相关论文: On the $L_p$-error of the Grenander-type estimator…
We investigate the asymptotic behavior of the $L_p$-distance between a monotone function on a compact interval and a smooth estimator of this function. Our main result is a central limit theorem for the $L_p$-error of smooth isotonic…
We investigate nonparametric estimation of a monotone baseline hazard and a decreasing baseline density within the Cox model. Two estimators of a nondecreasing baseline hazard function are proposed. We derive the nonparametric maximum…
We consider the smoothed maximum likelihood estimator and the smoothed Grenander-type estimator for a monotone baseline hazard rate $\lambda_0$ in the Cox model. We analyze their asymptotic behavior and show that they are asymptotically…
We consider a likelihood ratio method for testing whether a monotone baseline hazard function in the Cox model has a particular value at a fixed point. The characterization of the estimators involved is provided both in the nondecreasing…
We consider two isotonic smooth estimators for a monotone baseline hazard in the Cox model, a maximum smooth likelihood estimator and a Grenander-type estimator based on the smoothed Breslow estimator for the cumulative baseline hazard. We…
We aim at estimating a function $\lambda:[0,1]\to \mathbb {R}$, subject to the constraint that it is decreasing (or increasing). We provide a unified approach for studying the $\mathbb {L}_p$-loss of an estimator defined as the slope of a…
We consider Grenander type estimators for a monotone function $\lambda:[0,1]\to\mathbb{R}$, obtained as the slope of a concave (convex) estimate of the primitive of $\lambda$. Our main result is a central limit theorem for the Hellinger…
Let $f$ be a nonincreasing function defined on $[0,1]$. Under standard regularity conditions, we derive the asymptotic distribution of the supremum norm of the difference between $f$ and its Grenander-type estimator on sub-intervals of…
We consider the Cox regression model and prove some properties of the maximum partial likelihood estimator $\hat\beta_n$ and of the the Breslow estimator $\Lambda_n$. The asymptotic properties of these estimators have been widely studied in…
Cox proportional hazards model with measurement error is investigated. In Kukush et al. (2011) [Journal of Statistical Research 45, 77-94] and Chimisov and Kukush (2014) [Modern Stochastics: Theory and Applications 1, 13-32] asymptotic…
The generalized linear model is widely used in all areas of applied statistics and while correct asymptotic inference can be achieved under misspecification of the distributional assumptions, a correctly specified mean structure is crucial…
A class of estimating functions is introduced for the regression parameter of the Cox proportional hazards model to allow unknown failure statuses on some study subjects. The consistency and asymptotic normality of the resulting estimators…
Cox proportional hazards model with measurement errors is considered. In Kukush and Chernova (2017), we elaborated a simultaneous estimator of the baseline hazard rate $\lambda(\cdot)$ and the regression parameter $\beta$, with the…
The Cox regression, a semi-parametric method of survival analysis, is extremely popular in biomedical applications. The proportional hazards assumption is a key requirement in the Cox model. To accommodate non-proportional hazards, we…
The problem of nonparametric inference on a monotone function has been extensively studied in many particular cases. Estimators considered have often been of so-called Grenander type, being representable as the left derivative of the…
This paper studies Cox's regression hazard model with an unobservable random frailty where no specific distribution is postulated for the frailty variable, and the marginal lifetime distribution allows both parametric and non-parametric…
The purpose of this article is to provide an adaptive estimator of the baseline function in the Cox model with high-dimensional covariates. We consider a two-step procedure : first, we estimate the regression parameter of the Cox model via…
We provide an asymptotic linear representation for the Breslow estimator of the baseline cumulative hazard function in the Cox model. Our representation consists of an average of independent random variables and a term involving the…
The aim of this article is to propose a novel kernel estimator of the baseline function in a general high-dimensional Cox model, for which we derive non-asymptotic rates of convergence. To construct our estimator, we first estimate the…
Let $\hat f_n$ be the nonparametric maximum likelihood estimator of a decreasing density. Grenander characterized this as the left-continuous slope of the least concave majorant of the empirical distribution function. For a sample from the…