Distribution Function Estimate With Multiple Censored Data And Its Strong Consistency

In many research areas, such as industry, agriculture, medicine, economics, actuarial science and biological sciences, the data we have carried out statistical inference and hypothesis testing to analyze often can not be accurately observed. These observational data or a known specific observation falls within the range, or known or more than a single observation point in time, we call such a data type censored data. In recent years, censored data research statistician who has been gradually importance, in these studies, the distribution estimation occupies a very important part of statisticians and made a rich and effective methods of estimation.We can treat the distribution function estimation as survival function estimation, The methods for survival function such as:Life table method[34], Kaplan-Meier method[9], and Bayes method proposed by Susarla-Van Ryzin(1978), Turnbull(1974)[18] method for the doubly censored data proposed by Turnbull. Woodroofe[22] develop method for dis-tribution function estimation with random truncation and Groeneboom and Wellner[4] with interval censored data. But these methods are all for simple data type, in this arti-cle we will discuss a more complex data type and we should improve the above methods. In the article we give the distribution function estimate and proof its nature of strong consistency.In this paper, Chapter 1 gives a brief introduction of distribution of censoring data and researches that have been done before. Chapter 2 give the notation and do some preparation for estimation. Chapter 3 based on the approach of Gomez and Calle, we propose a two-step method for the estimation of the distribution function F(t) and give the proof of its strong consistency. Chapter 4 a simulation study is conducted to investigate the performance of the proposed estimator. Chapter 5 remark and conclusion.