A kernel mode estimate under random left truncation and time series model: asymptotic normality

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• 作者：Ouafae Benrabah ; Elias Ould Sa?d ; Abdelkader Tatachak
• 关键词：Asymptotic normality ; Kernel mode estimator ; Lynden ; Bell estimator ; Random left ; truncation (RLT) model ; Strong mixing condition ; 60G42 ; 62F12 ; 62G20
• 刊名：Statistical Papers
• 出版年：2015
• 出版时间：August 2015
• 年：2015
• 卷：56
• 期：3
• 页码：887-910
• 全文大小：548 KB
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• 作者单位：Ouafae Benrabah (1) (2)
  Elias Ould Sa?d (1) (2)
  Abdelkader Tatachak (3)
  
  1. Univ. Lille Nord de France, Lille, ?59000, France
  2. ULCO, LMPA, Calais, 80699, France
  3. Lab. MSTD, Department of Probability and Statistics, USTHB, BP 32, ?16111, ?El-Alia, Algeria
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Statistics
  Statistics for Business, Economics, Mathematical Finance and Insurance
  Probability Theory and Stochastic Processes
  Economic Theory
  Operation Research and Decision Theory
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1613-9798

文摘

Let \(\left\{ Y_{N}, N\ge 1\right\} \) be a sequence of random variables of interest and \(\left\{ T_{N}, N\ge 1\right\} \) be a sequence of truncating variables. For a given \(n-\)sample \(\left( n\le N\right) \) of truncated replicates of \(Y\) fulfilling the \(\alpha -\)mixing condition, we establish asymptotic normality and construct confidence intervals for a proposed kernel mode estimator (say, \(\widehat{\theta }_n\)) of the true mode \(\theta \) of \(Y\).