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You searched for +publisher:"Freie Universität Berlin" +contributor:("Prof. Dr. H. Skarabis"). One record found.

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Freie Universität Berlin

1. Hingst, Hans-Ulrich. Contributions to the random sample theory and remarks to a Bootstrap limit theorem.

Degree: 2003, Freie Universität Berlin

In the 1st chapter we look at a set ΩN , that consists of N objects with the same choice probability, respectively. We investigate a real feature X , which provides N values, within m pairwise distinct values; λN is the maximum of the absolute frequencies of the m values. We draw a random sample out of ΩN of size n without replacement. Theorem I.1 provides a bound B(n, N, λN / N ) ; this bound estimates the Euclidean distance between the joint probability functions of the sample variates at n-fold drawing with andm without replacement out of ΩN to the top. A pre-version of this estimation we've proposed at the International Congress of the Deutsche Statistische Gesellschaft in 2000 already. The estimation may be used for every scaling of X and for varying m = m (N) . The estimation is sharp, since for the class of those X that are mapping ΩN bijectively (m=N) , the equation sign is true - in this case the Euclidean distance of the joint probability functions (see above) is even the Euclidean distance of the choice probabilities of n objects between drawing with and without replacement out of ΩN. Corollaries from the estimation are formulations of two limit theorems: (i) Uniform convergence of the Euclidean distance of the joint probability functions (see above) against zero with increasing N , permitting varying m = m (N). (ii) Uniform convergence of the Euclidean distance between the probability functions of the m-dimensional Hypergeometric distribution and the m-variate Multinomialdistribution against zero with increasing N , permitting varying m = m (N). The convergence order of both limits is O(1/N) at least. In comparison with related results by Feller (1950 and later) and Johnson/Kotz/Balakrishnan (1997) we obtain better and more generalized statements. In the 2nd chapter we estimate the max. relative frequency (λN /N) under some conditions, that enable us to use the Kolmogorov / Smirnov - distance IDN , IDN := supt | IFN ( t ) - F ( t ) | with the empirical distribution function IFN and her almost sure limit function F . Applying the DKW-inequality or the Smirnov-LIL to the estimation of IDN , we get some different versions of the estimation of (λN /N). We show that, under some conditions, (λN /N) tends to the maximally jump of F. In the 3rd chapter we are concerned with a fundamental requirement of the Bootstrap limit theorem of Strobl (1995): The integral representation of a particular Frechet differential. The concept of a decomposition of the measure space \W allows us to give the conditions, under which this requirement is filled, for a norm in \W indexed by a special function space. The proved result includes a relevant result to this of Serfling (1981) as a special case. Advisors/Committee Members: n (gender), Prof. Dr. H. Skarabis (firstReferee), Prof. Dr. J. Gordesch (furtherReferee).

Subjects/Keywords: Degree of dependence of sample variates; uniform convergence of the Euclidean distance of the m-dimensional Hypergeometric distribution and the m-variate Multinomial distribution against zero when the number of pairwise distinct values m = m (N) may vary; maximum of the relative frequencies; maximum of the jumps of a distribution function; Bootstrap limit theorem; representation of a Fréchet differential of a statistical functional; decomposition of a particular space of probability measures.; 300 Sozialwissenschaften::300 Sozialwissenschaften, Soziologie::300 Sozialwissenschaften

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APA (6th Edition):

Hingst, H. (2003). Contributions to the random sample theory and remarks to a Bootstrap limit theorem. (Thesis). Freie Universität Berlin. Retrieved from http://dx.doi.org/10.17169/refubium-7956

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Hingst, Hans-Ulrich. “Contributions to the random sample theory and remarks to a Bootstrap limit theorem.” 2003. Thesis, Freie Universität Berlin. Accessed December 05, 2019. http://dx.doi.org/10.17169/refubium-7956.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Hingst, Hans-Ulrich. “Contributions to the random sample theory and remarks to a Bootstrap limit theorem.” 2003. Web. 05 Dec 2019.

Vancouver:

Hingst H. Contributions to the random sample theory and remarks to a Bootstrap limit theorem. [Internet] [Thesis]. Freie Universität Berlin; 2003. [cited 2019 Dec 05]. Available from: http://dx.doi.org/10.17169/refubium-7956.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Hingst H. Contributions to the random sample theory and remarks to a Bootstrap limit theorem. [Thesis]. Freie Universität Berlin; 2003. Available from: http://dx.doi.org/10.17169/refubium-7956

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

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