scholarly journals Adaptive Estimation of the Spectrum of a Stationary Gaussian Sequence

Bernoulli ◽  
2001 ◽  
Vol 7 (2) ◽  
pp. 267 ◽  
Author(s):  
Fabienne Comte
Keyword(s):  
Adaptive Estimation ◽  
Gaussian Sequence ◽  
Stationary Gaussian Sequence

scholarly journals Asymptotic distribution of sum and maximum for Gaussian processes

1999 ◽  
Vol 36 (4) ◽  
pp. 1031-1044 ◽  
Author(s):  
Hwai-Chung Ho ◽  
William P. McCormick
Keyword(s):  
Asymptotic Distribution ◽  
Gaussian Processes ◽  
Continuous Time ◽  
Joint Distribution ◽  
Covariance Function ◽  
Random Variables ◽  
Regularity Conditions ◽  
Gaussian Sequence ◽  
Stationary Gaussian Sequence ◽  
Standard Normal

Let {Xn, n ≥ 0} be a stationary Gaussian sequence of standard normal random variables with covariance function r(n) = EX0Xn. Let Under some mild regularity conditions on r(n) and the condition that r(n)lnn = o(1) or (r(n)lnn)−1 = O(1), the asymptotic distribution of is obtained. Continuous-time results are also presented as well as a tube formula tail area approximation to the joint distribution of the sum and maximum.

Asymptotic behavior of the record values in a stationary Gaussian sequence, with applications

2019 ◽  
Vol 69 (3) ◽  
pp. 707-720
Author(s):  
Haroon M. Barakat ◽  
M. A. Abd Elgawad
Keyword(s):  
Asymptotic Behavior ◽  
Weak Convergence ◽  
Sufficient Conditions ◽  
Record Values ◽  
Distribution Functions ◽  
Gaussian Sequence ◽  
Stationary Gaussian Sequence ◽  
Lower Record ◽  
Lower Record Values ◽  
Set Up

Abstract In this paper, we study the limit distributions of upper and lower record values of a stationary Gaussian sequence under an equi-correlated set up. Moreover, the class of limit distribution functions (df’s) of the joint upper (and the lower) record values of a stationary Gaussian sequence is fully characterized. As an application of this result, the sufficient conditions for the weak convergence of the record quasi-range, record quasi-mid-range, record extremal quasi-quotient and record extremal quasi-product are obtained. Moreover, the classes of the non-degenerate limit df’s of these statistics are derived.

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