A study of the accuracy of parameter estimation of probit model with rare events

Abstract

This thesis studies the accuracy of parameter estimation of probit model with rare events The ideas of Firth penalized maximum likelihood function and generalized Firth penalized maximum likelihood function for the logistics regression model are employed for probit model with rare events The simulation results show that the bias of maximum likelihood estimator of regression parameters of probit model can be reduced by the penalized term in penalized likelihood function Overall when sample size is small for example n=100 penalized MLE with = 0:1 performs better than other penalized MLE for event rate( π) < 0 01 While penalized MLE with = 0:5 performs better than other penalized MLE for event rate( π) > 0 05

Date of Award	2019
Original language	English
Supervisor	Yun-Chan Chi (Supervisor)