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Abstract.In this article, we introduce a non parametric regression estimator based on a relative error criterion, for left truncated and right censored data with functional predictors. Left truncation and right censoring are common forms of incomplete data in survival analysis, where the event time of interest is only observed within a certain interval which adds some challenges to the regression task. We establish the asymptotic normality of our estimator and develop a procedure for constructing confidence intervals for the predicted responses. The theoretical results obtained are supported using simulation studies and a real data example from the energy field. [ABSTRACT FROM AUTHOR]

This paper investigates theoretical and numerical asymptotic properties of a nonparametric M-estimator's regression function when the data are left truncated and associated. Using specific tools to this weak dependence, we study the strong uniform consistency of the proposed estimator and give its rate of convergence. A large Monte Carlo simulation study is carried out to comfort the good behavior of the M-estimator for different sample sizes and different truncation rates: First we show that the proposed estimator performs better than the Nadaraya-Watson estimator by looking at their respective closeness to the true univariate and bivariate regression function. Thereafter and to highlight the robustness of our estimator, we consider a regression model with a heavy-tailed error distribution and we compare the global mean square error of the two estimators. Finally, we study the behavior of the two estimators in the presence of outliers using the influence function to show the superiority of the M-estimator. [ABSTRACT FROM AUTHOR]

Let { X i , i ≥ 1 } be a sequence of independent and identically distributed random variables with distribution function F and probability density function f. We propose new type of kernel estimators for density and hazard functions that perform well at the boundary, when the variable of interest is positive and right censored. The estimators are constructed using asymmetric kernels with expectation 1. We establish uniform strong consistency rates and we study asymptotic properties and normality of the resulting estimators. A large simulation study is conducted to comfort the theoretical results. An application to real data is done. [ABSTRACT FROM AUTHOR]

This paper focuses on nonparametric regression modeling of time-series and incomplete observations. In this sense, the observations are subject to both left truncation and right censoring (LTRC) and satisfy an association dependency. Using the well-known kernel estimation method, we establish the strong uniform consistency with a rate of the kernel estimator proposed in this paper. Simulation studies are conducted to assess the impact of both incompleteness and association dependency on the estimation. [ABSTRACT FROM AUTHOR]

In this paper, we propose a non parametric M-estimator of the regression function and we investigate its asymptotic properties, when the response variable is subject to both random left truncation and right censoring. In most works, non parametric M-estimation requires the use of an objective function ψ supposed to be bounded. Here the results hold with unbounded objective function. The strong uniform consistency rate is established under α-mixing dependence. A large simulation study with one and bi-dimensional regressor is conducted for fixed and local bandwidths to highlight the good behavior of our estimator. [ABSTRACT FROM AUTHOR]

In this article, we study the asymptotic properties of the kernel estimator of the mode and density function when the data are twice censored. More specifically, we first establish a strong uniform consistency over a compact set with a rate of the kernel density estimator and then we give the consistency with rate and asymptotic normality for the kernel mode estimator. An application to confidence bands is given. [ABSTRACT FROM PUBLISHER]