Quantile regression with mismeasured or missing covariates

This award is funded under the American Recovery and Reinvestment Act of 2009 Public Law 111-5).

Quantile regression (Koenker and Bassett, 1978) has emerged as an important statistical methodology, and has been used in a wide range of applications including economics, biology, ecology and finance. Very often a data set is not perfectly obtained. Some variables may be measured with error, while others may contain missing observations. Ignoring measurement errors or missing observations could lead to substantial bias in estimation. For this reason, how to handle measurement errors and missing data has generated a large number of literatures. Unfortunately, most of the existing methods rely on a parametric likelihood form, and hence cannot be applied to quantile regression directly. This proposal targets at developing methods and theories for obtaining unbiased quantile estimates even in the presence of measurement errors and/or missing observations. The specific proposed research activities under this project include the following four aspects. (1) Develop estimation methods for linear quantile models allowing the existence of measurement errors, and investigate the asymptotic properties for the resulting estimator. (2) Extend the estimation method for linear quantile model to semiparametric models, which brings more flexibility and hence facilities a wider range of applications. (3) Develop related inference and model adequacy assessment tools. (4) Extend the proposed methods in 1 - 3 to address missing data problems in conditional quantile models, including estimation, inference and model assessment. The statistical methods to be employed for this proposal cover quantile regression, methods and theories for measurement errors and missing data problems, nonparametric and semi-parametric modeling, goodness-of-fit tests, bootstrapping methods and robust statistics.

The proposed research will lead to more accurate inference and more comprehensive qualifications in various research applications in epidemiology, HIV research, genetics, cancer research and environmental science, as measurement errors and missing data commonly exist in those applications. The methodologies to be developed by the investigators are of general interest to statistical research. The proposed research will be widely disseminated through publications, presentations in domestic and international conferences, and collaborations with clinical and public health researchers.