| Parameter estimation is one of the major tasks for a statistician. An efficient estimator is always desired. For the same parameter, there are usually several possible estimators. Some estimators may be more efficient than other estimators in one situation, but less efficient in another. For example, in the context of the random intercept statistical model, or the nested-error regression model, one estimator may be more efficient if the intraclass correlation is small and less efficient if the intraclass correlation is large. In the ideal case that the intraclass correlation is known, the choice is obvious. However, life is full of uncertainties and in most cases, the true values of the variance components are not known in advance. This thesis intends to provide a cutting-edge technique for estimation. The proposed approach makes use of a composite estimator that is a linear combination of two estimators, one that is believed to be more efficient for a small intraclass correlation coefficient and the other more efficient for a large intraclass correlation. In the case of a small intraclass correlation, the estimator that is more efficient in that situation would be dominant and when the intraclass correlation is large, the other estimator becomes dominant. This approach is applied in two important fields of applied statistics: small-area estimation in survey sampling and intraclass correlation estimation in statistical genetics. In both fields, the proposed estimator is compared to the existing estimators including the maximum likelihood estimators under the normality assumption. The comparisons are based on four very common distributions of the random effects: the double exponential distribution, the exponential distribution and the uniform distribution in addition to the normal distribution. Through Monte Carlo simulation studies for the full range of values of the intraclass correlation, the proposed estimators are more efficient than their competitors. This is the case especially when the intraclass correlation is small. For large intraclass correlation, the estimators have similar performances. Although in the case of the normal distribution, the restricted maximum likelihood estimator and the ordinary maximum likelihood estimator may be slightly more efficient, the advantage of this is offset by the computer intensive nature of the calculations. Therefore, the proposed estimators are preferred. |
