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Abstract:
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Quantile regression has been widely used as an important statistical methodology in a wide range of applications including economics, biology, ecology, and finance. However, it is well known that the quantile regression can be substantially biased when the covariates are measured with error. In this paper, we propose a new flexible method that produces nonparametric quantile estimation in the presence of multiple proxies of true covariate. Multiple proxy variables become more and more available for an unobserved explanatory variable in regression as the various sources of information become available. Under the classical multiple measurement error assumption of additive error and linear relationship, we combine the multiple proxy variables to enable the inference about quantile relationship between response variable and unobserved regressor. An application study shows that our methodology reveal the unobserved regressor and catch the quantile relationship well for various nonlinear data.
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