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

在分子生物学、排队理论、质量控制和其他实验情境中出现的某些问题也涉及到观察序列、序列中的模式和序列中模式的变化。这项研究定义了一个严格的数学框架，在其中检查这些问题，并带来承担现代统计方法。特别是，该研究解决了回归分析（传统的、稳健的和/或半线性的）的问题，以处理删减或截断的数据，并按顺序或预先确定的样本量检测变化点。此外，将发展序列分析的自举方法，并研究其统计性质。

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.