Browsing by Author "Zhao, Xingqiu"

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    Asymptotic normality of nonparametric M-estimators with applications to hypothesis testing for panel count data
    (2017) Zhao, Xingqiu; Zhang, Ying; Biostatistics, School of Public Health
    In semiparametric and nonparametric statistical inference, the asymptotic normality of estimators has been widely established when they are \sqrt{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^{-\dfrac{1}{2}} 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.
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    A nonparametric regression model for panel count data analysis
    (2019) Zhao, Huadong; Zhang, Ying; Zhao, Xingqiu; Yu, Zhangsheng; Biostatistics, School of Public Health
    Panel count data are commonly encountered in analysis of recurrent events where the exact event times are unobserved. To accommodate the potential non-linear covariate effect, we consider a non-parametric regression model for panel count data. The regression B-splines method is used to estimate the regression function and the baseline mean function. The B-splines-based estimation is shown to be consistent and the rate of convergence is obtained. Moreover, the asymptotic normality for a class of smooth functionals of regression splines estimators is established. Numerical studies were carried out to evaluate the finite sample properties. Finally, we applied the proposed method to analyze the non-linear effect of one of interleukin functions with the risk of childhood wheezing.