Nonlinear statistical inference and boundary crossing probabilities

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The proposed research is concerned with finding relationships between a response variable and other predictor variables, some of which are either not directly observable or measured with error. Examples include personal exposure to air pollutants, long-term systolic blood pressure, social ability and wealth. It is known that statistical methods ignoring the measurement error result in biased and inconsistent estimates. The goal of the proposed research is to develop novel methods to accurately estimate relationships in the presence of measurement error, which do not rely on restrictive assumptions and are therefore applicable to a wide range of problems. The anticipated results will advance statistical theory and methodology, as well as provide better tools for real data analysis.