Wang's Asymptotic Analysis Method and the ZiZhu High-Probability Concentration Threshold Theorem

This paper analyzes recursive estimation systems where accuracy, sample size, and failure probability are coupled through concentration inequalities. By introducing the scaling variable \ (xₖ=ₖNₖ\), I characterize the asymptotic behavior of such systems. The analysis reveals two orbit types: tight orbits achieving statistical efficiency limits, and non-tight orbits crossing thresholds with efficiency costs. I develop **Wang's Asymptotic Analysis Method**, providing a unified framework for analyzing recursive estimation under high-probability constraints, and prove the **Zizhu High-Probability Concentration Threshold Theorem**, establishing a fundamental information amount boundary for feasible system evolution.