Statistical Methods for Some Applied Problems

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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.