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

โœ Scribed by G. Mathew; W.P. McCormick

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
113 KB
Volume
70
Category
Article
ISSN
0378-3758

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โœฆ Synopsis

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.

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โœ Joรฃo Gomes; Orlando Oliveira ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 279 KB

Consider a stochastic process {X.}, n = 0, 1, 2 .... with initial value Xo and a sequence of independent, random variables, { Yi}, i ~ N with exponential distribution with parameter one, where X. + 1 = max(X., aX. + Y. + t), 0 < a < 1. In this paper, we show that this sequence behaves like the seque