  We study the Gaussian quasi-likelihood estimation of the parameter
$\theta:=(\alpha,\beta,\gamma)$ of the square-root diffusion process, also
known as the Cox-Ingersoll-Ross (CIR) model, observed at high frequency.
Different from the previous study [1] under low-frequency sampling,
high-frequency of data provides us with very simple form of the asymptotic
covariance matrix. Through easy-to-compute preliminary contrast functions, we
formulate a practical two-stage manner without numerical optimization in order
to conduct not only an asymptotically efficient estimation of the drift
parameters, but also high-precision estimator of the diffusion parameter.
Simulation experiments are given to illustrate the results.
  [1] L. Overbeck and T. Ryd\'en. Estimation in the Cox-Ingersoll-Ross model.
Econometric Theory, 13(3): 430-461, 1997.
