The behavior of maximum likelihood estimates (MLEs) and the likelihood ratio statistic in a family of problems involving pointwise nonparametric estimation of a monotone function is studied. This class of problems differs radically from the usual parametric or semiparametric situations in that the MLE of the monotone function at a point converges to the truth at rate n (slower than the usual √ ...

When using maximum likelihood methods to estimate genetic and environmental components of (co)variance, it is common to test hypotheses using likelihood ratio tests, since such tests have desirable asymptotic properties. In particular, the standard likelihood ratio test statistic is assumed asymptotically to follow a chi2 distribution with degrees of freedom equal to the number of parameters te...

The likelihood ratio spatial scan statistic has been widely used in spatial disease surveillance and spatial cluster detection applications. In order to better understand cluster mechanisms, an equivalent model-based approach is proposed to the spatial scan statistic that unifies currently loosely coupled methods for including ecological covariates in the spatial scan test. In addition, the uti...

In this paper, we consider the problem of testing two separate families of hypotheses via a generalization of the sequential probability ratio test. In particular, the generalized likelihood ratio statistic is considered and the stopping rule is the first boundary crossing of the generalized likelihood ratio statistic. We show that this sequential test is asymptotically optimal in the sense tha...

Empirical likelihood is developed for autoregressive models with innovations that form a martingale difference sequence. Limiting distributions of the log empirical likelihood ratio statistic for both the stable and unstable cases are established. Behavior of the log empirical likelihood ratio statistic is considered in nearly nonstationary models to assess the local power of unit root tests an...

In this paper we propose a smoothed jackknife empirical likelihood method to construct confidence intervals for the receiver operating characteristic (ROC) curve. By applying the standard empirical likelihood method for a mean to the jackknife sample, the empirical likelihood ratio statistic can be calculated by simply solving a single equation. Therefore, this procedure is easy to implement. W...

In this paper we propose a smoothed jackknife empirical likelihood method to construct confidence intervals for tail copulas or tail dependence functions for bivariate extremes. By applying the standard empirical likelihood method for a mean to the smoothed jackknife sample, the empirical likelihood ratio statistic can be calculated by simply solving a single equation. Therefore, this procedure...