A Note on Weighted Approximations to the Uniform Empirical and Quantile Processes

作者: David M. Mason

DOI: 10.1007/978-1-4684-6793-2_8

关键词: Asymptotic distributionElementary proofQuantileBrownian bridgeSequenceEmbeddingMathematicsApplied mathematicsWiener processEmpirical processMathematical economics

摘要: Recently, M. Csorgő, S. Horvath and Mason (1986a) obtained a weighted approximation to the uniform empirical quantile processes by sequence of Brownian bridges. The purpose this note is give short elementary proof their process. Their corresponding process follows in direct fashion from that imiform present proof, as was former, based on Komlos, Major Tusnady (1976) strong partial sum It shown, however, almost same can be derived older Skorokhod (1965) embedding. This alternate approximation, via embedding, likely sufficient for nearly all applications methodology has advantage its more suitable instructional purposes.

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