Academic Commons

Theses Doctoral

Statistical inference in two non-standard regression problems

Seijo, Emilio Francisco

This thesis analyzes two regression models in which their respective least squares estimators have nonstandard asymptotics. It is divided in an introduction and two parts. The introduction motivates the study of nonstandard problems and presents an outline of the contents of the remaining chapters. In part I, the least squares estimator of a multivariate convex regression function is studied in great detail. The main contribution here is a proof of the consistency of the aforementioned estimator in a completely nonparametric setting. Model misspecification, local rates of convergence and multidimensional regression models mixing convexity and componentwise monotonicity constraints will also be considered. Part II deals with change-point regression models and the issues that might arise when applying the bootstrap to these problems. The classical bootstrap is shown to be inconsistent on a simple change-point regression model, and an alternative (smoothed) bootstrap procedure is proposed and proved to be consistent. The superiority of the alternative method is also illustrated through a simulation study. In addition, a version of the continuous mapping theorem specially suited for change-point estimators is proved and used to derive the results concerning the bootstrap.

Files

  • thumnail for SeijoSolis_columbia_0054D_10886.pdf SeijoSolis_columbia_0054D_10886.pdf application/pdf 2.21 MB Download File

More About This Work

Academic Units
Statistics
Thesis Advisors
Sen, Bodhisattva
Degree
Ph.D., Columbia University
Published Here
August 8, 2012
Academic Commons provides global access to research and scholarship produced at Columbia University, Barnard College, Teachers College, Union Theological Seminary and Jewish Theological Seminary. Academic Commons is managed by the Columbia University Libraries.