  In this paper, we study the largest eigenvalues of sample covariance matrices
with elliptically distributed data. We consider the sample covariance matrix
$Q=YY^*,$ where the data matrix $Y \in \mathbb{R}^{p \times n}$ contains i.i.d.
$p$-dimensional observations $\mathbf{y}_i=\xi_iT\mathbf{u}_i,\;i=1,\dots,n.$
Here $\mathbf{u}_i$ is distributed on the unit sphere, $\xi_i \sim \xi$ is
independent of $\mathbf{u}_i$ and $T^*T=\Sigma$ is some deterministic matrix.
Under some mild regularity assumptions of $\Sigma,$ assuming $\xi^2$ has
bounded support and certain proper behavior near its edge so that the limiting
spectral distribution (LSD) of $Q$ has a square decay behavior near the
spectral edge, we prove that the Tracy-Widom law holds for the largest
eigenvalues of $Q$ when $p$ and $n$ are comparably large.
