Statistical Modelling 19 (5) (2019), 501–523

Improved local quantile regression

Xi Liu
School of Management,
Hefei University of Technology,
Hefei, Anhui,
China.


and

Department of Mathematics,
Brunel University London,
London,
UK.


Keming Yu,
Department of Mathematics,
Brunel University London,
London,
UK.
e-mail: Keming.Yu@brunel.ac.uk

Qifa Xu,
School of Management,
Hefei University of Technology,
Hefei, Anhui,
China.


Xueqing Tang,
School of Science,
Jiangnan University,
Wuxi, Jiangsu,
China.


Abstract:

Bivariate ordered logistic models (BOLMs) are appealing to jointly model the marginal distribution of two ordered responses and their association, given a set of covariates. When the number of categories of the responses increases, the number of global odds ratios to be estimated also increases, and estimation gets problematic.
We investigate a new kernel-weighted likelihood smoothing quantile regression method. The likelihood is based on a normal scale-mixture representation of asymmetric Laplace distribution (ALD). This approach enjoys the same good design adaptation as the local quantile regression (Spokoiny et al., 2013, Journal of Statistical Planning and Inference, 143, 1109–1129), particularly for smoothing extreme quantile curves, and ensures non-crossing quantile curves for any given sample. The performance of the proposed method is evaluated via extensive Monte Carlo simulation studies and one real data analysis.

Keywords:

Bandwidth selection; asymmetric Laplace distribution; non-parametric quantile regression; propagation condition; quantile crossing.

Downloads:

Example data and code in zipped archive.
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