Random Weighting Estimation of One-sided Confidence Intervals in Discrete Distributions

Random Weighting Estimation of One-sided Confidence Intervals in Discrete Distributions

Yalin Jiao (Northwestern Polytechnical University, China), Yongmin Zhong (RMIT University, Australia), Shesheng Gao (Northwestern Polytechnical University, China) and Bijan Shirinzadeh (Monash University, Australia)
Copyright: © 2011 |Pages: 9
DOI: 10.4018/ijimr.2011040102
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Abstract

This paper presents a new random weighting method for estimation of one-sided confidence intervals in discrete distributions. It establishes random weighting estimations for the Wald and Score intervals. Based on this, a theorem of coverage probability is rigorously proved by using the Edgeworth expansion for random weighting estimation of the Wald interval. Experimental results demonstrate that the proposed random weighting method can effectively estimate one-sided confidence intervals, and the estimation accuracy is much higher than that of the bootstrap method.
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Random Weighting Method

Assume that is a sample of independent and identically distributed random variables with common distribution function F. Let be the corresponding observed realizations of . Further, we shall denote and . Then, the random weighting process can be described as follows:

  • (i)

    Construct the sample (empirical) distribution function from , i.e.

    (1)

  • (ii)

    The random weighting estimation of is

    (2)

where is the characteristic function, and random vector obeys Dirichlet distribution D(1,,1), that is, and the joint density function of is , where and .

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