Dimension Reduction for High Dimensional Vector Autoregressive Models

Dimension reduction for high-dimensional data.

With advancing of modern technologies, high-dimensional data have prevailed in computational biology. The number of variables p is very large, and in many applications, p is larger than the number of observational units n. Such high dimensionality and the unconventional small-n-large-p setting have posed new challenges to statistical analysis methods. Dimension reduction, which aims to reduce t...

Vector Autoregressive Models

Order selection for vector autoregressive models

Order-selection criteria for vector autoregressive (AR) modeling are discussed. The performance of an order-selection criterion is optimal if the model of the selected order is the most accurate model in the considered set of estimated models: here vector AR models. Suboptimal performance can be a result of underfit or overfit. The Akaike information criterion (AIC) is an asymptotically unbiase...

Distance Transformation for Effective Dimension Reduction of High-Dimensional Data

In this paper we address the problem of high-dimensionality for data that lies on complex manifolds. In high-dimensional spaces, distances between the nearest and farthest neighbour tend to become equal. This behaviour hardens data analysis, such as clustering. We show that distance transformation can be used in an effective way to obtain an embedding space of lower-dimensionality than the orig...

Estimating Structured Vector Autoregressive Models

While considerable advances have been made in estimating high-dimensional structured models from independent data using Lasso-type models, limited progress has been made for settings when the samples are dependent. We consider estimating structured VAR (vector auto-regressive model), where the structure can be captured by any suitable norm, e.g., Lasso, group Lasso, order weighted Lasso, etc. I...