TY - JOUR
T1 - Smoothed nonparametric tests and approximations of p-values
AU - Maesono, Yoshihiko
AU - Moriyama, Taku
AU - Lu, Mengxin
N1 - Funding Information:
Acknowledgements The authors would like to thank the editor and two anonymous referees for their careful reading and valuable comments, which helped us to improve the manuscript significantly. The authors gratefully acknowledge JSPS KAKENHI Grant Nos. JP15K11995 and JP16H02790.
Publisher Copyright:
© 2017, The Institute of Statistical Mathematics, Tokyo.
PY - 2018/10/1
Y1 - 2018/10/1
N2 - We propose new smoothed sign and Wilcoxon’s signed rank tests that are based on kernel estimators of the underlying distribution function of the data. We discuss the approximations of the p-values and asymptotic properties of these tests. The new smoothed tests are equivalent to the ordinary sign and Wilcoxon’s tests in the sense of Pitman’s asymptotic relative efficiency, and the differences between the ordinary and new tests converge to zero in probability. Under the null hypothesis, the main terms of the asymptotic expectations and variances of the tests do not depend on the underlying distribution. Although the smoothed tests are not distribution-free, making use of the specific kernel enables us to obtain the Edgeworth expansions, being free of the underlying distribution.
AB - We propose new smoothed sign and Wilcoxon’s signed rank tests that are based on kernel estimators of the underlying distribution function of the data. We discuss the approximations of the p-values and asymptotic properties of these tests. The new smoothed tests are equivalent to the ordinary sign and Wilcoxon’s tests in the sense of Pitman’s asymptotic relative efficiency, and the differences between the ordinary and new tests converge to zero in probability. Under the null hypothesis, the main terms of the asymptotic expectations and variances of the tests do not depend on the underlying distribution. Although the smoothed tests are not distribution-free, making use of the specific kernel enables us to obtain the Edgeworth expansions, being free of the underlying distribution.
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U2 - 10.1007/s10463-017-0614-0
DO - 10.1007/s10463-017-0614-0
M3 - Article
AN - SCOPUS:85027985375
SN - 0020-3157
VL - 70
SP - 969
EP - 982
JO - Annals of the Institute of Statistical Mathematics
JF - Annals of the Institute of Statistical Mathematics
IS - 5
ER -