Detection of gross errors in observation results with the aid of the Chauvenet test

One gives the asymptotic distribution of the number N of gross observations, rejected by the Chauvenet method, for random variables with distribution function containing an unknown parameter, when as the estimator of the unknown parameter one makes use of the maximum likelihood estimator.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 153, pp. 153–159, 1986.In conclusion, I express my gratitude to I. A. Ibragimov for his interest in the problem and for his remarks.