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Title: Estimation of sparse functional quantile regression with measurement error: A SIMEX approach Authors:  Carmen Tekwe - Indiana University - Bloomington (United States) [presenting]
Abstract: Quantile regression is a semiparametric method used to model associations between variables. It is most helpful when the covariates have a complex relationship with the location, scale, and shape of the outcome distribution. Despite its robustness to distributional assumptions and outliers in the outcome, regression quantiles may be biased in the presence of measurement error in the covariates. The impact of function-valued covariates contaminated with heteroscedastic error has not yet been examined; although, studies have investigated the case of scalar-valued covariates. Here, we present a two-stage strategy to consistently fit linear quantile regression models with a function-valued covariate that may be measured with error. In the first stage, an instrumental variable is used to estimate the covariance matrix associated with the measurement error. In the second stage, simulation extrapolation (SIMEX) is used to correct the measurement error in the function-valued covariate. Point-wise standard errors are estimated by means of nonparametric bootstrap. We present simulation studies to assess the robustness of the measurement-error-corrected for functional quantile regression. Our methods are applied to National Health and Examination Survey data to assess the relationship between physical activity and body mass index among adults in the United States.