Abstract
We develop methodology for the estimation of regression parameters in models where one of the covariates is expensive or difficult to measure, and thus may sometimes be missing. In a regression setting where we have a response Y and predictor variables Z = (X, W), the one-dimensional component X may be missing for some of the data. We are concerned in particular with semiparametric efficient methods of regression which unfortunately depend upon knowledge of the probability distribution of X given (Y, W). We study the theoretical and computational properties of two adaptive solutions to the above problem. The first solution will employ methods of dimension reduction and local-linear regression. The second will fit the distribution of X given (Y, W) directly via a flexible semiparametric model. The second semiparametric solution is of a special form in that the semiparametric model is fit completely prior to the regression of Y on Z. We generalize the calculations involved into a new theory concerning plug-in semiparametric estimating equations. Finally, we present a case study which details the methods of fitting a normal mixture distribution to data which has undergone a power transformation. These methods are applied to data obtained from the study of tomato root cell initiation.
Gutierrez, Roberto Gabriel (1995). Topics in semiparametric and nonparametric regression with missing and mismeasured data. Texas A&M University. Texas A&M University. Libraries. Available electronically from
https : / /hdl .handle .net /1969 .1 /DISSERTATIONS -1574729.