Regression analysis using order statistics |
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| Authors: | Ayyub Sheikhi Ahad Jamalizadeh |
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| Institution: | (1) Department of Mathematics, Zhejiang University, Hangzhou, 310028, P. R. China;(2) Department of Statistics, Zhejiang Gongshang University, Hangzhou, 310035, P. R. China |
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| Abstract: | In this article, we study the joint distribution of X and two linear combinations of order statistics, a
T
Y
(2) and b
T
Y
(2), where a = (a
1, a
2)
T
and b = (b
1, b
2)
T
are arbitrary vectors in R
2 and Y
(2) = (Y
(1), Y
(2))
T
is a vector of ordered statistics obtained from (Y
1, Y
2)
T
when (X, Y
1, Y
2)
T
follows a trivariate normal distribution with a positive definite covariance matrix. We show that this distribution belongs
to the skew-normal family and hence our work is a generalization of Olkin and Viana (J Am Stat Assoc 90:1373–1379, 1995) and
Loperfido (Test 17:370–380, 2008). |
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| Keywords: | |
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