Statistical inference for the estimation of binomial proportions ratio with the inverse-direct sampling scheme

Name: Parichart Pattarapanitchai

keyword: Point estimator

; Ratio of binomial proportion

; Inverse binomial sampling

; Direct binomial sampling

; Normal asymptotic of an estimator

Abstract: A general problem of comparing the probabilities of success of Bernoulli experiments based on data from two independent samples is an issue in biological and medical studies. The ratio of two-proportion p1=p2 from two independent sequences of Bernoulli random variables, each sample is obtained in the context of direct or inverse binomial sampling, are considered. We focus on the so-called Special Inverse-Direct sampling scheme, where the first sample is obtained by inverse binomial sampling scheme with the probability of success p1 and stopping time which is defined by the specified number of success m, while the second sample is obtained with the probability of success p2 and fixed sample size n by direct binomial sampling scheme. The main purpose of this research is constructing the estimators using Delta method and investigate their statistical properties, asymptotic confidence intervals are constructed in the cases of special inverse-direct sampling scheme. The normally distributed are proven. The performances of the test hypotheses are studied. The normal approximation for special cases of point estimators of the ratio of Binomial proportions of two independent populations are provided. Using Monte Carlo simulations, we investigate its performances in terms of bias, variance, and mean square error. The results show that the normal approximation, which is relatively simple, gives a reliable result. The main accuracy characteristics of estimators corresponding to all possible combinations of sampling schemes are investigated. Mean values and mean squared errors of point estimators and some recommendations for an application of each of the estimators are given. Overall, in some parameter choices, the testing procedure by proposed estimators controls the probability of type I error and the power of the test. The real data application applied with proposed estimators is presented

Thammasat University. Thammasat University Library

Address: BANGKOK

Email: preserv@tu.ac.th

Name: Kamon Budsaba

Role: advisor

Name: Volodin, Andrei

Role: co-advisor

Created: 2020

Modified: 2565-12-26

Issued: 2022-12-26

วิทยานิพนธ์/Thesis

application/pdf

DOI: 10.14457/TU.the.2020.477

eng

DegreeName: Doctor of Philosophy

Level: Doctoral Degree

Descipline: Statistics

Grantor: Thammasat University

©copyrights Thammasat University

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