Statistical Papers

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Necessary sample sizes for categorial data

  • Stefan Huschens
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Abstract

This paper deals with the problem how to determine the necessary sample size for the estimation of the parameter π=(π1,...,πk) (πj ≥ 0, Σjπj=1) based on the vector f=(f1,...,fk) of relative frequencies with sample size n. The vector n-f has a multinomial distribution. For a given precision c, 0≤c≤1, and a given confidence number β, 0≤β≤1, there exists a smallest positive integer N0=N0(β, c, k) with P{|fj−πj|≤c; j=1, ...,k}≥β for all sample sizes n≥N0 and for all π. As results are given in this paper exact upper bounds for N0 and an improved asymptotical upper bound for N0 which is derived from the asymptotical multinormal approximation for the distribution of f.

Key words

sample size categorial data multinomial distribution probability inequalities 
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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Stefan Huschens
    • 1
  1. 1.Heidelberg

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