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Edgeworth Expansion and Bootstrap Approximation for Studentized Product-Limit Estimator with Truncated and Censored Data |
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| Authors: | Qihua Wang Bing-Yi Jing |
| Affiliation: | 1. Academy of Mathematics and Systems Science, Chinese Academy of Science , Beijing , China;2. Department of Statistics and Actual Science , The University of Hong Kong , Pokfulam , Hong Kong qhwang@amss.ac.cn;4. Department of Mathematics , Hong Kong University of Science and Technology , Kowloon , Hong Kong |
| Abstract: | The Yule-Walker estimators of the AR coefficients of a causal multidimensional AR model are obtained by replacing the autocovariances with their estimators in the Yule-Walker equations. It is shown that only unbiased-type estimators of the autocovariances yield consistency of the Yule-Walker estimators. Also, the asymptotic joint distribution of the Yule-Walker estimators is presented. |
| Keywords: | Bootstrap approximation Edgeworth expansion Left truncation Product-limit estimator Random censorship |