Parameter Estimation for the Critical Case of Continuous StateBranching Process with Immigration

The least squares estimation for the parameter of the critical case of continuous state branching process with immigration is put under examination when the branching rateε approaches zero. The velocity of the parameter when its least squares estimation value converges its real value is established when the branching rateε→0and the discrete observation frequency approaches infinitely great simultaneously, namely the central limit theorem and the moderate deviation principle.