Nonparametric Interval Estimation in One-Way Random-Effects Models

The structural method provided by Hannig et al. (2006 Hannig , J. , Iyer , H. , Patterson , P. (2006). Fiducial generalized confidence intervals. J. Amer. Statist. Assoc. 101:254–269.Taylor & Francis Online], Web of Science ®] , Google Scholar]) has proved to be a useful tool for constructing confidence intervals. However, it is difficult to apply this method to nonparametric problems since the pivotal quantity required in using it exists only in some special parametric models. Based on an extended structural method, this article discusses nonparametric interval estimation for smooth functions of the variances in one-way random-effects models. We use the bootstrap distribution estimator of a statistic to construct an approximate pivotal equation, and prove that the confidence interval derived by the approximate pivotal equation has asymptotically correct coverage probability. Simulation results are presented and show that the normal fiducial interval is not robust against non normality and that the proposed confidence interval has better finite-sample behaviors than the naive interval based on normal approximation.