TY - JOUR
T1 - Testing symmetry based on empirical likelihood
AU - Zhang, Jun
AU - Zhang, Jing
AU - Zhu, Xuehu
AU - Lu, Tao
N1 - Funding Information:
Jun Zhang’s research is supported by the National Natural Sciences Foundation of China (Grant No. 11401391). Xuehu Zhu’s research is supported by the National Natural Sciences Foundation of China (Grant No. 11601415) and China Postdoctoral Science Foundation (Grant No. 2016M590934).
Funding Information:
Jun Zhang's research is supported by the National Natural Sciences Foundation of China (Grant No. 11401391). Xuehu Zhu's research is supported by the National Natural Sciences Foundation of China (Grant No. 11601415) and China Postdoctoral Science Foundation (Grant No. 2016M590934). The authors thank the associate editor and two referees for their constructive suggestions that helped them to improve the early manuscript.
Publisher Copyright:
© 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group.
PY - 2018/10/3
Y1 - 2018/10/3
N2 - In this paper, we propose a general kth correlation coefficient between the density function and distribution function of a continuous variable as a measure of symmetry and asymmetry. We first propose a root-n moment-based estimator of the kth correlation coefficient and present its asymptotic results. Next, we consider statistical inference of the kth correlation coefficient by using the empirical likelihood (EL) method. The EL statistic is shown to be asymptotically a standard chi-squared distribution. Last, we propose a residual-based estimator of the kth correlation coefficient for a parametric regression model to test whether the density function of the true model error is symmetric or not. We present the asymptotic results of the residual-based kth correlation coefficient estimator and also construct its EL-based confidence intervals. Simulation studies are conducted to examine the performance of the proposed estimators, and we also use our proposed estimators to analyze the air quality dataset.
AB - In this paper, we propose a general kth correlation coefficient between the density function and distribution function of a continuous variable as a measure of symmetry and asymmetry. We first propose a root-n moment-based estimator of the kth correlation coefficient and present its asymptotic results. Next, we consider statistical inference of the kth correlation coefficient by using the empirical likelihood (EL) method. The EL statistic is shown to be asymptotically a standard chi-squared distribution. Last, we propose a residual-based estimator of the kth correlation coefficient for a parametric regression model to test whether the density function of the true model error is symmetric or not. We present the asymptotic results of the residual-based kth correlation coefficient estimator and also construct its EL-based confidence intervals. Simulation studies are conducted to examine the performance of the proposed estimators, and we also use our proposed estimators to analyze the air quality dataset.
KW - Correlation coefficient
KW - empirical likelihood
KW - kernel smoothing
KW - residuals
KW - symmetry
UR - http://www.scopus.com/inward/record.url?scp=85040976337&partnerID=8YFLogxK
U2 - 10.1080/02664763.2017.1421917
DO - 10.1080/02664763.2017.1421917
M3 - Article
AN - SCOPUS:85040976337
VL - 45
SP - 2429
EP - 2454
JO - Journal of Applied Statistics
JF - Journal of Applied Statistics
SN - 0266-4763
IS - 13
ER -