Unified estimators of smooth quantile and quantile density functions
Unified estimators of smooth quantile and quantile density functions
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DOI：
10.1016/s0378-3758(96)00110-3
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发表时间：
1997-04-15
影响因子：
0.9
通讯作者：
Parzen, E
中科院分区：
文献类型：
--
作者：
Cheng, C;Parzen, E
将分位数函数的各种光滑估计统一为样本分位数函数的广义核光滑估计。证明了分位数函数估计和分位数密度函数估计的超范数收敛性。收敛速度揭示了在开单位区间内的任何紧集上，这两个估计的同时一致的概率相合性。建立了分位数函数估计量的Berry-Esseen型定理，确定了样本分位数相对于光滑估计量的渐近亏量和最优光滑率.有限样本下估计的振动性（单调性、凸性等）的调查，并涉及到某些代数性质的平滑核。
Diverse smooth estimators of quantile functions are unified into generalized kernel smoothers of the sample quantile function. Sup-norm convergence of the quantile function estimators and the derived quantile density function estimators are established. The convergence rates reveal the simultaneous uniform in-probability consistency of both estimators on any compact set inside the open unit interval. A Berry-Esseen-type theorem of the quantile function estimators is established; the asymptotic deficiency of sample quantiles relative to the smooth estimators and optimal smoothing rate are determined. Oscillation behavior of the estimators in finite samples (monotonicity, convexity, etc.) is investigated, and is related to certain algebraic properties of the smoothing kernel.