From Parameter Estimation to Dispersion of Nonstationary Gauss-Markov Processes
share
This paper provides a precise error analysis for the maximum likelihood estimate â(u) of the parameter a given samples u = (u_1, ..., u_n)^ drawn from a nonstationary Gauss-Markov process U_i = a U_i-1 + Z_i, i≥ 1, where a> 1, U_0 = 0, and Z_i's are independent Gaussian random variables with zero mean and variance σ^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 dispersionJournal 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.
READ FULL TEXT