**Estimating
Distribution Functions from **
Survey Data Using Nonparametric Regression |

**Alicia
Johnson**

Colorado State University

Wednesday, 26 March 2003

1:10 PM

B103 Engineering Building
**ABSTRACT
**

Survey sampling often supplies information about a study variable only
for sampled elements. However, auxiliary information is often
available for the entire population. The relationship of the auxiliary
information with the study variable across the sample allows inferences
about the nonsampled portion of the population. Thus, auxiliary
information can be used to improve upon survey estimation. In
particular, finite population distribution function estimation can be
improved. Existing parametric estimators incorporate auxiliary
information by assuming it to have a linear relationship with the study
variable, which is often unreasonable or unverifiable in survey sampling.
A model-assisted nonparametric estimator based on local polynomial regression
is introduced which removes these parametric restrictions. A Monte
Carlo comparison of this estimator with parametric estimators demonstrates
its superior efficiency for estimation of the distribution function
and quantiles in most cases in which the parametric methods misspecify
the relationship between the auxiliary and study variables. Finally,
a semiparametric estimator is introduced which allows for the incorporation
of parametric fixed effects, including categorical variables.
When applied to a population of Northeastern lakes, this estimator is
more efficient on average than a more conventional estimator that does
not incorporate any auxiliary information.