RESEARCH ON PATTERNED COVARIANCES

拟议的研究旨在填补统计方面的主要空白， 分析生物医学数据，涉及具有模式化手段的模型， 可能存在缺失数据的模式协方差。 这些模型出现 在纵向数据和一些遗传学模型的分析中。 关于统计技术和计算机软件的进一步工作， 将寻求主要研究者来实施这些技术 在此期间，我们的长期目标是高度发展 传播的、易于使用的软件（例如，SAS或BMDP）。 这方面的研究工作将包括：（1）完成 开发的计算机软件的文档编制和测试;（2）测试 计算机软件的性能特性和 基本的统计程序;（3）制定可编程程序 用于寻找显式MLE模式的近似零分布;（4） 在局部选择下求渐近非零分布 假设;（5）表征线性协方差参数类， 是具有显式MLE的线性协方差矩阵的子矩阵;以及（6） 在期刊上发表这些新的统计技术的应用 应用研究人员可以使用。 该建议解决了制定和实施 统计技术是相对容易解释，一旦 尽管得出结果需要复杂的 数学 使统计技术可用于 生物医学研究人员将拥有实现 技术. 当软件不可用时，研究人员会求助于 替代（有时效率低下或不正确）技术， 计算机软件可用。

The proposed research is intended to fill major gaps in the statistical analysis of biomedical data that involve models with patterned means and patterned covariances possibly with missing data. These models arise naturally in the analysis of longitudinal data and some genetics models. Further work on statistical techniques and computer software developed by the Principal Investigator to implement these techniques will be pursued during this grant period with a long range goal of developing highly disseminated, easy to use software (e.g., for SAS or BMDP). Research efforts in this area will include: (1) the completion of documentation and testing of developed computer software; (2) testing of performance characteristics both of the computer software and the underlying statistical procedures; (3) formulating programmable procedures for finding approximate null distributions for explicit MLE patterns; (4) finding asymptotic nonnull distributions under local alternative hypotheses; (5) characterizing the class of linear covariance paterns that are submatrices of linear covariance paterns with explicit MLE; and (6) publishing applications of these new statistical techniques in journals accessible to applied researchers. This proposal addresses the difficulties of developing and implementing statistical techniques which are relatively easy to interpret once the results are in hand even though deriving the results requires sophisticated mathematics. The essence of making statistical techniques available to biomedical researchers is to have software which implements the techniques. When software is not available, researchers resort to alternative (and at times inefficient or incorrect) techniques for which computer software is available.