Design Consistency of a Penalized Spline Survey Regression Estimator
Kelly McConville, PhD Preliminary Seminar, CSU
Friday, April 23, 2010
3:00 p.m., Statistics building, room 006
In estimating finite population quantities, we seek estimators which are design consistent regardless of the accuracy of any assumed super population model. We consider a regression estimator composed of piece-wise penalized splines. After obtaining an explicit form for the finite population spline coefficients and the corresponding Horvitz-Thompson ‘plug-in’ estimators of those coefficients, we show design consistency of the penalized spline survey regression estimator. In the course of the proof, we establish a result on the uniform convergence in probability of the survey weighted quantile estimators. This result is obtained by deriving a survey weighted Hoeffding inequality for bounded random variables.
We also propose to investigate a number of other topics in model selection and estimation for complex survey data. These include a weighted least absolute shrinkage and selection operator (LASSO), a calibrated penalized splines survey regression estimator, and sparse principal components analysis. These topics are motivated by problems arising in the monitoring of natural resources by the United States Forest Service. In these problems, there is a substantial amount of auxiliary information, often in the form of spatial layers in a geographic information system (GIS). This auxiliary information is incorporated by the Forest Service into a variety of regression estimation and model selection methods. Our work seeks to evaluate the properties of these methods analytically, and to assess them empirically using simulation and application to real data.
Dr. F. Jay Breidt, Advisor
Dr. Thomas Lee, Co-advisor
Dr. Myung-Hee Lee, Committee Member
Dr. Jean Opsomer, Committee Member
Dr. Paul Doherty, FWCB, Outside Member