Extreme residuals in regression model. Minimax approach
Volume 2, Issue 3 (2015): PRESTO-2015, pp. 297–308
Pub. online: 5 October 2015
Type: Research Article
Open Access
Open Access
Received
26 August 2015
26 August 2015
Revised
22 September 2015
22 September 2015
Accepted
22 September 2015
22 September 2015
Published
5 October 2015
5 October 2015
Abstract
We obtain limit theorems for extreme residuals in linear regression model in the case of minimax estimation of parameters.
References
Billingsley, P.: Convergence of Probability Measures. Wiley, New York (1968). MR0233396
Galambos, J.: The Asymptotic Theory of Extreme Order Statistics. Wiley, New York (1978). MR0489334
Gnedenko, B.: Sur la distribution limite du terme maximum d’une série aléatoire. Ann. Math. 44, 423–453 (1943). MR0008655
Ivanov, A.V., Matsak, I.K.: Limit theorems for extreme residuals in linear and nonlinear regression models. Theory Probab. Math. Stat. 86, 79–91 (2013). MR2986451. doi:10.1090/S0094-9000-2013-00890-4
Ivanov, O.V., Matsak, I.K.: Limit theorems for extreme residuals in regression models with heavy tails of observation errors. Theory Probab. Math. Stat. 88, 99–108 (2014). MR3112637. doi:10.1090/S0094-9000-2014-00921-7
Leadbetter, M.R., Lindgren, G., Rootzén, H.: Extremes and Related Properties of Random Sequences and Processes. Springer (1983). MR0691492
Murtagh, B.A.: Advanced Linear Programming: Computation and Practice. Mcgraw-Hill, New York (1981). MR0609151
