Remarks on compound Poisson approximation of Gaussian random sequences

Enkelejd Hashorva and Jürg Hüsler

Statistics & Probability Letters, 2002, vol. 57, issue 1, 1-8

Abstract: Let {Xi, i[greater-or-equal, slanted]1} be a sequence of m-dependent stationary standard Gaussian random variables and some positive constants. In this note we generalise results of Raab (Extremes 1(3) (1999) 29.), who considered compound Poisson approximation for Wn=[summation operator]i=1n1{Xi>un} the number of exceedances above the level un. More precisely, the main result concerns an upper asymptotic bound for the total variational distance dTV(Wn,CP([lambda]*)) where with 2[less-than-or-equals, slant]r[less-than-or-equals, slant]2m and are independent Poisson random variables.

Keywords: Rate; of; convergence; Compound; Poisson; approximation; Stein-Chen; method; Extreme; values; Stationary; Gaussian; sequences; Quadratic; programming (search for similar items in EconPapers)
Date: 2002
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Citations: View citations in EconPapers (1)

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