Wavelet-variance-based estimation for composite stochastic processes

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This thesis concerns the theory of positive-definite completions and its mutually beneficial connections to the statistics of function-valued or continuously-indexed random processes, better known as functional data analysis. In particular, it dwells upon ...

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Is it possible to detect if the sample paths of a stochastic process almost surely admit a finite expansion with respect to some/any basis? The determination is to be made on the basis of a finite collection of discretely/noisily observed sample paths. We ...

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In the field of choice modeling, the availability of ever-larger datasets has the potential to significantly expand our understanding of human behavior, but this prospect is limited by the poor scalability of discrete choice models (DCMs): as sample sizes ...

2023

Robust discrete choice models with t-distributed kernel errors

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Higher Order Asymptotics: Applications to Satellite Conjunction and Boundary Problems

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Higher-order asymptotics provide accurate approximations for use in parametric statistical modelling. In this thesis, we investigate using higher-order approximations in two-specific settings, with a particular emphasis on the tangent exponential model. ...

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