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Based on an identifying Volterra type integral equation for randomly right censored observations from a lifetime distribution function F, we solve the corresponding estimating equation by an explicit and implicit Euler scheme. While the first approach results in some known estimators, the second one produces new semi-parametric and pre-smoothed Kaplan–Meier estimators which are real distribution functions rather than sub-distribution functions as the former ones are. This property of the new estimators is particular useful if one wants to estimate the expected lifetime restricted to the support of the observation time.
Specifically, we focus on estimation under the semi-parametric random censorship model (SRCM), that is, a random censorship model where the conditional expectation of the censoring indicator given the observation belongs to a parametric family. We show that some estimated linear functionals which are based on the new semi-parametric estimator are strong consistent, asymptotically normal, and efficient under SRCM. In a small simulation study, the performance of the new estimator is illustrated under moderate sample sizes. Finally, we apply the new estimator to a well-known real dataset.
Robots are widely used as a vehicle to spark interest in science and technology in learners. A number of initiatives focus on this issue, for instance, the Roberta Initiative, the FIRST Lego League, the World Robot Olympiad and RoboCup Junior. Robotic competitions are valuable not only for school learners but also for university students, as the RoboCup initiative shows. Besides technical skills, the students get some project exposure and experience what it means to finish their tasks on time. But qualifying students for future high-tech areas should not only be for students from developed countries. In this article, we present our experiences with research and education in robotics within the RoboCup initiative, in Germany and South Africa; we report on our experiences with trying to get the RoboCup initiative in South Africa going. RoboCup has a huge support base of academic institutions in Germany; this is not the case in South Africa. We present our ‘north–south’ collaboration initiatives in RoboCup between Germany and South Africa and discuss some of the reasons why we think it is harder to run RoboCup in South Africa.
This summer, RoboCup competitions were held for the 20th time in Leipzig, Germany. It was the second time that RoboCup took place in Germany, 10 years after the 2006 RoboCup in Bremen. In this article, we give an overview on the latest developments of RoboCup and what happened in the different leagues over the last decade. With its 20th edition, RoboCup clearly is a success story and a role model for robotics competitions. From our personal view point, we acknowledge this by giving a retrospection about what makes RoboCup such a success.