Simulation Study on Exchangeability and Significant Test on Survey Data

Abstract

The two years of Master of Science in Statistical and Economic Modeling program is the most rewarding time ever in my life. This thesis acts as a portfolio of project and applied experience while I am enrolled in the Master of Science in Statistical and Economic Modeling program. This thesis will summarize my graduate study in two parts: Simulation Study of Exchangeability for Binary Data, and Summary of Summer Internship at Center for Responsible Lending. The project of Simulation Study of Exchangeability for Binary Data contains materials from a team project, which jointly performed by Sheng Jiang, Xuan Sun and me. Abstracts for both projects are below in order.(1) Simulation Study of Exchangeability for Binary DataTo investigate tractable Bayesian tests on exchangeability, this project considers special cases of nonexchangeable random sequences: Markov chains. Asymptotic results of Bayes factor (BF) are derived. When null hypothesis is true, Bayes Factor in favor of the null goes to infinity at geometric rate (true odds is not one half). When null hypothesis is not true, Bayes Factor in favor of the null goes to 0 faster than geometric rate. The results are robust under misspecifications. Simulation studies are employed to see the performance of the test when the sample size is small, prior beliefs change and true parameters change.(2) Summary of Summer Internship at Center for Responsible LendingMy summer internship deals with a survey data from Social Science Research Solution about auto financing. The dataset includes about one thousand valid responses and 114 variables for each response. My efforts on exploratory statistic analysis unfolded many interesting findings. For example, African Americans and Latinos are receiving 2.02% higher APR on average than white buyers, excluding the effects of relevant variables. And what's more, a Fisher's Exact Test of Significance is widely used to discover the significance of a series of variables. Results are presented in organized neat tables. Findings are included in weekly reports. One example finding is that warranty add-­‐‑ons of a financed car has significant impacts on all three aspects of a loan, which is Annual Percent Rate, Loan Amount, and Monthly Payment.