RESEARCH ON PATTERNED COVARIANCES

拟议的研究旨在填补统计上的主要空白。 生物医学数据的分析涉及具有图案化手段的模型和 可能带有缺失数据的图案化协方差。这些模型产生了 当然，在分析纵向数据和一些遗传学模型时也是如此。 进一步开展统计技术和计算机软件方面的工作 实施这些技术的首席调查员将被追查 在这一资助期内，以高度发展的长远目标 分发的、易于使用的软件(例如，用于SAS或BMDP)。 这方面的研究工作将包括：(1)完成 编制文件和测试已开发的计算机软件；(2)测试 计算机软件和 基本统计程序；(3)制定可编程程序 用于寻找显式MLE模式的近似零分布；(4) 寻找局部选择下的渐近非零分布 假设；(5)刻画一类线性协方差模式 是具有显式最大似然估计的线性协方差模式的子矩阵；和(6) 这些新的统计技术在期刊中的出版应用 应用研究人员可以访问。 这项建议解决了开发和实施的困难 一种相对容易理解的统计技术 结果已经掌握，尽管得出结果需要复杂的技术 数学。将统计技术提供给 生物医学研究人员将拥有实现 技巧。当软件不可用时，研究人员求助于 替代(有时是低效或不正确的)技术 有计算机软件可用。

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.