Physical Sciences and Mathematics Commons^™

Robust And Efficient Regression, Qi Zheng

All Dissertations

This dissertation aims to address two problems in regression
analysis. One problem is the model selection and robust parameter estimation in high dimensional linear regressions. The other is concerning developing a robust and efficient estimator in nonparametric regressions.
In Chapter 1, we introduce the robust and efficient regression analysis, discuss those two interesting problems and our motivations, and present several exciting results.
We propose a novel robust penalized method for high dimensional linear regression in Chapter 2. Asymptotic properties are established and a data-driven procedure is developed to select adaptive penalties. We show it is the very first estimator to …

Adaptive Estimation, Douglas G. Steigerwald

Douglas G. Steigerwald

No abstract provided.

Locally Efficient Estimation Of Regression Parameters Using Current Status Data, Chris Andrews, Mark J. Van Der Laan, James M. Robins

U.C. Berkeley Division of Biostatistics Working Paper Series

In biostatistics applications interest often focuses on the estimation of the distribution of a time-variable T. If one only observes whether or not T exceeds an observed monitoring time C, then the data structure is called current status data, also known as interval censored data, case I. We consider this data structure extended to allow the presence of both time-independent covariates and time-dependent covariate processes that are observed until the monitoring time. We assume that the monitoring process satisfies coarsening at random.

Our goal is to estimate the regression parameter beta of the regression model T = Z*beta+epsilon where the …

Adaptive Estimation In Timeseries Regression Models, Douglas Steigerwald

Douglas G. Steigerwald

I develop adaptive estimators for linear regression with serially correlated errors. The efficiency results hold even when the serial correlation structure is unknown. Simulations indicate that efficiency gains can be substantial with samples of only 50 observations. We apply the method to a study of forward exchange rates.

On The Finite Sample Behavior Of Adaptive Estimators, Douglas Steigerwald

Douglas G. Steigerwald

With only 50 observations, the adaptive estimator produces confidence intervals that are 20 to 50 percent shorter than those produced by GLS procedures. The key feature is that the underlying error density is symmetric. Under asymmetry the interval length is shortened by a smaller amount.