We consider likelihood based inference in a class of logistic models for case-control studies with a partially observed covariate. The likelihood is a combination of a nonparametric mixture, a parametric likelihood and an empirical likelihood. We prove the asymptotic normality of the maximum likelihood estimator for the regression slope, the asymptotic chisquared distribution of the likelihood ...

In this paper we study U-statistics with side information incorporated using the method of empirical likelihood. Some basic properties of the proposed statistics are investigated. We find that by implementing the side information properly, the proposed U-statistics can have smaller asymptotic variance than the existing U-statistics in the literature. The proposed U-statistics can achieve asympt...

The size distribution of neuronal avalanches in cortical networks has been reported to follow a power law distribution with exponent close to -1.5, which is a reflection of long-range spatial correlations in spontaneous neuronal activity. However, identifying power law scaling in empirical data can be difficult and sometimes controversial. In the present study, we tested the power law hypothesi...

This paper is concerned with the null distribution of the likelihood ratio statistic for testing the equality of variances of q nonnormal populations. It is known that the null distribution of this statistic converges to w q 1 under normality. We extend this result by obtaining an asymptotic expansion under general conditions. Numerical accuracies are studied for some approximations of the perc...

In this paper the authors show how by adequately decomposing the null hypothesis of the multi-sample block sphericity test it is possible to easily obtain the expression for its likelihood ratio test statistic as well as a different look over the exact distribution of this statistic. This different view will enable the construction of very well-performing near-exact approximations for the distr...

In this note we establish the existence of the first two moments of the asymptotic trace statistic, which appears as weak limit of the likelihood ratio statistic for testing the cointegration rank in a vector autoregressive model and whose moments may be used to develop panel cointegration tests. Moreover, we justify the common practice to approximate these moments by simulating a certain stati...

This paper provides a means of accurately simulating explosive autoregressive processes, and uses this method to analyse the distribution of the likelihood ratio test statistic for an explosive second order autoregressive process. Nielsen (2001) has shown that for the asymptotic distribution of the likelihood ratio unit root test statistic in a higher order autoregressive model, the assumption ...

Spatial scan statistics are widely used for count data to detect geographical disease clusters of high or low incidence, mortality or prevalence and to evaluate their statistical significance. Some data are ordinal or continuous in nature, however, so that it is necessary to dichotomize the data to use a traditional scan statistic for count data. There is then a loss of information and the choi...

In practice, nuisance parameters in statistical models are often replaced by estimates based on an external source, for instance if estimates were published before or a second dataset is available. Next these estimates are assumed to be known when the parameter of interest is estimated, a hypothesis is tested or confidence intervals are constructed. By this assumption, the level of the test is,...

BACKGROUND A two-arm non-inferiority trial without a placebo is usually adopted to demonstrate that an experimental treatment is not worse than a reference treatment by a small pre-specified non-inferiority margin due to ethical concerns. Selection of the non-inferiority margin and establishment of assay sensitivity are two major issues in the design, analysis and interpretation for two-arm non...