Large Deviations for Resampling Methods and Simulations
Final rept. 1 May 96-30 Oct 99
OLD DOMINION UNIV RESEARCH FOUNDATION NORFOLK VA
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In this research project we studied two important problems in probability and statistics. First, we have established the large deviation principle for a sequence of probability measures defined on a product space, when the marginal and the conditional distributions possess the large deviation property. We have used the result to study the large deviation behavior of the bootstrap resampling procedure and robustness of location parameter tests in contaminated normal populations via Bahadur slopes and efficiencies. The second problem is concerned with the statistical analysis of longitudinal data. In recent years the GEE method has become a popular tool for analyzing discrete longitudinal data. The method uses a generalized quasi-score function to estimate the regression parameter, and moment estimates for the correlation parameter. Despite the popularity, the GEE method has some inherent pitfalls. In this research we have developed an alternative estimation procedure which overcomes those pitfalls. This alternative method is known as the Quasi-least squares QLS, since it uses a partial minimization based on the principle of generalized least squares. We have shown that the QLS estimates are feasible, consistent and asymptotically normal.
- Statistics and Probability