On the asymptotic normality of the estimator for ratio of binomial proportions

Name: Nattaka Thangkitanan

keyword: Ratio of binomial proportions

; Risk ratio

; Inverse and direct binomial sampling schemes

; Parameter estimation

; Asymptotic normality

; Accuracy properties of estimators

; Hypothesis testing

Abstract: In this article we investigate the accuracy of normal approximation for the distributions of the estimators for the ratio of probabilities in Bernoulli trials. The construction of estimators is done under two experimental schemes: direct binomial sampling with the fixed number of trials n, and inverse, when the observations are continued until m successes appear in the trials. The estimators are simulated by the Monte Carlo method and their variances are calculated. The empirical distribution functions are constructed by the data of statistical modeling. The divergence between empirical distribution function and its normal approximation distribution function in uniform metric are considered, and also quantile points (0.05 and 0.95) are compared. The accuracy properties of the normal approximation are investigated. In this article, the investigations of the accuracy of asymptotic normality are given for all possible schemes of experiments: direct–direct, direct–inverse, inverse–direct, inverse–inverse. Then, the obtained table values allow to rank the accurate performance of four schemes of Binomial experiments. According to the results of presented calculations, recommendations for a usage of particular trials are given. Moreover, we consider the two Special Cases: direct–inverse and inverse–direct. The feature of Special Cases is using the value from the first sample for construction the second sample. Eventually, we would compare the accurate performance of two Special Cases between the direct–inverse and inverse–direct from non-special cases. Finally, the most accurate approximation happens in Special Case of the direct-inverse sampling scheme. For this Special Case sampling scheme, the statistics for hypothesis testing of probabilities ratio are constructed.

Thammasat University. Thammasat University Library

Address: BANGKOK

Email: preserv@tu.ac.th

Name: Kamon Budsaba

Role: advisor

Name: Volodin, Andrei Igorevich

Role: co-advisor

Created: 2024

Modified: 2024-10-24

Issued: 2024-10-24

วิทยานิพนธ์/Thesis

application/pdf

DOI: 10.14457/TU.the.2023.380

eng

DegreeName: Doctor of Philosophy

Level: Doctoral Degree

Descipline: Statistics

Grantor: Thammasat University

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