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

Ouafae Benrabah (), Elias Ould Saïd () and Abdelkader Tatachak ()

Statistical Papers, 2015, vol. 56, issue 3, 887-910

Abstract: Let $$\left\{ Y_{N}, N\ge 1\right\} $$ Y N , N ≥ 1 be a sequence of random variables of interest and $$\left\{ T_{N}, N\ge 1\right\} $$ T N , N ≥ 1 be a sequence of truncating variables. For a given $$n-$$ n - sample $$\left( n\le N\right) $$ n ≤ N of truncated replicates of $$Y$$ Y fulfilling the $$\alpha -$$ α - mixing condition, we establish asymptotic normality and construct confidence intervals for a proposed kernel mode estimator (say, $$\widehat{\theta }_n$$ θ ^ n ) of the true mode $$\theta $$ θ of $$Y$$ Y . Copyright Springer-Verlag Berlin Heidelberg 2015

Keywords: Asymptotic normality; Kernel mode estimator; Lynden-Bell estimator; Random left-truncation (RLT) model; Strong mixing condition; 60G42; 62F12; 62G20 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s00362-014-0613-7

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