To my parents ii ACKNOWLEDGEMENTS My foremost thanks go to my advisors Dr. George Michailidis and Dr. Moulinath Banerjee. I thank them for their advice, patience, support, encouragement, insights and suggestions that helped shape my research skills. This thesis would not be possible without them. I am grateful to my two other committee members, Dr. for reviewing my work and providing me with va...

Changepoints are a very common feature of Big Data that arrive in the form of a data stream. In this paper, we study high-dimensional time series in which, at certain time points, the mean structure changes in a sparse subset of the coordinates. The challenge is to borrow strength across the coordinates in order to detect smaller changes than could be observed in any individual component series...

The change-point detection problem is cast into a delay estimation. Using a local piecewise polynomial representation and some elementary algebraic manipulations, we give an explicit characterization of a change-point as a solution of a given polynomial equation. A key feature of this polynomial equation is its coefficients being composed by short time window iterated integrals of the noisy sig...

Aim of this paper is reformulation of global image thresholding problem as a well-founded statistical method known as change-point detection (CPD) problem. Our proposed CPD thresholding algorithm does not assume any prior statistical distribution of background and object grey levels. Further, this method is less influenced by an outlier due to our judicious derivation of a robust criterion func...

We consider the problem of nonparametric estimation of signal singularities from indirect and noisy observations. Here by singularity we mean a discontinuity (change– point) of the signal or of its derivative. The model of indirect observations we consider is that of a linear transform of the signal, observed in white noise. The estimation problem is analyzed in a minimax framework. We provide ...

Most statistical analyses of fMRI data assume that the nature, timing and duration of the psychological processes being studied are known. However, in many areas of psychological inquiry, it is hard to specify this information a priori. Examples include studies of drug uptake, emotional states or experiments with a sustained stimulus. In this paper we assume that the timing of a subject's activ...