Limits of truncation experiments

• Autorzy: Marohn F.
• Języki publikacji: EN

Abstrakty

EN

Given n i.i.d. copies X1,…., X_n of a random variable X with distribution Pѵ, ѵ θ∈Θ⊂R_{k, we are only interested in those observations that fall into some set D = D(n) ⊂ R}^d having but a small probability of occurrence. The truncation set D is assumed to be known and non-random. Denoting the distribution of the truncated random variable X1_D(X) by P_nѵ we consider the triangular array of experiments (R^d, ß^d, (P_nѵθ ), n∈N, and investigate the asymptotic behavior of the n-fold products ((R^d)ⁿ, (ß^d)ⁿ, (P_nѵ)ⁿ_ѵ∈Θ ). Under a suitable density expansion,Gaussian shifts as well as Poisson experiments occur in the limit, where the latter case typically occurs when the number of expected observations falling in D is bounded. Finally, we investigate invariance properties of the occurring Poisson limits.

Słowa kluczowe

EN

statistical experiment; truncation model; Gaussian experiment; local asymptotic normality; Poisson experiment; Poisson process; translation invariance; scale invariance; independent increments

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2001
• Tom: Vol. 21, Fasc. 1
• Strony: 71--88
• Opis fizyczny: Bibliogr. 22 poz.

Twórcy

autor

Marohn F.

• Mathematisch-Geographische Fakultät, Katholische Universität Eichstatt, 85071, Eichstätt

Bibliografia

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