Statistics and Its Interface

Volume 10 (2017)

Number 2

Identifying interaction effects via additive quantile regression models

Pages: 255 – 265



Qianqian Zhu (Center for Applied Statistics, School of Statistics, Renmin University of China, Beijing, China; and Department of Statistics and Actuarial Science, University of Hong Kong)

Yanan Hu (School of Statistics, Renmin University of China, Beijing, China)

Maozai Tian (School of Statistics, Renmin University, Beijing, China; School of Statistics, Lanzhou Univ. of Finance & Economics, Lanzhou, Gansu, China; and School of Statistics & Information, Xinjiang Univ. of Finance & Economics, Urumchi, Xinjiang, China)


As additive quantile regression (AQR) models possess the properties of robustness and flexibility, they become increasingly popular in many applications. However, such models may fail when predictors reflect interaction effects in the response. In fact, we often encounter such a problem that the main effects are not significant but the pairwise interactions are in regression. The existence of such a situation is neither accidental nor ignorable. Overlooking the interaction effects may render many of the traditional statistical techniques used for studying data relationships invalid. In these situations, it is necessary to consider more reasonable models such as AQR model with pairwise interactions. This paper mainly studies estimation and testing for the AQR model with pairwise interactions. To estimate the unknown functions in the model, local linear fitting and ordinary backfitting methods are applied. The generalized likelihood ratio (GLR) type test statistic is constructed to test the overall significance of pairwise interactions, and bootstrap method is utilized to approximate the asymptotic distribution of the test statistic. Theoretical properties of estimators and GLR type test statistic are derived. Bandwidth selection based on plug-in method for pairwise interactions is discussed as well. Finally, simulation study and a simple empirical analysis are presented to illustrate the performance of the proposed model.


additive quantile models, backfitting algorithm, bandwidth selection, generalized likelihood ratio type testing, pairwise interaction

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Published 31 October 2016