title: Adjusted confidence intervals for a bounded parameter.
abstract: It is well known that the regular likelihood ratio test of a bounded parameter is not valid if the boundary value is being tested. This is the case for testing the null value of a scalar variance component. Although an adjusted test of variance component has been suggested to account for the effect of its lower bound of zero, no adjustment of its interval estimate has ever been proposed. If left unadjusted, the confidence interval of the variance may still contain zero when the adjusted test rejects the null hypothesis of a zero variance, leading to conflicting conclusions. In this research, we propose two ways to adjust the confidence interval of a parameter subject to a lower bound, one based on the Wald test and the other on the likelihood ratio test. Both are compatible to the adjusted test and parametrization-invariant. A simulation study and two examples are given in the framework of ACDE models in twin studies.
authors.affiliation: Department of Psychology, Boston College, 300 McGuinn, 140 Commonwealth Avenue, Chestnut Hil, MA 02467, USA. hao.wu.5@bc.edu
authors.forename: Hao
authors.initials: H
authors.lastname: Wu
authors.forename: Michael C
authors.initials: MC
authors.lastname: Neale
mesh_terms: D016001:Confidence Intervals; D006801:Humans; D016013:Likelihood Functions; D015233:Models, Statistical; D009010:Monte Carlo Method; D018433:Twin Studies as Topic / Q000706:statistics & numerical data