Thesis Defense: "Contribution to Data Science: Time Series, Uncertainty Quantification and Applications"

Abstract: Time series analysis is an essential tool in modern world statistical analysis. There are multiple instances where the time series shows nonlinear trends, or when the underlying error structure is non-Gaussian. Nonlinear prediction of time series can offer potential accuracy gains over linear methods when the process is nonlinear. In Chapter 3 and 4, we have proposed a quadratic prediction procedure which provides a better prediction accuracy when there exists non-linearity or non-Gaussianity in the time series, and a quantification of the amount of prediction gain we obtain using the quadratic prediction. We have provided the asymptotic distribution of polyspectral mean estimate and a proposed a linearity test using the same. In Chapter 4 and 5, we have proposed a predictive model for electoral campaigns using social media data and opinion polls. We have also provided a bot-identification algorithm in social media, primarily Twitter. In our last chapter, we have provided an optimal choice of m in m out of n bootstrap for sample extremes.

Hosts: Soumendra Lahiri and Tucker McElroy