  In this paper, we consider a one-dimensional Cox-Ingersoll-Ross (CIR) process
whose drift coefficient depends on unknown parameters. Considering the process
discretely observed at high frequency, we prove the local asymptotic normality
property in the subcritical case, the local asymptotic quadraticity in the
critical case, and the local asymptotic mixed normality property in the
supercritical case. To obtain these results, we use the Malliavin calculus
techniques developed recently for CIR process by Al\`os et {\it al.}
\cite{AE08} and Altmayer et {\it al.} \cite{AN14} together with the $L^p$-norm
estimation for positive and negative moments of the CIR process obtained by
Bossy et {\it al.} \cite{BD07} and Ben Alaya et {\it al.} \cite{BK12,BK13}. In
this study, we require the same conditions of high frequency
$\Delta_n\rightarrow 0$ and infinite horizon $n\Delta_n\rightarrow\infty$ as in
the case of ergodic diffusions with globally Lipschitz coefficients studied
earlier by Gobet \cite{G02}. However, in the non-ergodic cases, additional
assumptions on the decreasing rate of $\Delta_n$ are required due to the fact
that the square root diffusion coefficient of the CIR process is not regular
enough. Indeed, we assume $n\Delta_n^{3}\to 0$ for the critical case and
$\Delta_n^{2}e^{-b_0n\Delta_n}\to 0$ for the supercritical case.
