THE THEIL-SEN ESTIMATOR IN GENOMIC HIGH DIMENSIONAL MEARSUREMENT ERROR MODELS PERSPECTIVES

摘要

In a simple multivariate measurement error regression model, the classical least squares estimator does not consistently estimate the vector of the slope parameters. Under multi-normality, linear regression stands valid, although with some discount factor. The situation is entirely different when the multinormality assumption is dispensed with. In genomics studies, data models relate to excessively high dimensions where the multinormality assumption may rarely be tenable, and in addition, measurement errors in the regressor is universally anticipated. As such, robustness perspectives call for other estimators which may require less stringent distributional regularity assumptions. The Theil-Sen estimator in high-dimentional measurement error setups is studied here with due emphasis on genomics studies.