On finite sample statistics for Yule-Walker estimates

The expectation of the square of the reflection coefficient in small samples of white noise is derived. This variance of the reflection coefficient in white noise is a key factor in the statistics of the estimation of autoregressive (AR) models in small samples. Approximations of this expectation are constructed that are more accurate than the known first-order Taylor approximation. These better approximations are needed, because in some applications (radar applications, for example) the number of observations is small (say 63 observations) and asymptotic descriptions do not cover the estimates.