While earlier empirical studies found a negative saving effect of old-age dependency rates without considering longevity, recent studies have found that longevity has a positive effect on growth without considering old-age dependency rates. In this paper, we first justify the related yet...

Generalized likelihood ratio statistics have been proposed in Fan, Zhang and Zhang [Ann. Statist. 29 (2001) 153-193] as a generally applicable method for testing norparametic hypotheses about nonparametric functions. The likelihood ratio statistics are constructed based on the assumption that...

Likelihood ratio theory has had tremendous success in parametric inference, due to the fundamental theory of Wilks. Yet, there is no general applicable approach for nonparametric inferences based on function estimation. Maximum likelihood ratio test statistics in general may not exist in...

The empirical likelihood cannot be used directly sometimes when an infinite dimensional parameter of interest is involved. To overcome this difficulty, the sieve empirical likelihoods are introduced in this paper. Based on the sieve empirical likelihoods, a unified procedure is developed for...