##### Department of Mathematics,

University of California San Diego

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### Colloquium

## Danna Zhang

#### University of Chicago

## High-dimensional CLT for temporal dependent data

##### Abstract:

High-dimensional temporal dependent data arise in a wide range of disciplines. The fact that the classical CLT for i.i.d. random vectors may fail in high dimensions makes high-dimensional inference notoriously difficult. More challenges are imposed by temporal and cross-sectional dependence. In this talk, I will introduce the high-dimensional CLT for temporal dependent data. Its validity depends on the sample size $n$, the dimension $p$, the moment condition and the dependence of the underlying processes. An example is taken to appreciate the optimality of the allowed dimension $p$. Equipped with the high-dimensional CLT result, we have a new sight on many problems such as inference for covariances of high-dimensional time series which can be applied in the analysis of network connectivity, inference for multiple posterior means in MCMC experiments as well as Kolmogorov-Smirnov test for high-dimensional dependent data. I will also introduce an estimator for long-run covariance matrices and two resampling methods, i.e., Gaussian multiplier resampling and subsampling, to make the high-dimensional CLT more applicable. Our work is then corroborated by a simulation study with a hierarchical model.

Host: Dimitris Politis

### January 18, 2017

### 2:00 PM

### AP&M 6402

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