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Extremal Depth for Functional Data and Applications

函数型数据的极端深度及其应用

We propose a new notion called “extremal depth” (ED) for functional data, discuss its properties, and compare its performance with existing concepts. The proposed notion is based on a measure of extreme “outlyingness.” ED has several desirable properties that are not shared by other notions and is especially well suited for obtaining central regions of functional data and function spaces. In particular: (a) the central region achieves the nominal (desired) simultaneous…

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Network Delay Tomography using Flexicast Experiments

利用灵活组播实验进行网络时延层析估计

Summary Estimating and monitoring the quality of service of computer and communications networks is a problem of considerable interest. The paper focuses on estimating link level delay distributions from end-to-end path level data collected by using active probing experiments. This is an interesting large scale statistical inverse (deconvolution) problem. We describe a flexible class of probing experiments (‘flexicast’) for data collection and develop conditions under which…

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Nonparametric Inference Under Biased Sampling from a Finite Population

有限总体偏倚抽样下的非参数推断

We consider a biased sampling model that has been found useful in incorporating size biases inherent in many types of discovery data. The model postulates that the data are obtained from a finite population by selecting successively without replacement and with probability proportional to some measure of size. Unlike the ppswor scheme in survey sampling, it is assumed here that the size measure is a function of the unknown population values. In this article, we consider…

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Chi-Squared-Type Tests for Ordered Alternatives in Contingency Tables

列联表有序备择的卡方型检验

It is well known that the classical Pearson's chi-squared test for contingency tables does not have good power against ordered alternatives. Such alternatives arise naturally when there is an ordering in the rows or columns of the table. This article considers a general class of tests called cumulative chi-squared—type (CCS-type) tests for ordered alternatives. Different members of this class correspond to the choice of different weighting schemes. The properties of the…

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On the Behavior of Some Estimators from Probability Plots

概率图中若干估计量的性质

Probability plots are popular graphical methods used to assess distributional assumptions. Under a location-scale model, the plot tends to lie on a straight line. A common practice in this situation is to fit a line through the plot and use the intercept and slope of the fitted line as estimates of the location and scale parameters. What are the properties of these estimators? Estimators from weighted least squares lines are considered, and their asymptotic, finite-sample,…

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