Graduate Seminar

Location:  Livestream Only

Speaker: Amitabh Halder

PhD Student supervised by Affan Shoukat and Andrei Volodin

Title:  Asymptotic Normality and Corresponding Confidence Intervals for Yule's Q under Different Sampling Schemes

Zoom: https://uregina-ca.zoom.us/j/92053635111?pwd=U25NcEp6amlGV1YrRDdnUm5qNlhaUT09

Abstract:

Let \(p_1\) and \(p_2\) be the probabilities of success of the first and second independent Bernoulli trials, respectively. Yule's Q is defined as \(Q = \frac{\rho - 1}{\rho + 1}\), a function of the cross-product ratio \(\rho = \frac{p_1}{1 - p_1} \frac{1 - p_2}{p_2}\) of two independent binomial samples. For different sampling schemes, we provide estimators of Yule's Q and prove their asymptotic normality. After, we construct confidence intervals for Yule's Q for all combinations of direct and inverse sampling schemes.

In addition, we employ the Monte Carlo method for the estimations of coverage probability, expected width, and standard deviation of confidence intervals width to examine probability characteristics of confidence intervals to all relevant combinations of sampling schemes. Simulation outcomes exhibit that the confidence intervals occupy good accuracy properties. The proposed confidence intervals may be employed to real life data applications in all possible combinations of sampling schemes.