We study the estimate of the mean q of a Gaussian random variable  in    unknown and estimated by the chi-square variable

We particularly study the bounds and limits of the ratios of the risks, of the James-Stein estimator  and of its positive-part  with that of the maximum likelihood estimator X when p tends to infinity and n fixes on one hand, and on the other hand, when n and p tend simultaneously to infinity.

If  then we show that the ratios of the risks of the James-Stein estimator  and its positive-part  with that of the maximum likelihood estimator X tend to the same value  when  If n and p tend to infinity, then we show that the ratios of the risks tend to  We graphically illustrate the ratios of the risks corresponding to the James-Stein estimators  and its positive-part  with that of the maximum likelihood estimator X for diverse values of n and p.