Restoration of Monotonicity Respecting in Dynamic Regression

ABSTRACT

Dynamic regression models, including the quantile regression model and Aalen’s additive hazards model, are widely adopted to investigate evolving covariate effects. Yet lack of monotonicity respecting with standard estimation procedures remains an outstanding issue. Advances have recently been made, but none provides a complete resolution. In this article, we propose a novel adaptive interpolation method to restore monotonicity respecting, by successively identifying and then interpolating nearest monotonicity-respecting points of an original estimator. Under mild regularity conditions, the resulting regression coefficient estimator is shown to be asymptotically equivalent to the original. Our numerical studies have demonstrated that the proposed estimator is much more smooth and may have better finite-sample efficiency than the original as well as, when available as only in special cases, other competing monotonicity-respecting estimators. Illustration with a clinical study is provided.

KEYWORDS:

• Adaptive interpolation
• Additive complementary log–log survival model
• Additive hazards model
• Censored quantile regression
• Monotone function
• Quantile regression

Acknowledgment

The author thanks the reviewers for helpful comments and suggestions that have led to an improvement in the presentation.

Funding

This research was partially supported by the National Science Foundation grant DMS-1208874 and the National Institutes of Health grants HL113451 and AI050409.