Search: onr:"swepub:oai:gup.ub.gu.se/98075" > On a test statistic...
Fältnamn | Indikatorer | Metadata |
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000 | 02382naa a2200277 4500 | |
001 | oai:gup.ub.gu.se/98075 | |
003 | SwePub | |
008 | 240528s2004 | |||||||||||000 ||eng| | |
009 | oai:research.chalmers.se:bc3d14e7-4cf3-4fb4-b0d8-a23e85532ea6 | |
024 | 7 | a https://gup.ub.gu.se/publication/980752 URI |
024 | 7 | a https://research.chalmers.se/publication/980752 URI |
040 | a (SwePub)gud (SwePub)cth | |
041 | a eng | |
042 | 9 SwePub | |
072 | 7 | a ref2 swepub-contenttype |
072 | 7 | a art2 swepub-publicationtype |
100 | 1 | a Albin, Patrik,d 1960u Gothenburg University,Göteborgs universitet,Institutionen för matematisk statistik,Department of Mathematical Statistics,University of Gothenburg,Chalmers tekniska högskola,Chalmers University of Technology4 aut0 (Swepub:cth)palbin |
245 | 1 0 | a On a test statistic for linear trend |
264 | 1 | c 2004 |
520 | a Consider a change-point detection problem for the appearance of a linear trend in the independent variables $X_i$, where the null hypothesis $H_0$ is that $X_i=e_i$ are standardized discrete white noise, and the alternative is $$ X_i=\cases a_0+a_1(i/n)+e_i,&\text{for} i=1,2,\dots,k,\\ e_i,&\text{for} i=k+1,\dots,n, \endcases $$ for some $k$ and some real $a_0,a_1$. Under $H_0$, the test statistic $$ max_{[\alpha n]\leq k\leq n}\frac{(\sum_1^k X_i)^2}{k}+ \frac{(\sum_1^k((i/n)-(k+1)/2n)X_i)^2} {(\sum_1^k((i/n)-(k+1)/2n))^2} $$ tends in distribution to $\sup_{t\in[\alpha,1]}|Y(t)|^2$ as $n\to\infty$, where $Y(t)$ is a bivariate process defined in terms of a standard Wiener process $W(t)$, $$ Y(t)=\left(\frac {W(t)}{\sqrt{t}},\frac{\sqrt{3}tW(t)- \sqrt{12}\int_0^t W(s)\,ds}{\sqrt{t^3}} \right). $$ In this paper, the asymptotic behaviour of $$P(\sup_{t\in[\alpha,t]}|Y(t)|^2>u)$$ and of $$P(\sup_{t\in[\exp(-e^{u/2}/u),1]}|Y(t)|^2>u+2x)$$ are shown to be $-\ln\alpha$ and $1-\exp(-e^{-x})$, respectively, as $u\to\infty$. | |
650 | 7 | a NATURVETENSKAPx Matematikx Sannolikhetsteori och statistik0 (SwePub)101062 hsv//swe |
650 | 7 | a NATURAL SCIENCESx Mathematicsx Probability Theory and Statistics0 (SwePub)101062 hsv//eng |
710 | 2 | a Göteborgs universitetb Institutionen för matematisk statistik4 org |
773 | 0 | t Extremesg 6:3, s. 247-258q 6:3<247-258x 1386-1999x 1572-915X |
856 | 4 8 | u https://gup.ub.gu.se/publication/98075 |
856 | 4 8 | u https://research.chalmers.se/publication/98075 |
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