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Joint Econometrics and Statistics Workshop

Optimal estimation of functionals of high-dimensional mean and covariance matrix

Haolei Weng (Michigan State University)

Friday 06 March 2020 12:00 - 13:00

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About this event

Motivated by portfolio allocation and linear discriminant analysis, we consider estimating a functional involving both the mean vector and covariance matrix. We study the minimax estimation of the functional in the high-dimensional sparse setting. Akin to past works on functional estimation, we show that the optimal rate for estimating the functional undergoes a phase transition between regular parametric rate and some form of high-dimensional estimation rate. We further show that the optimal rate is attained by a carefully designed plug-in estimator based on de-biasing, while a family of naive plug-in estimators are proved to fall short. We further generalize the estimation problem and techniques that allow robust inputs of mean and covariance matrix estimators. Extensive numerical experiments lend further supports to our theoretical results.

Econometrics and Statistics seminars are held on Fridays in term time at 12:00-13:00, ONLINE, unless specified otherwise.

Seminar organisers: Dr Tatiana Komarova and Dr Yunxiao Chen.

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