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Browsing by Subject "Empirical process"
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Item A spline-based nonparametric analysis for interval-censored bivariate survival data(Institute of Statistical Science, 2022) Wu, Yuan; Zhang, Ying; Zhou, Junyi; Biostatistics, School of Public HealthIn this manuscript we propose a spline-based sieve nonparametric maximum likelihood estimation method for joint distribution function with bivariate interval-censored data. We study the asymptotic behavior of the proposed estimator by proving the consistency and deriving the rate of convergence. Based on the sieve estimate of the joint distribution, we also develop an efficient nonparametric test for making inference about the dependence between two interval-censored event times and establish its asymptotic normality. We conduct simulation studies to examine the finite sample performance of the proposed methodology. Finally we apply the method to assess the association between two subtypes of mild cognitive impairment (MCI): amnestic MCI and non-amnestic MCI, for Huntington disease (HD) using data from a 12-year observational cohort study on premanifest HD individuals, PREDICT-HD.Item Modeling longitudinal data with interval censored anchoring events(2018-03-01) Chu, Chenghao; Zhang, Ying; Tu, WanzhuIn many longitudinal studies, the time scales upon which we assess the primary outcomes are anchored by pre-specified events. However, these anchoring events are often not observable and they are randomly distributed with unknown distribution. Without direct observations of the anchoring events, the time scale used for analysis are not available, and analysts will not be able to use the traditional longitudinal models to describe the temporal changes as desired. Existing methods often make either ad hoc or strong assumptions on the anchoring events, which are unveri able and prone to biased estimation and invalid inference. Although not able to directly observe, researchers can often ascertain an interval that includes the unobserved anchoring events, i.e., the anchoring events are interval censored. In this research, we proposed a two-stage method to fit commonly used longitudinal models with interval censored anchoring events. In the first stage, we obtain an estimate of the anchoring events distribution by nonparametric method using the interval censored data; in the second stage, we obtain the parameter estimates as stochastic functionals of the estimated distribution. The construction of the stochastic functional depends on model settings. In this research, we considered two types of models. The first model was a distribution-free model, in which no parametric assumption was made on the distribution of the error term. The second model was likelihood based, which extended the classic mixed-effects models to the situation that the origin of the time scale for analysis was interval censored. For the purpose of large-sample statistical inference in both models, we studied the asymptotic properties of the proposed functional estimator using empirical process theory. Theoretically, our method provided a general approach to study semiparametric maximum pseudo-likelihood estimators in similar data situations. Finite sample performance of the proposed method were examined through simulation study. Algorithmically eff- cient algorithms for computing the parameter estimates were provided. We applied the proposed method to a real data analysis and obtained new findings that were incapable using traditional mixed-effects models.Item Statistical Inference on Panel Data Models: A Kernel Ridge Regression Method(Taylor & Francis, 2021) Zhao, Shunan; Liu, Ruiqi; Shang, Zuofeng; Mathematical Sciences, School of ScienceWe propose statistical inferential procedures for nonparametric panel data models with interactive fixed effects in a kernel ridge regression framework. Compared with the traditional sieve methods, our method is automatic in the sense that it does not require the choice of basis functions and truncation parameters. The model complexity is controlled by a continuous regularization parameter which can be automatically selected by the generalized cross-validation. Based on the empirical process theory and functional analysis tools, we derive the joint asymptotic distributions for the estimators in the heterogeneous setting. These joint asymptotic results are then used to construct the confidence intervals for the regression means and the prediction intervals for future observations, both being the first provably valid intervals in literature. The marginal asymptotic normality of the functional estimators in a homogeneous setting is also obtained. Our estimators can also be readily modified and applied to other widely used semiparametric models, such as partially linear models. Simulation and real data analyses demonstrate the advantages of our method.