Document Zbl 0634.62039

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An estimator of the moment generating function of a random variable from the results of observations. (English. Russian original) Zbl 0634.62039

Theory Probab. Math. Stat. 32, 141-151 (1986); translation from Teor. Veroyatn. Mat. Stat. 32, 121-131 (1985).

Summary: An estimator of the function \(f(t)=E \exp (t\xi)\) from a sample of the r.v. \(\xi\) is described. The law of large numbers and the central limit theorem are proved for this estimator in certain function spaces. A confidence band for f(t) is constructed.

Cited in 2 Reviews

MSC:

62G05	Nonparametric estimation
62G15	Nonparametric tolerance and confidence regions
60F05	Central limit and other weak theorems
62E20	Asymptotic distribution theory in statistics

Keywords:

law of large numbers; central limit theorem; confidence band

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