This paper considers a linear regression model with possible multicollinearity.
When the matrix $\mathbf{A}^t\mathbf{A}$ is nearly singular, the least squares estimator (LSE)
gets unstable. Typical solutions for this problem include the generalized ridge estimator
due to Hoerl and Kennard(1970a,b) and its derivatives. Among them, 
we focus on an adaptive ridge estimator discussed by Wang and Chow(1990) under normality. 
We assume the error term $\mathbf{e}$ is distributied as a spherically symmetric distributiuon 
and derive a sufficient condition so that the estimator is superior to the LSE
under mean squared error (MSE) and quadratic loss.
Several numerical examples are also given.