Technical Program

Paper Detail

Paper Title From Parameter Estimation to Dispersion of Nonstationary Gauss-Markov Processes
Paper IdentifierTH2.R6.4
Authors Peida Tian, Victoria Kostina, California Institute of Technology, United States
Session Lossy Compression
Location Sorbonne, Level 5
Session Time Thursday, 11 July, 11:40 - 13:00
Presentation Time Thursday, 11 July, 12:40 - 13:00
Manuscript  Click here to download the manuscript
Abstract This paper provides a precise error analysis for the maximum likelihood estimate $\hat{a}(u)$ of the parameter $a$ given samples $u = (u_1, \ldots, u_n)^\top$ drawn from a nonstationary Gauss-Markov process $U_i = a U_{i-1} + Z_i,~i\geq 1$, where $a> 1$, $U_0 = 0$, and $Z_i$'s are independent Gaussian random variables with zero mean and variance $\sigma^2$. We show a tight nonasymptotic exponentially decaying bound on the tail probability of the estimation error. Unlike previous works, our bound is tight already for a sample size of the order of hundreds. We apply the new estimation bound to find the dispersion for lossy compression of nonstationary Gauss-Markov sources. We show that the dispersion is given by the same integral formula derived in our previous work~\cite{tian2018dispersion} for the (asymptotically) stationary Gauss-Markov sources, i.e., $|a| < 1$. New ideas in the nonstationary case include a deeper understanding of the scaling of the maximum eigenvalue of the covariance matrix of the source sequence, and new techniques in the derivation of our estimation error bound.