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Lecture 1 - Sample Covariance Operators: Normal Approximation and Concentration

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Short Course

In this short course, several problems related to statistical estimation of covariance operators and their spectral characteristics will be discussed. The problems will be studied in a dimension-free framework in which the data lives in high-dimensional or infinite-dimensional spaces and “complexity” of estimation is characterized by the so called “effective rank” of the true covariance operator rather than by the dimension of the ambient space. In this framework, sharp moment bounds and concentration inequalities for the operator norm error of sample covariance will be proved in the Gaussian case showing that the “effective rank” characterizes the size of this error.

In addition to this, a number of recent results on normal approximation and concentration of functions of sample covariance operators, including their spectral projections, will be discussed.

This talk is part of the Cambridge Centre for Analysis talks series.

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