"Text-based data, collaborative filtering, covariance matrix estimation, and other statistical problems"

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My research to date has been broadly based, with contributions to many areas of statistics; accordingly, this proposal ranges over a number of projects. (1) Statistical methods for text-based documents: (a) Automated computerized dating of documents, via nearest neighbours, maximum likelihood analogues, quantile regression, and other methods, and (b) Nonparametric temporal sequencing of document collections when none have been dated, by constructing noisy matrices of distances between documents pairs using singular value decomposition, and combinatorial optimization of objective functions that measure sequence correctness. (2) Nonlinear methods for collaborative filtering: (a) Predicting ratings users will give to products from large sparse matrices of user ratings via nonlinear SVD methods to improve prediction, and (b) Penalization problems related to the `large p small n' context. (3) Estimating large covariance matrices: (a) Allocating Fisher information for inference on the matrix structure given no prior information, (b) Shrinkage, empirical Bayes, penalization, regularization and sparseness methods to improve estimation, (c) Non-negative definiteness constraints, and (d) Choice of norms for assessing performance. Other problems include (a) Inference in certain exponential dispersion models generated by exponential tilting of extreme stable laws, (b) Inference in stable processes, (c) Deconvolution problems, and (d) Dependency structures in stationary point processes.