Facultade de Fisioterapia

Quantile regression and its empirical likelihood with missing response at random

Shen, Yu; Liang, Han-Ying
Abstract:
In this paper, we study the linear quantile regression model when response data are missing at random. Based on the inverse probability weight method, we establish an estimation equation on quantile regression and define standard quantile regression estimator of unknown parameter. At the same time, we construct the empirical likelihood (EL) ratio function for the unknown parameter, and define the maximum EL estimator of the unknown parameter. Under suitable assumptions, we investigate the asymptotic normality of the proposed estimators and prove the EL ratio statistics has a standard chi-squared limiting distribution. A simulation study is done to investigate the finite sample performance of the estimators and compare the difference of the proposed EL method and bootstrap approach.
Year:
2018
Type of Publication:
Article
Keywords:
Asymptotic normality; Empirical likelihood; Maximum empirical likelihood estimation; Missing at random; Quantile regression; PARTIALLY LINEAR-MODELS; LONGITUDINAL DATA; INFERENCE; VARIABLES
Journal:
Statistical Papers
Volume:
59
Number:
2
Pages:
685-707
Month:
June
DOI:
10.1007/s00362-016-0784-5
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