Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: U-quantiles are applied in robust statistics, like the Hodges-Lehmann estimator of location for example. They have been analysed in the case of independent random variables with the help of a generalized Bahadur representation. Our main aim is to extend these results to U-quantiles of strongly mixing random variables and functionals of absolutely regular sequences.  obtain the central limit theorem and the law of the iterated logarithm for U-quantiles as straightforward corollaries. Furthermore,  improve the existing result for sample quantiles of mixing data.
['Martin Wendler']
I am writing a research paper on a idea Bahadur representation for U-quantiles of dependent data
[{"from": "human", "value": "I am writing a research paper on a idea Bahadur representation for U-quantiles of dependent data"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: U-quantiles are applied in robust statistics, like the Hodges-Lehmann estimator of location for example. They have been analysed in the case of independent random variables with the help of a generalized Bahadur representation. Our main aim is to extend these results to U-quantiles of strongly mixing random variables and functionals of absolutely regular sequences.  obtain the central limit theorem and the law of the iterated logarithm for U-quantiles as straightforward corollaries. Furthermore,  improve the existing result for sample quantiles of mixing data."}]