Adaptive estimation of the conditional intensity of marker-dependent counting processes

Learning and adaptive estimation for marker-dependent counting processes

We consider the problem of statistical learning for the intensity of a counting process with covariates. In this context, we introduce an empirical risk, and prove risk bounds for the corresponding empirical risk minimizers. Then, we give an oracle inequality for the popular algorithm of aggregation with exponential weights. This provides a way of constructing estimators that are adaptive to the smoothness and to the structure of the intensity. We prove that these estimators are adaptive over anisotropic Besov balls. The probabilistic tools are maximal inequalities using the generic chaining m…

Likelihood for generally coarsened observations from multi-state or counting process models

We consider first the mixed discrete-continuous scheme of observation in multistate models; this is a classical pattern in epidemiology because very often clinical status is assessed at discrete visit times while times of death or other events are observed exactly. A heuristic likelihood can be written for such models, at least for Markov models; however, a formal proof is not easy and has not been given yet. We present a general class of possibly non-Markov multistate models which can be represented naturally as multivariate counting processes. We give a rigorous derivation of the likelihood …

Conditional density estimation in a censored single-index regression model

Under a single-index regression assumption, we introduce a new semiparametric procedure to estimate a conditional density of a censored response. The regression model can be seen as a generalization of Cox regression model and also as a profitable tool to perform dimension reduction under censoring. This technique extends the results of Delecroix et al. (2003). We derive consistency and asymptotic normality of our estimator of the index parameter by proving its asymptotic equivalence with the (uncomputable) maximum likelihood estimator, using martingales results for counting processes and argu…

条件 Aalen–Johansen 估计

Conditional Aalen--Johansen estimation

提出适用于任意有限状态跳过程、可纳入内外部协变量的条件 Aalen–Johansen 非参数估计量，并证明其强一致一致性与渐近正态性。

Two likelihood-based semiparametric estimation methods for panel count data with covariates

We consider estimation in a particular semiparametric regression model for the mean of a counting process with ``panel count'' data. The basic model assumption is that the conditional mean function of the counting process is of the form $E\{\mathbb{N}(t)|Z\}=\exp(β_0^TZ)Λ_0(t)$ where $Z$ is a vector of covariates and $Λ_0$ is the baseline mean function. The ``panel count'' observation scheme involves observation of the counting process $\mathbb{N}$ for an individual at a random number $K$ of random time points; both the number and the locations of these time points may differ across individual…

随机时变网络距离下的相关性界、混合性与m-依赖性及其在Cox过程中的应用

Correlation bounds, mixing and m-dependence under random time-varying network distances with an application to Cox-Processes

该研究针对动态网络下的多元随机过程，提出基于相关性、时变β-混合与条件独立性的三类弱依赖概念并证明相关结果，还将其用于动态交互网络拟合优度检验的渐近分析及共享单车数据建模。