Theoretical Statistics and Mathematics Unit, ISI Delhi

Bootstrap for functions of associated random variables with applications

by Mansi Garg and Isha Dewan

Let $\{ X_n, n \ge 1 \}$ be a sequence of stationary associated random variables. In this paper, we obtain consistent estimators of the distribution function and the variance of the sample mean based on $\{ g(X_n), n \ge 1 \}$, $g: \mathbb{R} \to \mathbb{R}$ using Circular Block Bootstrap (CBB). We extend these results to derive consistent estimators of the distribution function and the variance of U-statistics. As applications, we obtain interval estimators for L-moments. We also discuss consistent point estimators for L-moments. Finally, as an illustration, we obtain point estimators and confidence intervals for L-moments of a stationary autoregressive process with a minification structure which is fitted to a hydrological dataset.

isid/ms/2016/09 [fulltext]

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