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 ijimr.2011040102.m01 is a sample of independent and identically distributed random variables with common distribution function F. Let ijimr.2011040102.m02 be the corresponding observed realizations of ijimr.2011040102.m03. Further, we shall denote ijimr.2011040102.m04 and ijimr.2011040102.m05. Then, the random weighting process can be described as follows:

  • (i)

    Construct the sample (empirical) distribution function ijimr.2011040102.m06 from ijimr.2011040102.m07, i.e.

    ijimr.2011040102.m08
    (1)

  • (ii)

    The random weighting estimation of ijimr.2011040102.m09 is

    ijimr.2011040102.m10
    (2)

where ijimr.2011040102.m11 is the characteristic function, and random vector ijimr.2011040102.m12 obeys Dirichlet distribution D(1,ijimr.2011040102.m13,1), that is, ijimr.2011040102.m14 and the joint density function of ijimr.2011040102.m15 is ijimr.2011040102.m16, where ijimr.2011040102.m17and ijimr.2011040102.m18.

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