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平滑经验过程与分位数过程之间的距离
We consider Bahadur-Kiefer representations for smoothed quantile processes. We prove that the asymptotics of the distance between smoothed empirical and quantile processes can be completely different from that of the unsmoothed ones. We obtain a complete characterization of the possible limits.
随机删失下核密度估计Lp距离的中心极限定理
A sequence of independent nonnegative random variables with common distribution function $F$ is censored on the right by another sequence of independent identically distributed random variables. These two sequences are also assumed to be independent. We estimate the density function $f$ of $F$ by a sequence of kernel estimators $f_n(t) = (\int^\infty_{-\infty}K((t - x)/h(n))d\hat{F}_n(x))/h(n),$ where $h(n)$ is a sequence of numbers, $K$ is kernel density function and $\hat{F}_n$…
分位数过程及其统计应用
A Preliminary Study of Quantile Processes A Weak Convergence of the Normed Sample Quantile Process Strong Approximations of the Normed Quantile Process Two Approaches to Constructing Simultaneous Confidence Bounds for Quantiles Weak Convergence of Quantile Processes in Weighted Sup-Norm Metrics and Further Strong Approximations On Bahadur's Representation of Sample Quantiles and on Kiefer's Theory of Deviations Between the Sample Quantile and Empirical Processes Quadratic…
分位数过程的强逼近
Let $q_n(y), 0 < y < 1,$ be a quantile process based on a sequence of i.i.d. rv with distribution function $F$ and density function $f.$ Given some regularity conditions on $F$ the distance of $q_n(y)$ and the uniform quantile process $u_n(y),$ respectively defined in terms of the order statistics $X_{k:n}$ and $U_{k:n} = F(X_{k:n}),$ is computed with rates. As a consequence we have an extension of Kiefer's result on the distance between the empirical and quantile processes,…