Before revision:  Our statistics are based on a well-known property of the \% r +1 -th eigenvalue of the sample covariance matrix of the data (having defined r as the number of common factors ): whilst under the null the \left( r+1\right) -
After revision:  Our statistics are based on a well-known property of the \% r +1 Letting r be the number of common factors ): whilst under the null the \left( r+1\right) -