adaptive variable selection via convex optimization
- Estimating the proportion of false null hypotheses among a large number of independently tested hypotheses
- Global testing under sparse alternatives: ANOVA, multiple comparisons and the higher criticism
- Properties of higher criticism under strong dependence
- Model Selection for High-Dimensional Regression under the Generalized Irrepresentability Condition
- Rate optimal multiple testing procedure in high-dimensional regression
- A strong law of large numbers related to multiple testing Normal means