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Title: A nonstationarity copula-based conditional quantile approach: Application to extreme daily stream-flow in Canada Authors:  Bruno Remillard - HEC Montreal (Canada)
Taoufik Bouezmarni - Universite de Sherbrooke (Canada)
Bouchra R Nasri - McGill University (Canada) [presenting]
Abstract: Hydrological frequency analysis is commonly used by engineers and hydrologists to provide the basic information on planning, design, and management of hydraulic and water resources systems under the assumption of stationarity. However, with increasing evidence of climate change, the assumption of stationarity, a prerequisite for traditional frequency analysis, might be invalid, making the conventional analysis pointless. Recently, some approaches were proposed in order to estimate extreme conditional quantiles in nonstationary frequency analysis settings, namely the so-called covariate method, where the covariates are incorporated into the parameters of the distribution function of the response variable, and the quantile regression method. However, these two methods cannot fully describe the dependence between the variable of interest and its covariates. In order to overcome this limitation, in addition to dealing with nonstationarity, we propose a new estimator for conditional quantile based on copula functions. We study its asymptotic behavior and we suggest a bootstrap procedure in order to construct uniform confidence bands around the conditional quantile function; as a by-product, we also obtain a formal goodness-of-fit test. Finally, we present a simulation study demonstrating the finite sample performance of the proposed estimator and we illustrate its usefulness with an application to a hydro-climatic dataset.