On Bahadur's Representation of Sample Quantiles
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This article is published in Annals of Mathematical Statistics.The article was published on 1967-10-01 and is currently open access. It has received 229 citations till now. The article focuses on the topics: Representation (systemics) & Quantile.read more
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Empirical processes with applications to statistics
Galen R. Shorack,Jon A. Wellner +1 more
TL;DR: In this paper, a broad cross-section of the literature available on one-dimensional empirical processes is summarized, with emphasis on real random variable processes as well as a wide-ranging selection of applications in statistics.
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Limiting distributions for $L\sb 1$ regression estimators under general conditions
TL;DR: In this article, the authors derived the asymptotic distributions under more general conditions on the behavior of the distribution function near 0, and showed that these distributions are asymPT-normal.
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On a geometric notion of quantiles for multivariate data
TL;DR: In this paper, an extension of the concept of quantiles in multidimensions that uses the geometry of multivariate data clouds has been considered, based on blending and generalization of the key ideas used in the construction of spatial median and regression quantiles, both of which have been extensively studied in the literature.
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A general bahadur representation of M-estimators and its application to linear regression with nonstochastic designs
Xuming He,Qi-Man Shao +1 more
TL;DR: This paper obtained strong Bahadur representations for a general class of M-estimators that satisfy the condition that the random variables are independent but not necessarily identically distributed random variables.
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The Oscillation Behavior of Empirical Processes
TL;DR: In this article, the authors studied the local behavior of empirical processes for independent identically distributed random variables on the real line and obtained best rates of convergence for various types of density estimators as well as error estimates for the Bahadur representation of the quantile process.
References
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An Introduction to Probability Theory and Its Applications
David A. Freedman,William Feller +1 more
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On convergence of stochastic processes
TL;DR: In this paper, it is shown that certain known invariance principles can under some hypotheses be improved by enlarging the class of functions for which (2) holds by considering spaces S other than the customary ones.
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An invariance principle for the law of the iterated logarithm.
Volker Strassen,Volker Strassen +1 more
TL;DR: In this paper, it was shown that with probability one the set of limit points of the sequence (ηn)n≧3 with respect to the uniform topology coincides with the sets of absolutely continuous functions x on "0, 1" such that x(0) = 0, 1, and ηn = 0 for any a ≧ 1.