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Full-Text Articles in Physical Sciences and Mathematics
One And Two-Step Estimation Of Time Variant Parameters And Nonparametric Quantiles, Bogdan Gadidov
One And Two-Step Estimation Of Time Variant Parameters And Nonparametric Quantiles, Bogdan Gadidov
Doctor of Data Science and Analytics Dissertations
This dissertation develops and discusses several one-step and two-step smoothing methods of time variant nonparametric quantiles and time variant parameters from probability models. First, we investigate and develop nonparametric techniques for measuring extreme quantiles. The method involves aggregating data by an explanatory variable such as time and smoothing the resulting data with a nonparametric method like kernel, local polynomial or spline smoothing. We demonstrate both in application and simulation that this two-step procedure of quantile estimation is superior to the parametric quantile regression. We then develop a one-step method which combines the strength of maximum likelihood estimation with a local …
Variational Inference For Quantile Rgression, Bufei Guo
Variational Inference For Quantile Rgression, Bufei Guo
Arts & Sciences Electronic Theses and Dissertations
Quantile regression (QR) (Koenker and Bassett, 1978), is an alternative to classic lin- ear regression with extensive applications in many fields. This thesis studies Bayesian quantile regression (Yu and Moyeed, 2001) using variational inference, which is one of the alternative methods to the Markov chain Monte Carlo (MCMC) in approximating intractable posterior distributions. The lasso regularization is shown to be effective in improving the accuracy of quantile regression (Li and Zhu, 2008). This thesis developed variational inference for quantile regression and regularized quantile regression with the lasso penalty. Simulation results show that variational inference is a computationally more efficient alternative …
Bayesian Analysis For The Intraclass Model And For The Quantile Semiparametric Mixed-Effects Double Regression Models, Duo Zhang
Dissertations, Master's Theses and Master's Reports
This dissertation consists of three distinct but related research projects. The first two projects focus on objective Bayesian hypothesis testing and estimation for the intraclass correlation coefficient in linear models. The third project deals with Bayesian quantile inference for the semiparametric mixed-effects double regression models. In the first project, we derive the Bayes factors based on the divergence-based priors for testing the intraclass correlation coefficient (ICC). The hypothesis testing of the ICC is used to test the uncorrelatedness in multilevel modeling, and it has not well been studied from an objective Bayesian perspective. Simulation results show that the two sorts …