120 citations · 545 across the 20 of their papers we have counts for
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On the variability of the sample covariance matrix under complex elliptical distributions
Elias Raninen, Esa Ollila, David E. Tyler
We derive the form of the variance-covariance matrix for any affine equivariant matrix-valued statistics when sampling from complex elliptical distributions. We then use this resul…
Shrinking the Sample Covariance Matrix using Convex Penalties on the Matrix-Log Transformation
David E. Tyler, Mengxi Yi
For -dimensional data, penalized versions of the sample covariance matrix are important when the sample size is small or modest relative to . Since the negative log-likelihoo…
Asymptotic and bootstrap tests for the dimension of the non-Gaussian subspace
Klaus Nordhausen, Hannu Oja, David E. Tyler +1
Dimension reduction is often a preliminary step in the analysis of large data sets. The so-called non-Gaussian component analysis searches for a projection onto the non-Gaussian pa…
Breakdown Properties of the M-Estimators of Multivariate Scatter
David E. Tyler
The M-estimators of multivariate scatter are known to have breakdown points no greater than 1/(p+1), where p is the dimension of the data. In high dimension, the breakdown points a…
The spatial sign covariance matrix with unknown location
Alexander Dürre, Daniel Vogel, David E. Tyler
The consistency and asymptotic normality of the spatial sign covariance matrix with unknown location are shown. Simulations illustrate the different asymptotic behavior when using…
Robust estimators for non-decomposable elliptical graphical models
Daniel Vogel, David E. Tyler
Asymptotic properties of scatter estimators for elliptical graphical models are studied. Such models impose a given pattern of zeros on the inverse of the shape matrix of an ellipt…