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)
DOI: 10.4018/978-1-4666-3634-7.ch006
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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 978-1-4666-3634-7.ch006.m01 is a sample of independent and identically distributed random variables with common distribution function F. Let 978-1-4666-3634-7.ch006.m02 be the corresponding observed realizations of 978-1-4666-3634-7.ch006.m03 Further, we shall denote 978-1-4666-3634-7.ch006.m04 and 978-1-4666-3634-7.ch006.m05 Then, the random weighting process can be described as follows:

  • Construct the sample (empirical) distribution function 978-1-4666-3634-7.ch006.m06 from 978-1-4666-3634-7.ch006.m07 i.e.


  • The random weighting estimation of 978-1-4666-3634-7.ch006.m09 is


where 978-1-4666-3634-7.ch006.m11 is the characteristic function, and random vector 978-1-4666-3634-7.ch006.m12 obeys Dirichlet distribution 978-1-4666-3634-7.ch006.m13 that is, 978-1-4666-3634-7.ch006.m14 and the joint density function of 978-1-4666-3634-7.ch006.m15 is 978-1-4666-3634-7.ch006.m16 where 978-1-4666-3634-7.ch006.m17and 978-1-4666-3634-7.ch006.m18

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