Graduate Student Seminar Day

This project concerns the most effective dimension reduction (EDR) space in functional regression settings. Our investigation is motivated by finding a smaller set of derived variables that contains just as much predictive power as the original set. The main idea originated from cumulative slicing for multivariate data in Zhu et al. (2010 JASA), which assesses the EDR space by cumulatively pooling the observed data into incremental slices and performing a spectral decomposition on the space spanned by the resulting slices. Compared to sliced inverse regression, it sidesteps the need of partitioning the data into an arbitrary number of slices and thus ensures the maximum use of the data. It is desirable to adopt this idea due to the ”curse of dimensionality” encountered in functional regression. Resolving this issue makes possible the estimation of the EDR space for sparsely observed noisy functional data – a challenging setting in FDA where only a few measurements are available for some or even all of the subjects. To this end, we propose a nonparametric method to overcome the sparsity issue by pooling information together from all subjects in each slice. We present some preliminary numerical results. Speaker: Jason Ricci, PhD candidate, year 2 Title: Calibration of a Generalized Hawkes Processes with Latent Point Types to Large Datasets Abstract: It is well known that the classical Hawkes Process has modeling applications in many fields including biology, neuroscience, seismology, and finance. Motivated by high-frequency finance and algorithmic trading, we propose a larger class of marked point processes that may better represent the DGP for real-world, natural systems. In this class, points are classified as those that influence the underlying intensity process and those that do not, where such classification is latent. Moreover, we provide efficient quasi-maximum-likelihood calibration methods that makes calibration of parameters in large datasets possible. Finally, Sequential Monte Carlo estimators are used for real-time estimation of the state of the corresponding intensity process. It is well known that the classical Hawkes Process has modeling applications in many fields including biology, neuroscience, seismology, and finance. Motivated by high-frequency finance and algorithmic trading, we propose a larger class of marked point processes that may better represent the DGP for real-world, natural systems. In this class, points are classified as those that influence the underlying intensity process and those that do not, where such classification is latent. Moreover, we provide efficient quasi-maximum-likelihood calibration methods that makes calibration of parameters in large datasets possible. Finally, Sequential Monte Carlo estimators are used for real-time estimation of the state of the corresponding intensity process. Speaker: Zeynep Baskurt, PhD candidate, year 4 Title: A composite likelihood approach using the evidential paradigm to analyze genetic association in pedigrees Abstract: Royall (1997) proposed the evidential paradigm, an alternative to Frequentist and Bayesian paradigms for interpreting data as evidence. The evidential paradigm uses the likelihood ratio (LR) for two simple hypotheses as an objective measure of the strength of statistical evidence. In genetic studies, LRs are commonly used to measure evidence. However, evidential association of pedigrees is not straightforward due to complex family structures. We propose to use composite likelihoods to construct LRs for evidential analysis of families. We show how to make these LRs robust from model misspecification; that they have good operational characteristics; and are consistent with competing methods. Royall (1997) proposed the evidential paradigm, an alternative to Frequentist and Bayesian paradigms for interpreting data as evidence. The evidential paradigm uses the likelihood ratio (LR) for two simple hypotheses as an objective measure of the strength of statistical evidence. In genetic studies, LRs are commonly used to measure evidence. However, evidential association of pedigrees is not straightforward due to complex family structures. We propose to use composite likelihoods to construct LRs for evidential analysis of families. We show how to make these LRs robust from model misspecification; that they have good operational characteristics; and are consistent with competing methods.