Density estimation under random censorship and order restrictions: From asymptotic to small samples

• 成果类型: Article
• 署名作者: Efromovich, S
• 署名单位: University of New Mexico
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/016214501753168334
• 发表日期: 2001
• 页码: 667-684
• 关键词: nonparametric-estimation; CONVERGENCE

摘要

Do a random censorship and/or order restrictions (e.g., nonnegativity, monotonicity, convexity) affect estimation of a smooth density under mean integrated squared error (MISE)? Under mild assumptions, the known asymptotic results, which are concerned only with rates, answer no. This answer, especially for censored data, contradicts practical experience and statistical intuition. So what can be said about constants of MISE convergence? It is shown that asymptotically (a) censorship does affect the constant, and this allows one to find a relationship between sample sizes of directly observed and censored datasets that implies the same precision of estimation, and (b) an order restriction does not affect the constant, and thus no isotonic estimation is needed. Intensive Monte Carlo simulations show that the lessons of the sharp asymptotics are valuable for small sample sizes. Also, the estimator developed is illustrated both on simulated data and a dataset of lifetimes of conveyer blades used at wastewater treatment plants.