  In this paper, we investigate the asymptotic behavior of spiked eigenvalues
of the noncentral Fisher matrix defined by ${\mathbf F}_p={\mathbf C}_n(\mathbf
S_N)^{-1}$, where ${\mathbf C}_n$ is a noncentral sample covariance matrix
defined by $(\mathbf \Xi+\mathbf X)(\mathbf \Xi+\mathbf X)^*/n$ and $\mathbf
S_N={\mathbf Y}{\mathbf Y}^*/N$. The matrices $\mathbf X$ and $\mathbf Y$ are
two independent {Gaussian} arrays, with respective $p\times n$ and $p\times N$
and the Gaussian entries of them are \textit {independent and identically
distributed} (i.i.d.) with mean $0$ and variance $1$. When $p$, $n$, and $N$
grow to infinity proportionally, we establish a phase transition of the spiked
eigenvalues of $\mathbf F_p$. Furthermore, we derive the \textit{central
limiting theorem} (CLT) for the spiked eigenvalues of $\mathbf F_p$. As an
accessory to the proof of the above results, the fluctuations of the spiked
eigenvalues of ${\mathbf C}_n$ are studied, which should have its own
interests. Besides, we develop the limits and CLT for the sample canonical
correlation coefficients by the results of the spiked noncentral Fisher matrix
and give three consistent estimators, including the population spiked
eigenvalues and the population canonical correlation coefficients.
