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.
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Volume (Year): 55 (2001)
Issue (Month): 4 (December)
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- He, Xuming, et al, 1990. "Tail Behavior of Regression Estimators and Their Breakdown Points," Econometrica, Econometric Society, vol. 58(5), pages 1195-1214, September.
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