A bootstrap approximation to the joint distribution of sum and maximum of a stationary sequence

Abstract

This paper establishes the asymptotic validity for the moving block bootstrap as an approximation to the joint distribution of the sum and the maximum of a stationary sequence. An application is made to statistical inference for a positive time series where an extreme value statistic and sample mean provide the maximum likelihood estimates for the model parameters. A simulation study illustrates small sample size behavior of the bootstrap approximation.

Department(s)

Mathematics

Document Type

Article

DOI

https://doi.org/10.1016/s0378-3758(98)00002-0

Keywords

moving block bootstrap, stationary sequence, mixing coefficients

Publication Date

1998

Journal Title

Journal of statistical planning and inference

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