Browsing by Subject "nonparametric maximum likelihood"

Now showing 1 - 2 of 2
  • Thumbnail Image
    Item
    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.
  • Thumbnail Image
    Item
    Distribution‐free estimation of local growth rates around interval censored anchoring events
    (Wiley, 2019) Chu, Chenghao; Zhang, Ying; Tu, Wanzhu; Biostatistics, School of Public Health
    Biological processes are usually defined on timelines that are anchored by specific events. For example, cancer growth is typically measured by the change in tumor size from the time of oncogenesis. In the absence of such anchoring events, longitudinal assessments of the outcome lose their temporal reference. In this paper, we considered the estimation of local change rates in the outcomes when the anchoring events are interval‐censored. Viewing the subject‐specific anchoring event times as random variables from an unspecified distribution, we proposed a distribution‐free estimation method for the local growth rates around the unobserved anchoring events. We expressed the rate parameters as stochastic functionals of the anchoring time distribution and showed that under mild regularity conditions, consistent and asymptotically normal estimates of the rate parameters could be achieved, with a biom13015-gra-0001 convergence rate. We conducted a carefully designed simulation study to evaluate the finite sample performance of the method. To motivate and illustrate the use of the proposed method, we estimated the skeletal growth rates of male and female adolescents, before and after the unobserved pubertal growth spurt (PGS) times.