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ASYMPTOTIC NORMALITY OF NONPARAMETRIC M-ESTIMATORS WITH APPLICATIONS TO HYPOTHESIS TESTING FOR PANEL COUNT DATA.

Authors :
Xingqiu Zhao
Ying Zhang
Source :
Statistica Sinica; Apr2017, Vol. 27 Issue 2, p931-950, 20p
Publication Year :
2017

Abstract

In semiparametric and nonparametric statistical inference, the asymptotic normality of estimators has been widely established when they are √n-consistent. In many applications, nonparametric estimators are not able to achieve this rate. We have a result on the asymptotic normality of nonparametric M-estimators that can be used if the rate of convergence of an estimator is n<superscript>-1/2</superscript> or slower. We apply this to study the asymptotic distribution of sieve estimators of functionals of a mean function from a counting process, and develop nonparametric tests for the problem of treatment comparison with panel count data. The test statistics are constructed with spline likelihood estimators instead of nonparametric likelihood estimators. The new tests have a more general and simpler structure and are easy to implement. Simulation studies show that the proposed tests perform well even for small sample sizes. We find that a new test is always powerful for all the situations considered and is thus robust. For illustration, a data analysis example is provided. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
10170405
Volume :
27
Issue :
2
Database :
Complementary Index
Journal :
Statistica Sinica
Publication Type :
Academic Journal
Accession number :
130241237
Full Text :
https://doi.org/10.5705/ss.202014.0021