In this work, a statistical analysis is performed for a simple constrained high-order Yule-Walker (YW) tone frequency estimator obtained from the first equation of the constrained high-order YW equations. Explicit expressions for its estimation bias and variance are efficiently derived by virtue of a Taylor series expansion technique. Especially, being explicit in terms of frequency, data length and Signal-to-Noise Ratio (SNR) value, the resulting bias expression can not be obtained by using the asymptotic analyses used for the parameter estimation methods. The obtained expressions are compared with their counterparts of the Pisarenko tone frequency estimator. Simulations are performed to support the theoretical results.