On a Test Statistic for Linear Trend |
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Authors: | JMP Albin D Jaru?ková |
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Institution: | (1) Department of Mathematics, Chalmers, University of Technology, SE-412 Göteborg, Sweden;(2) Department of Mathematics, Faculty of Civil Engineering, Czech Technical University, Thákurova 7, CZ-166 29 Praha 6, Czech Republic |
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Abstract: | Let {W(s)}
s
0 be a standard Wiener process. The supremum of the squared Euclidian norm Y (t) 2, of the R2-valued process Y(t)=( 1/t
W(t), {12/t
3 int0
t
s dW (s)– {3/t} W(t)), t , 1], is the asymptotic, large sample distribution, of a test statistic for a change point detection problem, of appearance of linear trend. We determine the asymptotic behavior P {sup
t
, 1] Y(t) 2 > u as u , of this statistic, for a fixed (0,1), and for a moving = (u) 0 at a suitable rate as u . The statistical interest of our results lie in their use as approximate test levels. |
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Keywords: | change point detection 2-process" target="_blank">gif" alt="chi" align="MIDDLE" BORDER="0">2-process extremes Gaussian process linear trend Ornstein– Uhlenbeck process test of linear trend |
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