Quantile regression with rank-based samples
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Date
2016
Authors
Ayilara, Olawale Fatai
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Abstract
Quantile Regression, as introduced by Koenker, R. and Bassett, G. (1978), provides
a complete picture of the relationship between the response variable and covariates
by estimating a family of conditional quantile functions. Also, it offers a natural
solution to challenges such as; homoscedasticity and sometimes unrealistic normality
assumption in the usual conditional mean regression. Most of the results for quantile
regression are based on simple random sampling (SRS). In this thesis, we study
the quantile regression with rank-based sampling methods. Rank-based sampling
methods have a wide range of applications in medical, ecological and environmental
research, and have been shown to perform better than SRS in estimating several
population parameters. We propose a new objective function which takes into
account the ranking information to estimate the unknown model parameters based
on the maxima or minima nomination sampling designs. We compare the mean
squared error of the proposed quantile regression estimates using maxima (or minima)
nomination sampling design and observe that it provides higher relative e ciency
when compared with its counterparts under SRS design for analyzing the upper
(or lower) tails of the distribution of the response variable. We also evaluate the
performance of our proposed methods when ranking is done with error.
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Keywords
Quantile Regression, Rank Based Sampling, Nomination Sampling