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Limits of truncation experiments

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Języki publikacji
EN
Abstrakty
EN
Given n i.i.d. copies X1,…., Xn of a random variable X with distribution Pѵ, ѵ θ∈Θ⊂Rk, we are only interested in those observations that fall into some set D = D(n) ⊂ Rd 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 X1D(X) by P we consider the triangular array of experiments (Rd, ßd, (Pnѵθ ), n∈N, and investigate the asymptotic behavior of the n-fold products ((Rd)n, (ßd)n, (P)nѵ∈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.
Rocznik
Strony
71--88
Opis fizyczny
Bibliogr. 22 poz.
Twórcy
autor
  • Mathematisch-Geographische Fakultät, Katholische Universität Eichstatt, 85071, Eichstätt
Bibliografia
  • [1] P. K. Andersen, Ø. Borgan, R. D. Gill and N. Keiding, Statistical Models Based on Counting Processes, Springer Ser. Statist., New York 1993.
  • [2] M. Falk, On testing the extreme value index via the POT-method, Ann. Statist. 23 (1995), pp. 2013-2035,
  • [3] M. Falk, Local asymptotic normality of truncated empirical processes, Ann. Statist. 26 (1998), pp. 692-718.
  • [4] M. Falk, J. Hüsler and R.-D. Reiss, Laws of Small Numbers: Extremes and Rare Events, DMV Seminar, Birkhäuser, Basel 1994.
  • [5] M. Falk and F. Liese, LAN of thinned empirical processes with an application to fuzzy set density estimation, Extremes 1 (1998), pp. 323-349.
  • [6] M. Falk and F. Marohn, On asymptotically optimal tests for conditional distributions, Ann. Statist 21 (1993), pp. 45-60.
  • [7] M. Falk and R.-D. Reiss, Statistical inference for conditional curves: Poisson process approach, Ann. Statist. 20 (1992), pp. 779-796.
  • [8] A. Janssen, Limits of translation invariant experiments, J. Multivariate Anal. 20 (1986), pp. 129-142.
  • [9] A. Janssen and F. Märohn, On statistical information of extreme order statistics, local extreme value alternatives, and Poisson point processes, J. Multivariate Anal, 48 (1994), pp. 1-30.
  • [10] A. Janssen, H. Milbrodt and H. Strasser, Infinitely Divisible Statistical Experiments, Lecture Notes in Statist 27, Springer, Berlin-Heidelberg 1985.
  • [11] L. Le Cam, Sur les contraintes imposées par les passages á la limite usuels en statistique, Bull. Inst, Internat. Statist., Proc. 39th Session, Vienna, Vol. XLV, Book 4 (1973), pp. 169-177.
  • [12] L. Le Cam, Asymptotic Methods in Statistical Decision Theory, Springer Ser. Statist, New York 1986.
  • [13] L. Le Cam and G. L. Yang, Asymptotics in Statistics. Some Basic Concepts, Springer Ser. Statist, New York 1990.
  • [14] F. Marohn, Local asymptotic normality of truncation models, Statist Decisions 17 (1999), pp. 237-253.
  • [15] H. Milbrodt and H. Strasser, Limits of triangular arrays of experiments, in: A. Janssen, H. Milbrodt and H. Strasser, Infinitely Divisible Statistical Experiments, Lecture Notes in Statist. 27, Springer, Berlin-Heidelberg 1985, pp. 14-54.
  • [16] R.-D. Reiss, Approximate Distributions of Order Statistics. With Applications to Nonparametric Statistics, Springer Ser. Statist., New York 1989.
  • [17] R.-D. Reiss, A Course on Point Processes, Springer Ser. Statist, New York 1993.
  • [18] S. I. Resnick, Extreme Values, Regular Variation, and Point Processes, Springer, New York 1987.
  • [19] H. Strasser, Scale invariance of statistical experiments, Probab. Math. Statist. 5 (1985), pp. 1-20.
  • [20] H. Strasser, Statistical experiments with independent increments, in: A. Janssen, H. Milbrodt and H. Strasser, Infinitely Divisible Statistical Experiments, Lecture Notes in Statist. 27, Springer, Berlin-Heidelberg 1985, pp. 124-153.
  • [21] H. Strasser, Mathematical Theory of Statistics, De Gruyter, Berlin-New York 1985.
  • [22] E. Torgersen, Comparison of Statistical Experiments, Cambridge University Press, Cambridge 1991.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-536b1a40-e216-4a3e-bb2b-e5d009ece161
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