Convergence rate of Krasulina estimator

Jiangning Chen

Statistics & Probability Letters, 2019, vol. 155, issue C, -

Abstract: Principal component analysis (PCA) is one of the most commonly used statistical procedures with a wide range of applications. Consider the points X1,X2,…,Xn are vectors drawn i.i.d. from a distribution with mean zero and covariance Σ, where Σ is unknown. Let An=XnXnT, then E[An]=Σ. This paper considers the problem of finding the smallest eigenvalue and eigenvector of matrix Σ. A classical estimator of this type is due to (Krasulina, 1969). We are going to state the convergence proof of Krasulina for the smallest eigenvalue and corresponding eigenvector, and then find their convergence rate.

Keywords: PCA; Incremental; Online updating; Covariance matrix; Rate of convergence; Adaptive estimation (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1016/j.spl.2019.108562

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