Log In Sign Up

Minimax Estimation of Partially-Observed Vector AutoRegressions

by   Guillaume Dalle, et al.

To understand the behavior of large dynamical systems like transportation networks, one must often rely on measurements transmitted by a set of sensors, for instance individual vehicles. Such measurements are likely to be incomplete and imprecise, which makes it hard to recover the underlying signal of interest.Hoping to quantify this phenomenon, we study the properties of a partially-observed state-space model. In our setting, the latent state X follows a high-dimensional Vector AutoRegressive process X_t = θ X_t-1 + ε_t. Meanwhile, the observations Y are given by a noise-corrupted random sample from the state Y_t = Π_t X_t + η_t. Several random sampling mechanisms are studied, allowing us to investigate the effect of spatial and temporal correlations in the distribution of the sampling matrices Π_t.We first prove a lower bound on the minimax estimation error for the transition matrix θ. We then describe a sparse estimator based on the Dantzig selector and upper bound its non-asymptotic error, showing that it achieves the optimal convergence rate for most of our sampling mechanisms. Numerical experiments on simulated time series validate our theoretical findings, while an application to open railway data highlights the relevance of this model for public transport traffic analysis.


page 23

page 26


Exact Minimax Estimation for Phase Synchronization

We study the phase synchronization problem with measurements Y=z^*z^*H+σ...

Nonparametric density estimation for intentionally corrupted functional data

We consider statistical models where functional data are artificially co...

Missing Data in Sparse Transition Matrix Estimation for Sub-Gaussian Vector Autoregressive Processes

High-dimensional time series data exist in numerous areas such as financ...

A frequency domain analysis of the error distribution from noisy high-frequency data

Data observed at high sampling frequency are typically assumed to be an ...

Predictability limit of partially observed systems

Applications from finance to epidemiology and cyber-security require acc...

SDP Achieves Exact Minimax Optimality in Phase Synchronization

We study the phase synchronization problem with noisy measurements Y=z^*...