Statistical Methods for Some Applied Problems

摘要DMS 0102529-一些应用问题的统计方法将与适当的统计推理工具一起开发用于一些现实生活问题的随机模型和方法。拟议研究的结果将适用于重要的应用领域，并与之直接相关。第一个主题涉及多用户计算机网络中由用户命令流引起的问题的统计方法。这些数据的统计建模在网络入侵检测、设计具有学习能力的智能计算机/互联网环境等方面有着重要的应用。目标是开发一种实用的方法来分析单个用户，或者更一般地，分析来自固定给定源的随机命令序列。我们的方法允许系统识别用户的统计签名，并识别可能采用合法用户的电子身份的伪装者。由于数据的切变大小和复杂性，这些数据构成了巨大的实际挑战，并且我们目前的方法在两个公开可用的测试数据上具有非常好的操作特性(虚警和漏警)。第二个主题涉及基于多变量中值的数据深度函数的新概念的发展。给出了计算一个重要的多元中值函数的新算法，以及与之相关的数据深度的闭合公式。该方法将为多变量数据分析、推断、回归、图像处理等提供可靠、实用的工具。第三个主题是关于信息异质截尾下增长曲线比较的回归分析和非参数方法。在许多肿瘤生长抑制研究中，肿瘤大小是在一段时间内记录的，形成了每个实验对象的生长曲线。通常的非信息性审查模型通常不适用，因为受试者可能会因为治疗的毒性效应而被排除在研究之外。我们建议开发统计检验来比较肿瘤生长速度和回归系数的估计，在存在信息量的异质审查的情况下。拟议的测试程序有望得到广泛应用，因为它们自然纠正了审查偏见，保持了高效率，并且不需要对增长曲线或审查机制进行分布假设。

Abstract DMS 0102529 ---------- STATISTICAL METHODS FOR SOME APPLIED PROBLEMSStochastic models and methods for a number of real-life problems will be developed together with appropriate statistical inference tools. Results of the proposed research will be applicable and directly relevant to important areas of applications. The first topic concerns statistical methodology for problems originating by users' command streams in a multi-users computer network. Statistical modeling of such data has important applications in networks' intrusion-detection, in designing intelligent computer/internet environments with learning capabilities, and more. The goal is to develop a practical methodology for profiling individual users or, more generally, random sequences of commands originating from a fixed given source. Our methods allow the system to recognize 'statistical signature' of users, and to flag out masqueraders who might assume the e-identity of a legitimate user. The data pose huge practical challenges, because of its shear size and complexion and our current method has very good operating characteristics(false- and missing- alarms) on two publicly available test data. The second topic concerns the development of a new concept of data-depth functions, based on multivariate medians. We provided a new algorithm for calculating an important multivariate median function, and a closed form formula for the associated data depth. The methodology will lead to robust, practical tools for multivariate data analysis, inference, regression, image processing, and more. The third topic concerns regression analysis and nonparametric methods for the comparisons of growth curves under informative heterogeneous censoring. In many tumor growth inhibition studies, tumor sizes are recorded over a period of time, forming a growth curve for each experimental subject. The usual noninformative-censoring model is often not applicable, because subjects could be censored out of the study due to treatments toxicity effects. We propose to develop statistical tests for the comparison of tumor growth rates and estimates of regression coefficients, in the presence of informative heterogeneous censoring. The proposed testing procedures are expected to be widely used, since they naturally correct the censorship bias, retain high efficiency and require no distributional assumption of the growth curves or the censoring mechanism.