2,961 research outputs found
Asymptotics for High-Dimensional Data
We develop an asymptotic theory for norms of sample mean vectors of
high-dimensional data. An invariance principle for the norms is derived
under conditions that involve a delicate interplay between the dimension ,
the sample size and the moment condition. Under proper normalization,
central and non-central limit theorems are obtained. To facilitate the related
statistical inference, we propose a plug-in calibration method and a
re-sampling procedure to approximate the distributions of the norms. Our
results are applied to multiple tests and inference of covariance matrix
structures.Comment: 3
Regularized estimation of linear functionals of precision matrices for high-dimensional time series
This paper studies a Dantzig-selector type regularized estimator for linear
functionals of high-dimensional linear processes. Explicit rates of convergence
of the proposed estimator are obtained and they cover the broad regime from
i.i.d. samples to long-range dependent time series and from sub-Gaussian
innovations to those with mild polynomial moments. It is shown that the
convergence rates depend on the degree of temporal dependence and the moment
conditions of the underlying linear processes. The Dantzig-selector estimator
is applied to the sparse Markowitz portfolio allocation and the optimal linear
prediction for time series, in which the ratio consistency when compared with
an oracle estimator is established. The effect of dependence and innovation
moment conditions is further illustrated in the simulation study. Finally, the
regularized estimator is applied to classify the cognitive states on a real
fMRI dataset and to portfolio optimization on a financial dataset.Comment: 44 pages, 4 figure
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