Invariance principles and change-point analysis for error-in-variables models

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Title of Proposal: Invariance Principles and Change-Point Analysis for Error-in-Variables ModelsError-in-variables models (EIVM's) constitute an over 130-year-old area of Statistics. In these models two or more variables of interest are assumed to have a certain form of a relationship, and they are observed with measurement errors. This complicates inferring about unknown parameters of this relationship. EIVM's are also known as measurement error models, or regression models with errors in independent variables. Studies of EIVM's have been stimulated by an increasing demand of data analysis in numerous applications of EIVM's that include virtually every area of science and technology, such as medicine, agriculture and econometrics, for example. My research program primarily deals with new asymptotic studies for statistical inference in EIVM's, based on large samples of observations. At the same time, these studies present, and are substantially based on solving, some open problems in the areas of Probability Theory on self-normalized/Studentized partial sums and partial sums processes of independent random variables. Consequently, the anticipated significance of this proposal amounts to establishing new methodologies and results both in statistical inference and probability theory by means of a close interplay between these areas of research. Invariance principles for self-norma- lized/Studentized partial sums and partial sums processes of independent random variables are new in EIVM's. They provide a source for data-based inference in EIVM's, like, for example, readily available or easily derivable large-sample approximate confidence intervals/regions for unknown parameters in these models. They also allow studying EIVM's under some new, most general conditions. Moreover, they play a crucial role in one of the main directions of my proposed research, namely, in developing procedures for studying change-point problems in EIVM's. Such problems arise naturally in applications when one is concerned with possible changes that may have occurred in an EIVM while collecting data for statistical inference therein.