ASYMPTOTIC DISTRIBUTION OF LIKELIHOOD RATIO STATISTIC FOR TESTING SPHERICTY IN GROWTH CURVE MODELS

In this paper, asymptotic expansions of the distribution of the likelihood ratio statistic for testing sphericity in a crowth curve model have been derived in the null and nonnull cases when the alternatives are dose to the null hypothesis. These expansions are given in series form of beta distributions.

THE ASYMPTOTIC DISTRIBUTIONS OF EMPIRICAL LIKELIHOOD RATIO STATISTICS IN THE PRESENCE OF MEASUREMENT ERROR

Suppose that several different imperfect instruments and one perfect instrument are independently used to measure some characteristics of a population. Thus, measurements of two or more sets of samples with varying accuracies are obtained. Statistical inference should be based on the pooled samples. In this article, the authors also assumes that all the imperfect instruments are unbiased. They consider the problem of combining this information to make statistical tests for parameters more relevant. They define the empirical likelihood ratio functions and obtain their asymptotic distributions in the presence of measurement error.

The statistical study of precursory anom alies observed in Chinese Seismological Network

By using the precursory anomalies at fixed seismological stations or observational points in China, which are obtained every year from the Assembly of National Seismologic Consideration (ANSC) from 1988 to 1996, to study the relationship between the anomalies in a certain year and the earthquakes occurring in the Chinese mainland in the next year. Based on the anomalies before 84 moderate or large earthquakes, it is concluded that except for the means of ground water level, the anomalous ratios for the other six means of earthquake forecasting in seismic regions are smaller than that in aseismic regions or that in the whole mainland of China. The means which has the maximum anomalous ratio is the means of ground water level, and the regions where the maximum ratio is observed are Xinjiang Uygur Autonomous Region, Sichuan and Yunnan provinces. The means which have the second anomalous ratios are the hydrogeochemistry and deformation and the regions where the second ratio is obtained are Xinjiang Uygur Autonomous Region, Yunnan Province. The means which has the minimum ratio is geomagnetism, the regions where the minimum ratio is observed are Inner Mongolia Autonomous Region and South China. The composite nomalous ratios for all means are 26.85% in seismic regions, 25.11% in aseismic regions. The latter also is the background level of precursory anomalies in Chinese Seismological Network. The anomalous ratios are 26.30% for the earthquakes of M S about 5.0 within the range of 200 km distant from the epicenter, 29.19% for earthquakes about 6.0 within 300 km, and 29.44% for earthquakes about 7.0 within 500 km.

EMPIRICAL LIKELIHOOD INFERENCE FOR LOGISTIC EQUATION WITH RANDOM PERTURBATION

Empirical likelihood(EL) combined with estimating equations(EE) provides a modern semi-parametric alternative to classical estimation techniques such as maximum likelihood estimation(MLE). This paper not only uses closed form of conditional expectation and conditional variance of Logistic equation with random perturbation to perform maximum empirical likelihood estimation(MELE) for the model parameters, but also proposes an empirical likelihood ratio statistic(ELRS) for hypotheses concerning the interesting parameter. Monte Carlo simulation results show that MELE and ELRS provide competitive performance to parametric alternatives.

Test Homogeneity of Order-restricted Means

Suppose that an order restriction is imposed among several p-variate normal mean vectors. We are interested in testing the homogeneity of these mean vectors under this restriction. This problem is an extension of Sasabuchi, Tanaka and Tsukamoto＇s problem.