Mathematical Sciences: Sequential Experimentation, Regression Analysis, and Related Topics in Probability

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Certain problems arising in molecular biology, in queueing theory, in quality control and in other experimental situations as well, involve sequences of observations and patterns within the sequences and change of pattern within the sequences. This research defines a rigorous mathematical framework within which to examine these problems and to bring to bear modern statistical methodologies. In particular, the research addresses the problem of regression analysis (traditional, robust and/or semilinear) to handle censored or truncated data and to detect change-points either sequentially or at a predetermined sample size. In addition, bootstrap methods for sequential analysis will be developed and their statistical properties will be investigated.