Tail behavior of the least-squares estimator
The tail behavior of the least-squares estimator in the linear regression model was studied in He et al. (Econometrica 58 (1990) 1195) under a fixed design for finite n. We now consider a random design matrix Xn and the case n-->[infinity] and study the probability with [gamma]n=F-1(1-1/n), a population analog of the maximal error. Unlike in the situation with fixed n and [gamma]-->[infinity], for n-->[infinity] we find fairly good tail behavior of LSE for normal F, for both fixed and random designs, even under heavy-tailed distribution for Xn.
Year of publication: |
2001
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Authors: | Jurecková, Jana ; Koenker, Roger ; Portnoy, Stephen |
Published in: |
Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 55.2001, 4, p. 377-384
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Publisher: |
Elsevier |
Keywords: | Domain of attraction Extreme values Least-squares estimator Tail behavior |
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