The uniform asymptotics on the sample quantile process. (English) Zbl 1081.60513
Summary: We prove the uniform asymptotics for the sample quantile process. In the way of developing asymptotic Gaussianity of the sample quantile process, we obtain topological properties for the space of functions that are left continuous with right limits, \(L_\mathbb{R}(0,1)\). We also obtain the uniform consistency and the uniform log log law for the sample quantile process.
MSC:
60F15 | Strong limit theorems |
60F17 | Functional limit theorems; invariance principles |
60G42 | Martingales with discrete parameter |